@article{papanicolaou_fu_krishnamurthy_khorrami_2023, title={A Deep Neural Network Algorithm for Linear-Quadratic Portfolio Optimization with MGARCH and Small Transaction Costs}, ISSN={2169-3536}, url={http://dx.doi.org/10.1109/ACCESS.2023.3245570}, DOI={10.1109/ACCESS.2023.3245570}, abstractNote={We analyze a fixed-point algorithm for reinforcement learning (RL) of optimal portfolio mean-variance preferences in the setting of multivariate generalized autoregressive conditional-heteroskedasticity (MGARCH) with a small penalty on trading. A numerical solution is obtained using a neural network (NN) architecture within a recursive RL loop. A fixed-point theorem proves that NN approximation error has a big-oh bound that we can reduce by increasing the number of NN parameters. The functional form of the trading penalty has a parameter $\epsilon >0$ that controls the magnitude of transaction costs. When $\epsilon $ is small, we can implement an NN algorithm based on the expansion of the solution in powers of $\epsilon $ . This expansion has a base term equal to a myopic solution with an explicit form, and a first-order correction term that we compute in the RL loop. Our expansion-based algorithm is stable, allows for fast computation, and outputs a solution that shows positive testing performance.}, journal={IEEE Access}, publisher={Institute of Electrical and Electronics Engineers (IEEE)}, author={Papanicolaou, Andrew and Fu, Hao and Krishnamurthy, Prashanth and Khorrami, Farshad}, year={2023}, pages={1–1} }
@article{papanicolaou_fu_krishnamurthy_healy_khorrami_2023, title={An optimal control strategy for execution of large stock orders using long short-term memory networks}, volume={26}, ISSN={["1755-2850"]}, DOI={10.21314/JCF.2023.003}, abstractNote={We simulate the execution of a large stock order with real data and a general power law in the Almgren and Chriss model. The example we consider is the liquidation of a large position executed over the course of a single trading day in a limit order book. Transaction costs are incurred because large orders walk the order book (that is, they consume order book liquidity beyond the best bid/ask price). We model the order book with a power law that is proportional to trading volume, and thus transaction costs are inversely proportional to a power of the trading volume. We obtain a policy approximation by training a long short-term memory (LSTM) neural network to minimize the transaction costs accumulated when execution is carried out as a sequence of smaller suborders. Using historical Standard & Poor’s 100 price and volume data, we evaluate our LSTM strategy relative to strategies based on the time-weighted average price (TWAP) and volume-weighted average price (VWAP). For execution of a single stock, the input to the LSTM is the cross-section of data on all 100 stocks, including prices, volumes, TWAPs and VWAPs. By using this data cross-section, the LSTM should be able to exploit interstock codependence in volume and price movements, thereby reducing transaction costs for the day. Our tests on Standard & Poor’s 100 data demonstrate that in fact this is so, as our LSTM strategy consistently outperforms TWAP- and VWAP-based strategies.}, number={4}, journal={JOURNAL OF COMPUTATIONAL FINANCE}, author={Papanicolaou, A. and Fu, H. and Krishnamurthy, P. and Healy, B. and Khorrami, F.}, year={2023}, month={Mar}, pages={37–65} }
@article{dai_krishnamurthy_papanicolaou_khorrami_2023, title={State constrained stochastic optimal control for continuous and hybrid dynamical systems using DFBSDE}, volume={155}, ISSN={["1873-2836"]}, DOI={10.1016/j.automatica.2023.111146}, abstractNote={We develop a computationally efficient learning-based forward–backward stochastic differential equations (FBSDE) controller for both continuous and hybrid dynamical (HD) systems subject to stochastic noise and state constraints. Solutions to stochastic optimal control (SOC) problems satisfy the Hamilton–Jacobi–Bellman (HJB) equation. Using current FBSDE-based solutions, the optimal control can be obtained from the HJB equations using deep neural networks (e.g., long short-term memory (LSTM) networks). To ensure the learned controller respects the constraint boundaries, we enforce the state constraints using a soft penalty function. In addition to previous works, we adapt the deep FBSDE (DFBSDE) control framework to handle HD systems consisting of continuous dynamics and a deterministic discrete state change. We demonstrate our proposed algorithm in simulation on a continuous nonlinear system (cart–pole) and a hybrid nonlinear system (five-link biped).}, journal={AUTOMATICA}, author={Dai, Bolun and Krishnamurthy, Prashanth and Papanicolaou, Andrew and Khorrami, Farshad}, year={2023}, month={Sep} }
