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Minimizing or maximizing the expected time to reach zero. (English) Zbl 0613.93067
The authors consider stochastic control systems described by the Ito differential equation $dx(t)=a(t)\cdot dt+b(t)\cdot dw(t)$ with nonanticipative controls a(t) and b(t) to be chosen in an admissible set. Deriving an improved verification lemma of its own interest, they solve the problems of finding optimal controls which minimize or maximize the expected time to reach the zero state. They also discuss an application to a portfolio problem.
Reviewer: A.Kistner

93E20Optimal stochastic control (systems)
60G40Stopping times; optimal stopping problems; gambling theory
60J60Diffusion processes
49K45Optimal stochastic control (optimality conditions)
60J70Applications of Brownian motions and diffusion theory
91B28Finance etc. (MSC2000)
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