Book Review: Optimal stochastic control, stochastic target problems, and backward SDE
نویسندگان
چکیده
منابع مشابه
Forward-backward SDE games and stochastic control under model uncertainty
We study optimal stochastic control problems under model uncertainty. We rewrite such problems as (zero-sum) stochastic differential games of forward-backward stochastic differential equations. We prove general stochastic maximum principles for such games, both in the zero-sum case (finding conditions for saddle points) and for the non-zero sum games (finding conditions for Nash equilibria). We...
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Within a general abstract framework, we show that any optimal control problem in standard form can be translated into a stochastic target problem as defined in [17], whenever the underlying filtered probability space admits a suitable martingale representation property. This provides a unified way of treating these two classes of stochastic control problems. As an illustration, we show, within ...
متن کاملOptimal Control under Stochastic Target Constraints
We study a class of Markovian optimal stochastic control problems in which the controlled process Z is constrained to satisfy an a.s. constraint Z(T ) ∈ G ⊂ R P − a.s. at some final time T > 0. When the set is of the form G := {(x, y) ∈ R × R : g(x, y) ≥ 0}, with g non-decreasing in y, we provide a Hamilton-Jacobi-Bellman characterization of the associated value function. It gives rise to a sta...
متن کاملStochastic Collocation for Optimal Control Problems with Stochastic PDE Constraints
We discuss the use of stochastic collocation for the solution of optimal control problems which are constrained by stochastic partial differential equations (SPDE). Thereby the constraining SPDE depends on data which is not deterministic but random. Assuming a deterministic control, randomness within the states of the input data will propagate to the states of the system. For the solution of SP...
متن کاملOptimal Control Problems of Forward-Backward Stochastic Volterra Integral Equations with Closed Control Regions
Abstract. Optimal control problems of forward-backward stochastic Volterra integral equations (FBSVIEs, in short) with closed control regions are formulated and studied. Instead of using spike variation method as one may imagine, here we turn to treat the non-convexity of the control regions by borrowing some tools in set-valued analysis and adapting them into our stochastic control systems. A ...
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 2016
ISSN: 0273-0979,1088-9485
DOI: 10.1090/bull/1548