@article{papanicolaou_2022, title={Consistent time‐homogeneous modeling of SPX and VIX derivatives}, volume={32}, ISSN={0960-1627 1467-9965}, url={http://dx.doi.org/10.1111/mafi.12348}, DOI={10.1111/mafi.12348}, abstractNote={Abstract}, number={3}, journal={Mathematical Finance}, publisher={Wiley}, author={Papanicolaou, Andrew}, year={2022}, month={May}, pages={907–940} }
@article{avellaneda_healy_papanicolaou_papanicolaou_2022, title={Principal Eigenportfolios for U.S. Equities}, volume={13}, ISSN={1945-497X}, url={http://dx.doi.org/10.1137/20M1383501}, DOI={10.1137/20M1383501}, abstractNote={We analyze portfolios constructed from the principal eigenvector of the equity returns' correlation matrix and compare these portfolios with the capitalization weighted market portfolio. It is well known empirically that principal eigenportfolios are a good proxy for the market portfolio. We quantify this property through the large-dimensional asymptotic analysis of a spike model with diverging top eigenvalue, comprising a rank-one matrix and a random matrix. We show that, in this limit, the top eigenvector of the correlation matrix is close to the vector of market betas divided componentwise by returns standard deviation. Historical returns data are generally consistent with this analysis of the correspondence between the top eigenportfolio and the market portfolio. We further examine this correspondence using eigenvectors obtained from hierarchically constructed tensors where stocks are separated into their respective industry sectors. This hierarchical approach results in a principal factor whose portfolio weights are all positive for a greater percentage of time compared to the weights of the vanilla eigenportfolio computed from the correlation matrix. Returns from hierarchical construction are also more robust with respect to the duration of the time window used for estimation. All principal eigenportfolios that we observe have returns that exceed those of the market portfolio between 1994 and 2020. We attribute these excess returns to the brief periods where short holdings are more than a small percentage of portfolio weight.}, number={3}, journal={SIAM Journal on Financial Mathematics}, publisher={Society for Industrial & Applied Mathematics (SIAM)}, author={Avellaneda, Marco and Healy, Brian and Papanicolaou, Andrew and Papanicolaou, George}, year={2022}, month={Jul}, pages={702–744} }
@article{bossu_carr_papanicolaou_2022, title={Static replication of European standard dispersion options}, volume={22}, ISSN={1469-7688 1469-7696}, url={http://dx.doi.org/10.1080/14697688.2022.2040743}, DOI={10.1080/14697688.2022.2040743}, abstractNote={Dispersion options may be replicated using vanilla basket calls whose basket weights span an n-dimensional continuum}, number={5}, journal={Quantitative Finance}, publisher={Informa UK Limited}, author={Bossu, Sébastien and Carr, Peter and Papanicolaou, Andrew}, year={2022}, month={Mar}, pages={799–811} }
@article{li_papanicolaou_2022, title={Statistical Arbitrage for Multiple Co-integrated Stocks}, volume={86}, ISSN={0095-4616 1432-0606}, url={http://dx.doi.org/10.1007/s00245-022-09838-3}, DOI={10.1007/s00245-022-09838-3}, abstractNote={In this article, we analyse optimal statistical arbitrage strategies from stochastic control and optimisation problems for multiple co-integrated stocks with eigenportfolios being factors. Optimal portfolio weights are found by solving a Hamilton–Jacobi–Bellman (HJB) partial differential equation, which we solve for both an unconstrained portfolio and a portfolio constrained to be market neutral. Our analyses demonstrate sufficient conditions on the model parameters to ensure long-term stability of the HJB solutions and stable growth rates for the optimal portfolios. To gauge how these optimal portfolios behave in practice, we perform backtests on historical stock prices of the S&P 500 constituents from year 2000 through year 2021. These backtests suggest three key conclusions: that the proposed co-integrated model with eigenportfolios being factors can generate a large number of co-integrated stocks over a long time horizon, that the optimal portfolios are sensitive to parameter estimation, and that the statistical arbitrage strategies are more profitable in periods when overall market volatilities are high.}, number={1}, journal={Applied Mathematics & Optimization}, publisher={Springer Science and Business Media LLC}, author={Li, Thomas Nanfeng and Papanicolaou, Andrew}, year={2022}, month={Jun} }
