We consider the problem of optimally controlling a one-dimensional Wiener process with Poissonian jumps until it leaves the interval . The exact optimal control is obtained in a particular case… Click to show full abstract
We consider the problem of optimally controlling a one-dimensional Wiener process with Poissonian jumps until it leaves the interval . The exact optimal control is obtained in a particular case by solving the differential-difference equation satisfied by the value function. An approximate solution is also presented in a more general case. This approximate solution is appropriate when the jump size is small.
               
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