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- W2025951566 abstract "In this paper, we define and study a new class of optimal stochastic control problems which is closely related to the theory of backward SDEs and forward-backward SDEs. The controlled process $(X^nu,Y^nu)$ takes values in ${mathbb R}^d times {mathbb R}$ and a given initial data for $X^{nu}(0)$. Then the control problem is to find the minimal initial data for $Y^{nu}$ so that it reaches a stochastic target at a specified terminal time T. The main application is from financial mathematics, in which the process $X^{nu}$ is related to stock price, $Y^{nu}$ is the wealth process, and $nu$ is the portfolio. We introduce a new dynamic programming principle and prove that the value function of the stochastic target problem is a discontinuous viscosity solution of the associated dynamic programming equation. The boundary conditions are also shown to solve a first order variational inequality in the discontinuous viscosity sense. This provides a unique characterization of the value function which is the minimal initial data for $Y^{nu}$." @default.
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- W2025951566 date "2002-01-01" @default.
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- W2025951566 title "Stochastic Target Problems, Dynamic Programming, and Viscosity Solutions" @default.
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- W2025951566 doi "https://doi.org/10.1137/s0363012900378863" @default.
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