Stochastic Target Problems, Dynamic Programming, and Viscosity Solutions
نویسندگان
چکیده
منابع مشابه
Stochastic Target Problems, Dynamic Programming, and Viscosity Solutions
In this paper, we de ne and study a new class of optimal stochastic control problems which is closely related to the theory of Backward SDE's and forward-backward SDE's. The controlled process (X ; Y ) takes values in IRd IR and a given initial data for X (0). Then, the control problem is to nd the minimal initial data for Y so that it reaches a stochastic target at a speci ed terminal time T ....
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We study a class of stochastic target games where one player tries to find a strategy such that the state process almost-surely reaches a given target, no matter which action is chosen by the opponent. Our main result is a geometric dynamic programming principle which allows us to characterize the value function as the viscosity solution of a non-linear partial differential equation. Because ab...
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Given a controlled stochastic process, the reachability set is the collection of all initial data from which the state process can be driven into a target set at a specified time. Differential properties of these sets are studied by the dynamic programming principle which is proved by the Jankov-von Neumann measurable selection theorem. This principle implies that the reachability sets satisfy ...
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Motivated by applications in mathematical finance [3] and stochastic analysis [16], we continue our study of second order backward stochastic equations (2BSDE). In this paper, we derive the dynamic programming equation for a certain class of problems which we call as the second order stochastic target problems. In contrast with previous formulations of similar problems, we restrict control proc...
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ژورنال
عنوان ژورنال: SIAM Journal on Control and Optimization
سال: 2002
ISSN: 0363-0129,1095-7138
DOI: 10.1137/s0363012900378863