@article{da lio_mceneaney_2002, title={Finite time-horizon risk-sensitive control and the robust limit under a quadratic growth assumption}, volume={40}, ISSN={["1095-7138"]}, DOI={10.1137/S0363012998345159}, abstractNote={The finite time--horizon risk-sensitive limit problem for continuous nonlinear systems is considered. Previous results are extended to cover more typical examples. In particular, the cost may grow quadratically, and the diffusion coefficient may depend on the state. It is shown that the risk-sensitive value function is the solution of the corresponding dynamic programming equation. It is also shown that this value converges to the value of the robust control problem as the cost becomes infinitely risk averse, with corresponding scaling of the diffusion coefficient.}, number={5}, journal={SIAM JOURNAL ON CONTROL AND OPTIMIZATION}, author={Da Lio, F and McEneaney, WM}, year={2002}, month={Jan}, pages={1628–1661} }
 @article{fleming_mceneaney_2001, title={Robust limits of risk sensitive nonlinear filters}, volume={14}, ISSN={["0932-4194"]}, DOI={10.1007/PL00009879}, number={2}, journal={MATHEMATICS OF CONTROL SIGNALS AND SYSTEMS}, author={Fleming, WH and McEneaney, WM}, year={2001}, pages={109–142} }
 @article{fleming_mceneaney_2000, title={A max-plus-based algorithm for a Hamilton-Jacobi-Bellman equation of nonlinear filtering}, volume={38}, ISSN={["0363-0129"]}, DOI={10.1137/S0363012998332433}, abstractNote={The Hamilton--Jacobi--Bellman (HJB) equation associated with the {robust/\hinfty} filter (as well as the Mortensen filter) is considered. These filters employ a model where the disturbances have finite power. The HJB equation for the filter information state is a first-order equation with a term that is quadratic in the gradient. Yet the solution operator is linear in the max-plus algebra. This property is exploited by the development of a numerical algorithm where the effect of the solution operator on a set of basis functions is computed off-line. The precomputed solutions are stored as vectors of coefficients of the basis functions. These coefficients are then used directly in the real-time computations.}, number={3}, journal={SIAM JOURNAL ON CONTROL AND OPTIMIZATION}, author={Fleming, WH and McEneaney, WM}, year={2000}, month={Mar}, pages={683–710} }
 @article{helton_kronewitter_mceneaney_stankus_2000, title={Singularly perturbed control systems using non-commutative computer algebra}, volume={10}, ISSN={["1049-8923"]}, DOI={10.1002/1099-1239(200009/10)10:11/12<983::AID-RNC535>3.0.CO;2-#}, number={11-12}, journal={INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL}, author={Helton, JW and Kronewitter, FD and McEneaney, WM and Stankus, M}, year={2000}, pages={983–1003} }
 @article{mceneaney_1998, title={A uniqueness result for the Isaacs equation corresponding to nonlinear H infinity control}, volume={11}, ISSN={["0932-4194"]}, DOI={10.1007/BF02750395}, number={4}, journal={MATHEMATICS OF CONTROL SIGNALS AND SYSTEMS}, author={McEneaney, WM}, year={1998}, pages={303–334} }
 @article{mceneaney_1998, title={Robust/H-infinity, filtering for nonlinear systems}, volume={33}, number={5}, journal={Systems and Control Letters}, author={McEneaney, W. M.}, year={1998}, pages={315–325} }
 @article{mceneaney_1997, title={A robust control framework for option pricing}, volume={22}, ISSN={["0364-765X"]}, DOI={10.1287/moor.22.1.202}, abstractNote={ A new approach is taken to the problem of option pricing. In the standard framework, the option pricing problem involves determining a price such that the option writer can guarantee a certain bound on the cost almost surely. Due to this form, the problem may be reformulated in terms of deterministic differential games of the type employed in robust and H∞ control. Different models yield different prices. The standard model yields the Black and Scholes price. Both a deterministic model and the standard model with the Ito integral replaced by the Stratonovich integral yield the price corresponding to a stop-loss hedging technique. With these methods, it can also easily be shown that for the standard model with a bounded, stochastic volatility, the Black and Scholes price corresponding to the upper bound for volatility is sufficient to hedge the option. }, number={1}, journal={MATHEMATICS OF OPERATIONS RESEARCH}, author={McEneaney, WM}, year={1997}, month={Feb}, pages={202–221} }
 @article{dupuis_mceneaney_1997, title={Risk-sensitive and robust escape criteria}, volume={35}, ISSN={["0363-0129"]}, DOI={10.1137/S0363012995281626}, abstractNote={The problem of controlling a noisy process so as to prevent it from leaving a prescribed set has a number of interesting applications. In this paper, new approaches to this problem are considered. First, a risk-sensitive criterion for a stochastic diffusion process model is examined, and it is shown that the value is a classical solution of a related PDE. The qualitative properties of this criterion are favorably contrasted with those of existing criteria in the risk-averse limit. It is proved that in the risk-averse limit the value of the risk-sensitive criterion converges to a viscosity solution of a first-order PDE. It is then demonstrated that the value function of a deterministic differential game is also a viscosity solution to the PDE. This game gives a robust control formulation of the escape time problem and is analogous to H$^{\infty}$ control. In particular, the opposing player attempts to push the process out of the prescribed set and suffers an L2 cost for his efforts. Lower bounds on the escape time as a function of this cost are obtained.}, number={6}, journal={SIAM JOURNAL ON CONTROL AND OPTIMIZATION}, author={Dupuis, P and McEneaney, WM}, year={1997}, month={Nov}, pages={2021–2049} }