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Stochastic linear quadratic regulators with indefinite control weight costs. (English) Zbl 0916.93084
The authors consider an optimal control problem of a stochastic linear quadratic regulator with general control weights. The problem reduces to the solution of a stochastic Riccati equation, which is a backward stochastic differential equation. Sufficient conditions are given, under which the Riccati equation has a unique solution.

MSC:
93E20 Optimal stochastic control
49N10 Linear-quadratic optimal control problems
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