### Abstract

The controlled process X(t) with values in ( minus infinity , 0) is given by a stochastic differential equation dX(t) equals mu (t)dt plus sigma (t)dW//t, X(0) equals x, where the nonanticipative controls mu and sigma are to be chosen so that ( mu (t), sigma (t)) remains in a given set S. The object is to maximize (minimize) the expectation of beta **T where 0 less than beta less than 1( beta greater than 1) and T is the hitting time of zero. A complete solution is given for any specified set, and an application is made to continuous-time red-and-black.

Original language | English (US) |
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Pages (from-to) | l253-1265 |

Journal | SIAM Journal on Control and Optimization |

Volume | 25 |

Issue number | 5 |

State | Published - Sep 1 1987 |

Externally published | Yes |

### ASJC Scopus subject areas

- Control and Optimization
- Applied Mathematics

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## Cite this

Orey, S., Pestien, V., & Sudderth, W. (1987). REACHING ZERO RAPIDLY.

*SIAM Journal on Control and Optimization*,*25*(5), l253-1265.