@article{amir-ghassemi_papanicolaou_perlow_2021, title={Aggregate Alpha in the Hedge Fund Industry: A Further Look at Best Ideas}, volume={48}, ISSN={0095-4918 2168-8656}, url={http://dx.doi.org/10.3905/jpm.2021.1.313}, DOI={10.3905/jpm.2021.1.313}, abstractNote={1. F. Amir-Ghassemi 1. is a partner at Epsilon Asset Management in New York, NY. (research{at}epsilonmgmt.com) 2. A. Papanicolaou 1. is an assistant professor in the Department of Mathematics at North Carolina State University in Raleigh, NC. (apapani{at}ncsu.edu) 3. M. Perlow 1. is a partner at Epsilon Asset Management in New York, NY. (research{at}epsilonmgmt.com) This article is an examination of the stock-picking behavior of nearly 1,500 hedge funds using regulatory mandated position-level data from the SEC (Form 13F). Using data from June 1999 to December 2018, abnormal excess alpha is found on both a gross and dollar basis. Breaking the 20-year sample into two periods, the authors note a significant decline in gross alpha after the 2008 global financial crisis. In contrast, dollar alphas remain economically and statistically significant. This finding coincides with an increase in aggregate assets in the post-crisis period, suggesting asset growth may be impeding gross alphas. To test this hypothesis, the authors analyze the Best Ideas within manager portfolios. They find no significant difference between the alphas generated by managers’ Best Ideas and the rest of their portfolios, suggesting asset growth is not a significant determinant of alpha deterioration. These findings broadly contrast with prior studies conducted on mutual funds, suggesting differences in portfolio construction and incentive effects.}, number={3}, journal={The Journal of Portfolio Management}, publisher={Pageant Media US}, author={Amir-Ghassemi, F. and Papanicolaou, A. and Perlow, M.}, year={2021}, month={Dec}, pages={220–239} }
@misc{dai_krishnamurthy_papanicolaou_khorrami_2021, title={State Constrained Stochastic Optimal Control Using LSTMs}, url={http://dx.doi.org/10.23919/ACC50511.2021.9482832}, DOI={10.23919/acc50511.2021.9482832}, abstractNote={In this paper, we propose a new methodology for state constrained stochastic optimal control (SOC) problems. The solution is based on past work in solving SOC problems using forward-backward stochastic differential equations (FB-SDE). Our approach in solving the FBSDE utilizes a deep neural network (DNN), specifically Long Short-Term Memory (LSTM) networks. LSTMs are chosen to solve the FBSDE to address the curse of dimensionality, non-linearities, and long time horizons. In addition, the state constraints are incorporated using a hard penalty function, resulting in a controller that respects the constraint boundaries. Numerical instability that would be introduced by the penalty function is dealt with through an adaptive update scheme. The control design methodology is applicable to a large class of control problems. The performance and scalability of our proposed algorithm are demonstrated by numerical simulations.}, journal={2021 American Control Conference (ACC)}, publisher={IEEE}, author={Dai, Bolun and Krishnamurthy, Prashanth and Papanicolaou, Andrew and Khorrami, Farshad}, year={2021}, month={May} }
@article{avellaneda_li_papanicolaou_wang_2021, title={Trading Signals in VIX Futures}, volume={28}, ISSN={1350-486X 1466-4313}, url={http://dx.doi.org/10.1080/1350486X.2021.2010584}, DOI={10.1080/1350486x.2021.2010584}, abstractNote={ABSTRACT We propose a new approach for trading VIX futures. We assume that the term structure of VIX futures follows a Markov model. Our trading strategy selects a position in VIX futures by maximizing the expected utility for a day-ahead horizon given the current shape and level of the term structure. Computationally, we model the functional dependence between the VIX futures curve, the VIX futures positions, and the expected utility as a deep neural network with five hidden layers. Out-of-sample backtests of the VIX futures trading strategy suggest that this approach gives rise to reasonable portfolio performance, and to positions in which the investor will be either long or short VIX futures contracts depending on the market environment.}, number={3}, journal={Applied Mathematical Finance}, publisher={Informa UK Limited}, author={Avellaneda, Marco and Li, Thomas Nanfeng and Papanicolaou, Andrew and Wang, Gaozhan}, year={2021}, month={May}, pages={275–298} }
