M. Soner; "Stochastic Target Problems", Oct.17, 2007, 13:40, FENS G035

Faculty of Engineering and Natural Sciences
FENS SEMINARS
IE 551 - Graduate Seminar

Stochastic Target Problems
by
Mete Soner

Abstract: Consider a simple deterministic game played by two players, Paul and Jane. In this game a closed set on a plane A and an interior starting point are given. Starting from this point, goal of Jane is to exit from A as quickly as possible. Paul's goal is to maximize the exit time. Towards these goals, Jane chooses a direction to move one unit of length. After Jane's choice Paul may decide to reserve the direction. Infact, if one thinks of Paul's decision to have equıal probability but insist to exit in all events, then the resulting is an equaivalent but a random problem. In this talk, I will outline a theory to solve these type of stochastic control problems. We call them "stochastic target problems". In these problems, the controller would like to steer a random process into a given deterministic target set by a judicial choice of controls. Although, main examples are from financial pricing problems, it may be of independent interest as a new class of optimal control problems. In this talk, I will descibe the problem and develop tools for its analysis. I will also describe simple pricing problems to motivate this study as well. Interestingly, the game played by Jane and Paul approximates the mean curvature flow from differential geometry.

Mete Soner has recently joined Sabancı University as the Işık İnselbağ Professor. Prior to that, he was at Koç University, where he served as the Dean of the College of Administrative Sciences and Economics. Professor Soner received his Ph.D. from the Division of Applied Mathematics of Brown University. After a one-year postdoctoral stay at the Institute for Applied Mathematics, he joined the Department of Mathematical Sciences at Carnegie Mellon. He then moved to Princeton and became the Paul M. Wyhtes '55 Professor of Engineering and Finance. During his tenure at Princeton he was affiliated with the Program in Applied and Computational Mathematics, the Department of Operations Research and Financial Engineering (ORFE) and the Bendheim Center of Finance. Professor Soner has co-authored a book with Wendell Fleming, on viscosity solutions and stochastic control and
authored or co-authored several articles on nonlinear partial differential equations, viscosity solutions, stochastic optimal control and mathematical finance. Professor Soner is a member of the Turkish Academy of Sciences, TÜBA, since December 2001, and he received the TÜBİTAK-TWAS Science award in 2002.

October 17, 2007, 13:40, FENS G035