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)|
|Journal||SIAM Journal on Control and Optimization|
|State||Published - Sep 1 1987|
ASJC Scopus subject areas
- Control and Optimization
- Applied Mathematics