@article{bossu_carr_papanicolaou_2020, title={A functional analysis approach to the static replication of European options}, volume={21}, ISSN={1469-7688 1469-7696}, url={http://dx.doi.org/10.1080/14697688.2020.1810857}, DOI={10.1080/14697688.2020.1810857}, abstractNote={The replication of any European contingent claim by a static portfolio of calls and puts with strikes forming a continuum, formally proven by Carr and Madan [Towards a theory of volatility trading. In Volatility: New Estimation Techniques for Pricing Derivatives, edited by R.A. Jarrow, Vol. 29, pp. 417–427, 1998 (Risk books)], is part of the more general theory of integral equations. We use spectral decomposition techniques to show that exact payoff replication may be achieved with a discrete portfolio of special options. We discuss applications for fast pricing of vanilla options that may be suitable for large option books or high frequency option trading, and for model pricing when the characteristic function of the underlying asset price is known.}, number={4}, journal={Quantitative Finance}, publisher={Informa UK Limited}, author={Bossu, Sébastien and Carr, Peter and Papanicolaou, Andrew}, year={2020}, month={Nov}, pages={637–655} }
@article{avellaneda_healy_papanicolaou_papanicolaou_2020, title={PCA for Implied Volatility Surfaces}, volume={2}, ISSN={2640-3943}, url={http://dx.doi.org/10.3905/jfds.2020.1.032}, DOI={10.3905/jfds.2020.1.032}, abstractNote={Principal component analysis (PCA) is a useful tool when trying to construct factor models from historical asset returns. For the implied volatilities of US equities, there is a PCA-based model with a principal eigenportfolio whose return time series lies close to that of an overarching market factor. The authors show that this market factor is the index resulting from the daily compounding of a weighted average of implied-volatility returns, with weights based on the options’ open interest and Vega. The authors also analyze the singular vectors derived from the tensor structure of the implied volatilities of S&P 500 constituents and find evidence indicating that some type of open interest- and Vega-weighted index should be one of at least two significant factors in this market. TOPICS: Statistical methods, simulations, big data/machine learning Key Findings • Principal component analysis of a comprehensive dataset of implied volatility surfaces from options on US equities shows that their collective behavior is captured by just nine factors, whereas the effective spatial dimension of the residuals is closer to 500 than to the nominal dimension of 28,000, revealing the large redundancy in the data. • Portfolios of implied volatility surface returns, weighed suitably by open interest and Vega, track the principal eigenportfolio associated with a market portfolio of options, in analogy to equity portfolios. • Retention of the tensor structure in the eigenportfolio analysis improves the tracking between the open interest–Vega weighted (tensor) implied volatility surface returns portfolio and the (tensor) eigenportfolio, indicating that data structure matters.}, number={2}, journal={The Journal of Financial Data Science}, publisher={Pageant Media US}, author={Avellaneda, Marco and Healy, Brian and Papanicolaou, Andrew and Papanicolaou, George}, year={2020}, month={Mar}, pages={85–109} }
@article{amaral_papanicolaou_2019, title={PRICE IMPACT OF LARGE ORDERS USING HAWKES PROCESSES}, volume={61}, ISSN={1446-1811 1446-8735}, url={http://dx.doi.org/10.1017/S1446181119000038}, DOI={10.1017/S1446181119000038}, abstractNote={We introduce a model for the execution of large market orders in limit order books, and use a linear combination of self-exciting Hawkes processes to model asset-price dynamics, with the addition of a price-impact function that is concave in the order size. A criterion for a general price-impact function is introduced, which is used to show how specification of a concave impact function affects order execution. Using our model, we examine the immediate and permanent impacts of large orders, analyse the potential for price manipulation, and show the effectiveness of the time-weighted average price strategy. Our model shows that price depends on the balance between the intensities of the Hawkes process, which can be interpreted as a dependence on order-flow imbalance.}, number={02}, journal={The ANZIAM Journal}, publisher={Cambridge University Press (CUP)}, author={Amaral, L. R. and Papanicolaou, A.}, year={2019}, month={Apr}, pages={161–194} }
