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Zbl 0613.93067
Heath, D.; Orey, S.; Pestien, V.; Sudderth, W.
Minimizing or maximizing the expected time to reach zero. (English)
[J] SIAM J. Control Optimization 25, 195-205 (1987). ISSN 0363-0129; ISSN 1095-7138/e

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.
[A.Kistner]

MSC 2000:: *93E20 Optimal stochastic control (systems)
60G40 Optimal stopping
60J60 Diffusion processes
49K45 Optimal stochastic control (necessity and sufficiency)
60J70 Appl. of diffusion theory
91B28 Finance etc.

Keywords: zero reachability; stochastic control systems; nonanticipative controls; portfolio problem

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