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

الملخص EN

Let X(t) be a controlled one-dimensional standard Brownian motion starting from x∈(−d,d).

The problem of optimally controlling X(t) until |X(t)|=d for 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.