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- W2228305672 abstract "We consider the problem of finding the minimal initial data of a controlled process which guaranteesto reach a controlled target with a given probability of success or, more generally, with a given level ofexpected loss. By suitably increasing the state space and the controls, we show that this problem canbe converted into a stochastic target problem, i.e. find the minimal initial data of a controlled processwhich guarantees to reach a controlled target with probability one. Unlike the existing literature onstochastic target problems, our increased controls are valued in an unbounded set. In this paper, weprovide a new derivation of the dynamic programming equation for general stochastic target problemswith unbounded controls, together with the appropriate boundary conditions. These results are appliedto the problem of quantile hedging in financial mathematics, and are shown to recover the explicitsolution of Follmer and Leukert. We then consider the problem of miximizing a utility function underthis type of quantile constraint. The previous study allows to characterize the domain in which thevalue fuction lies and we provide an Hamilton-Jacobi-Bellman representation of the associated valuefunction. Contrary to standard state constraint problems, the domain is not given a-priori and we donot need to impose conditions on its boundary." @default.
- W2228305672 created "2016-06-24" @default.
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- W2228305672 date "2009-01-01" @default.
- W2228305672 modified "2023-09-24" @default.
- W2228305672 title "Quantile hedging and optimal control under stochastic target constraints" @default.
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