@article{avellaneda_papanicolaou_2019, title={STATISTICS OF VIX FUTURES AND APPLICATIONS TO TRADING VOLATILITY EXCHANGE-TRADED PRODUCTS}, volume={22}, ISSN={0219-0249 1793-6322}, url={http://dx.doi.org/10.1142/S0219024918500619}, DOI={10.1142/s0219024918500619}, abstractNote={ We study the dynamics of VIX futures and ETNs/ETFs. We find that contrary to classical commodities, VIX and VIX futures exhibit large volatility and skewness, consistent with the absence of cash-and-carry arbitrage. The constant-maturity futures (CMF) term-structure can be modeled as a stationary stochastic process in which the most likely state is contango with VIX [Formula: see text] and a long-term futures price [Formula: see text]. We analyze the behavior of ETFs and ETNs based on constant-maturity rolling futures strategies, such as VXX, XIV and VXZ, assuming stationarity and through a multi-factor model calibrated to historical data. We find that buy-and-hold strategies consisting of shorting ETNs that roll long futures, or buying ETNs that roll short futures, will produce theoretically-sure profits if it is assumed that CMFs are stationary and ergodic. To quantify further, we estimate a 2-factor lognormal model with mean-reverting factors to VIX and CMF historical data from 2011 to 2016. The results confirm the profitability of buy-and-hold strategies, but also indicate that the latter have modest Sharpe ratios, of the order of [Formula: see text] or less, and high variability over 1-year horizon simulations. This is due to the surges in VIX and CMF backwardations which are observed sporadically in the volatility futures market. }, number={01}, journal={International Journal of Theoretical and Applied Finance}, publisher={World Scientific Pub Co Pte Lt}, author={Avellaneda, M. and Papanicolaou, A.}, year={2019}, month={Feb}, pages={1850061} }
@article{chandra_papanicolaou_2019, title={Singular Perturbation Expansion for Utility Maximization with Order-ε Quadratic Transaction Costs}, volume={22}, DOI={10.1142/S0219024919500390}, number={7}, journal={International Journal of Theoretical and Applied Finance}, author={Chandra, Shiva and Papanicolaou, Andrew}, year={2019}, pages={1950039} }
@article{papanicolaou_2018, title={Backward SDEs for control with partial information}, volume={29}, ISSN={0960-1627 1467-9965}, url={http://dx.doi.org/10.1111/mafi.12174}, DOI={10.1111/mafi.12174}, abstractNote={Abstract}, number={1}, journal={Mathematical Finance}, publisher={Wiley}, author={Papanicolaou, Andrew}, year={2018}, month={Feb}, pages={208–248} }
@article{papanicolaou_2018, title={Extreme-Strike Comparisons and Structural Bounds for SPX and VIX Options}, volume={9}, ISSN={1945-497X}, url={http://dx.doi.org/10.1137/141001615}, DOI={10.1137/141001615}, abstractNote={This article explores the relationship between the SPX and VIX options markets. High-strike VIX call options are used to hedge tail risk in the SPX, which means that SPX options are a reflection of the extreme-strike asymptotics of VIX options, and vice versa. This relationship can be quantified using moment formulas in a model-free way. Comparisons are made between VIX and SPX implied volatilities along with various examples of stochastic volatility models.}, number={2}, journal={SIAM Journal on Financial Mathematics}, publisher={Society for Industrial & Applied Mathematics (SIAM)}, author={Papanicolaou, A.}, year={2018}, month={Jan}, pages={401–434} }
@article{papanicolaou_spiliopoulos_2017, title={Dimension Reduction in Statistical Estimation of Partially Observed Multiscale Processes}, volume={5}, ISSN={2166-2525}, url={http://dx.doi.org/10.1137/16M1085930}, DOI={10.1137/16m1085930}, abstractNote={We consider partially observed multiscale diffusion models that are specified up to an unknown vector parameter. We establish for a very general class of test functions that the filter of the original model converges to a filter of reduced dimension. Then, this result is used to justify statistical estimation for the unknown parameters of interest based on the model of reduced dimension but using the original available data. This allows to learn the unknown parameters of interest while working in lower dimensions, as opposed to working with the original high dimensional system. Simulation studies support and illustrate the theoretical results.}, number={1}, journal={SIAM/ASA Journal on Uncertainty Quantification}, publisher={Society for Industrial & Applied Mathematics (SIAM)}, author={Papanicolaou, Andrew and Spiliopoulos, Konstantinos}, year={2017}, month={Jan}, pages={1220–1247} }
