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Forcing a stochastic process to stay in or to leave a given region. (English) Zbl 0728.93078

The paper deals with the problem of forcing a nonlinear controlled diffusion process to stay in a given region until a given time or to leave this region before that time. A one-dimensional problem characterized by an uncontrolled process described by a Brownian motion without drift is explicitly solved. Finally the same control problem with a risk-sensitive cost criterion is considered.
Reviewer: G.Di Masi (Padova)

MSC:

93E20 Optimal stochastic control
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