Optimal Control for Controllable Stochastic Linear Systems

2019/06/09 by Xiuchun Bi, Jingrui Sun, Bi, Xiuchun +3 · 1 citation
Economics, Econometrics and Finance · Social Sciences · Decision Sciences · #Stochastic processes and financial applications #Insurance, Mortality, Demography, Risk Management #Probability and Risk Models

paper · pdf · doi:10.48550/arxiv.1906.03603

Abstract

This paper is concerned with a constrained stochastic linear-quadratic optimal control problem, in which the terminal state is fixed and the initial state is constrained to lie in a stochastic linear manifold. The controllability of stochastic linear systems is studied. Then the optimal control is explicitly obtained by considering a parameterized unconstrained backward LQ problem and an optimal parameter selection problem. A notable feature of our results is that, instead of solving an equation involving derivatives with respect to the parameter, the optimal parameter is characterized by an algebraic equation.

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• Linear-Quadratic Optimal Control for Backward Stochastic Differential Equations with Random Coefficients

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