@article{fouque_papanicolaou_sircar_2017, title={Perturbation Analysis for Investment Portfolios Under Partial Information with Expert Opinions}, volume={55}, ISSN={0363-0129 1095-7138}, url={http://dx.doi.org/10.1137/15M1006854}, DOI={10.1137/15m1006854}, abstractNote={We analyze the Merton portfolio optimization problem when the growth rate is an unobserved Gaussian process whose level is estimated by filtering from observations of the stock price. We use the Kalman filter to track the hidden state(s) of expected returns given the history of asset prices, and then use this filter as input to a portfolio problem with an objective to maximize expected terminal utility. Our results apply for general concave utility functions. We incorporate time-scale separation in the fluctuations of the returns process, and utilize singular and regular perturbation analysis on the associated partial-information HJB equation, which leads to an intuitive interpretation of the additional risk caused by uncertainty in expected returns. The results are an extension of the partially informed investment strategies obtained by the Black--Litterman model, wherein investors' views on upcoming performance are incorporated into the optimization along with any degree of uncertainty that the investor may have in these views.}, number={3}, journal={SIAM Journal on Control and Optimization}, publisher={Society for Industrial & Applied Mathematics (SIAM)}, author={Fouque, J.-P. and Papanicolaou, A. and Sircar, R.}, year={2017}, month={Jan}, pages={1534–1566} }
@article{papanicolaou_2016, title={Analysis of VIX Markets with a Time-Spread Portfolio}, volume={23}, ISSN={1350-486X 1466-4313}, url={http://dx.doi.org/10.1080/1350486X.2017.1290534}, DOI={10.1080/1350486x.2017.1290534}, abstractNote={ABSTRACT This paper explores the relationship between option markets for the S&P500 (SPX) and Chicago Board Options Exchange’s CBOE’s Volatility Index (VIX). Results are obtained by using the so-called time-spread portfolio to replicate a future contract on the squared VIX. The time-spread portfolio is interesting because it provides a model-free link between derivative prices for SPX and VIX. Time spreads can be computed from SPX put options with different maturities, which results in a term structure for squared volatility. This term structure can be compared to the VIX-squared term structure that is backed-out from VIX call options. The time-spread portfolio is also used to measure volatility-of-volatility (vol-of-vol) and the volatility leverage effect. There may emerge small differences in these measurements, depending on whether time spreads are computed with options on SPX or options on VIX. A study of 2012 daily options data shows that vol-of-vol estimates utilizing SPX data will reflect the volatility leverage effect, whereas estimates that exclusively utilize VIX options will predominantly reflect the premia in the VIX-future term structure.}, number={5}, journal={Applied Mathematical Finance}, publisher={Informa UK Limited}, author={Papanicolaou, A.}, year={2016}, month={Sep}, pages={374–408} }
@article{lee_papanicolaou_2016, title={PAIRS TRADING OF TWO ASSETS WITH UNCERTAINTY IN CO-INTEGRATION'S LEVEL OF MEAN REVERSION}, volume={19}, ISSN={0219-0249 1793-6322}, url={http://dx.doi.org/10.1142/S0219024916500540}, DOI={10.1142/s0219024916500540}, abstractNote={ This paper considers a stochastic control problem derived from a model for pairs trading under incomplete information. We decompose an individual asset's drift into two parts: an industry drift plus some additional stochasticity. The extra stochasticity may be unobserved, which means the investor has only partial information. We solve the control problem under both full and partial informations for utility function [Formula: see text], and we make comparisons. We show the existence of stable solution to the associated matrix Riccati equations in both cases for [Formula: see text], but for [Formula: see text] there remains potential for infinite value functions in finite time. Also, we quantify the expected loss in utility due to partial information, and present a numerical study to illustrate the contribution of this paper. }, number={08}, journal={International Journal of Theoretical and Applied Finance}, publisher={World Scientific Pub Co Pte Lt}, author={Lee, Sangmin and Papanicolaou, Andrew}, year={2016}, month={Dec}, pages={1650054} }
