Maximizing the Mean Exit Time of a Brownian Motion from an Interval

[摘要] LetX(t)be a controlled one-dimensional standard Brownian motion starting fromx∈(−d,d). The problem of optimally controllingX(t)until|X(t)|=dfor the first time is solved explicitly in a particular case. The maximal value that the instantaneous reward given for survival in(−d,d)can take is determined.

[学科分类] 应用数学