@article{fouque_papanicolaou_sircar_2015, title={Filtering and portfolio optimization with stochastic unobserved drift in asset returns}, volume={13}, ISSN={1539-6746 1945-0796}, url={http://dx.doi.org/10.4310/CMS.2015.v13.n4.a5}, DOI={10.4310/cms.2015.v13.n4.a5}, abstractNote={We consider the problem of ltering and control in the setting of portfolio optimization in nancial markets with random factors that are not directly observable. The example that we present is a commodities portfolio where yields on futures contracts are observed with some noise. Through the use of perturbation methods, we are able to show that the solution to the full problem can be approximated by the solution of a solvable HJB equation plus an explicit correction term.}, number={4}, journal={Communications in Mathematical Sciences}, publisher={International Press of Boston}, author={Fouque, Jean-Pierre and Papanicolaou, Andrew and Sircar, Ronnie}, year={2015}, pages={935–953} }
@article{papanicolaou_spiliopoulos_2014, title={Filtering the Maximum Likelihood for Multiscale Problems}, volume={12}, ISSN={1540-3459 1540-3467}, url={http://dx.doi.org/10.1137/140952648}, DOI={10.1137/140952648}, abstractNote={Filtering and parameter estimation under partial information for multiscale diffusion problems are studied in this paper. The nonlinear filter converges in the mean-square sense to a filter of reduced dimension. Based on this result, we establish that the conditional (on the observations) log-likelihood process has a correction term given by a type of central limit theorem. We prove that an appropriate normalization of the log-likelihood minus a log-likelihood of reduced dimension converges weakly to a normal distribution. In order to achieve this we assume that the operator of the (hidden) fast process has a discrete spectrum and an orthonormal basis of eigenfunctions. We then propose to estimate the unknown model parameters using the reduced log-likelihood, which is beneficial because reduced dimension means that there is significantly less runtime for this optimization program. We also establish consistency and asymptotic normality of the maximum likelihood estimator. Simulation results illustrate our ...}, number={3}, journal={Multiscale Modeling & Simulation}, publisher={Society for Industrial & Applied Mathematics (SIAM)}, author={Papanicolaou, Andrew and Spiliopoulos, Konstantinos}, year={2014}, month={Jan}, pages={1193–1229} }
@article{fuertes_papanicolaou_2014, title={Implied Filtering Densities on the Hidden State of Stochastic Volatility}, volume={21}, ISSN={1350-486X 1466-4313}, url={http://dx.doi.org/10.1080/1350486X.2014.891357}, DOI={10.1080/1350486x.2014.891357}, abstractNote={We explore the inversion of derivatives prices to obtain an implied probability measure on volatility's hidden state. Stochastic volatility is a hidden Markov model (HMM), and HMMs ordinarily warrant filtering. However, derivative data is a set of conditional expectations that are already observed in the market, so rather than use filtering techniques we compute an \textit{implied distribution} by inverting the market's option prices. Robustness is an issue when model parameters are probably unknown, but isn't crippling in practical settings because the data is sufficiently imprecise and prevents us from reducing the fitting error down to levels where parameter uncertainty will show. When applied to SPX data, the estimated model and implied distributions produce variance swap rates that are consistent with the VIX, and also pick up some of the monthly effects that occur from option expiration. We find that parsimony of the Heston model is beneficial because we are able to decipher behavior in estimated parameters and implied measures, whereas the richer Heston model with jumps produces a better fit but also has implied behavior that is less revealing.}, number={6}, journal={Applied Mathematical Finance}, publisher={Informa UK Limited}, author={Fuertes, Carlos and Papanicolaou, Andrew}, year={2014}, month={Apr}, pages={483–522} }
@article{papanicolaou_sircar_2013, title={A regime-switching Heston model for VIX and S&P 500 implied volatilities}, volume={14}, ISSN={1469-7688 1469-7696}, url={http://dx.doi.org/10.1080/14697688.2013.814923}, DOI={10.1080/14697688.2013.814923}, abstractNote={Volatility products have become popular in the past 15 years as a hedge against market uncertainty. In particular, there is growing interest in options on the VIX volatility index. A number of recent empirical studies have examine whether there is significantly greater risk premium in VIX option prices compared with S&P 500 option prices. We address this issue by proposing and analysing a stochastic volatility model with regime switching. The basic Heston model cannot capture VIX-implied volatilities, as has been documented. We show that the incorporation of sharp regime shifts can bridge this shortcoming. We take advantage of asymptotic and Fourier methods to make the extension tractable, and we present a fit to data, both in times of crisis and relative calm, which shows the effectiveness of the regime switching.}, number={10}, journal={Quantitative Finance}, publisher={Informa UK Limited}, author={Papanicolaou, Andrew and Sircar, Ronnie}, year={2013}, month={Jul}, pages={1811–1827} }
@article{papanicolaou_2013, title={Dimension Reduction in Discrete Time Portfolio Optimization with Partial Information}, volume={4}, url={http://dx.doi.org/10.1137/120897596}, DOI={10.1137/120897596}, abstractNote={This paper considers the problem of portfolio optimization in a market with partial information and discretely observed price processes. Partial information refers to the setting where assets have unobserved factors in the rate of return and the level of volatility. Standard filtering techniques are used to compute the posterior distribution of the hidden variables, but there is difficulty in finding the optimal portfolio because the dynamic programming problem is non-Markovian. However, fast time scale asymptotics can be exploited to obtain an approximate dynamic program (ADP) that is Markovian and is therefore much easier to compute. Of consideration is a model where the latent variables (also referred to as hidden states) have fast mean reversion to an invariant distribution that is parameterized by a Markov chain $\theta_t$, where $\theta_t$ represents the regime-state of the market and reverts to its own invariant distribution over a much longer time scale. Data and numerical examples are also presented, and there appears to be evidence that unobserved drift results in an information premium.}, number={1}, journal={SIAM Journal on Financial Mathematics}, publisher={Society for Industrial & Applied Mathematics (SIAM)}, author={Papanicolaou, Andrew}, year={2013}, month={Jan}, pages={916–960} }
@article{papanicolaou_2012, title={Nonlinear Filters for Hidden Markov Models of Regime Change with Fast Mean-Reverting States}, volume={10}, ISSN={1540-3459 1540-3467}, url={http://dx.doi.org/10.1137/110819937}, DOI={10.1137/110819937}, abstractNote={We consider filtering for a hidden Markov model that evolves with multiple time scales in the hidden states. In particular, we consider the case where one of the states is a scaled Ornstein--Uhlenbeck process with fast reversion to a shifting-mean that is controlled by a continuous time Markov chain modeling regime change. We show that the nonlinear filter for such a process can be approximated by an averaged filter that asymptotically coincides with the true nonlinear filter of the regime-changing Markov chain as the rate of mean-reversion approaches infinity. The asymptotics exploit weak convergence of the state variables to an invariant distribution, which is significantly different from the strong convergence used to obtain asymptotic results in [A. Papanicolaou, Asymptot. Anal., 70 (2010), pp. 155--176].}, number={3}, journal={Multiscale Modeling & Simulation}, publisher={Society for Industrial & Applied Mathematics (SIAM)}, author={Papanicolaou, Andrew}, year={2012}, month={Jan}, pages={906–935} }
@article{papanicolaou_2010, title={Filtering for fast mean-reverting processes}, volume={70}, ISSN={0921-7134}, url={http://dx.doi.org/10.3233/ASY-2010-1011}, DOI={10.3233/ASY-2010-1011}, abstractNote={We consider nonlinear filtering applications to target tracking based on a vector of multi-scaled models where some of the processes are rapidly mean reverting to their local equilibria. We focus attention on target tracking problems because multiple scaled models with fast mean-reversion (FMR) are a simple way to model latency in the response of tracking systems. The main results of this paper show that nonlinear filtering algorithms for multi-scale models with FMR states can be simpli ed signi cantly by exploiting the FMR structures, which leads to a simplified Baum-Welch recursion that is of reduced dimension. We implement the simplified algorithms with numerical simulations and discuss their eciency and robustness.}, number={3-4}, journal={Asymptotic Analysis}, publisher={IOS Press}, author={Papanicolaou, Andrew}, year={2010}, pages={155–176} }