On a solution of the optimal stopping problem for processes with independent increments

Alexander A. Novikov · Albert Nikolaevich Shiryaev

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Stochastic processes and financial applications Probability and Statistical Research Probability and Risk Models

Abstract

We discuss a solution of the optimal stopping problem for the case when a reward function is a power function of a process with independent stationary increments (random walks or Levy processes) on an infinite time interval. It is shown that an optimal stopping time is the first crossing time through a level defined as the largest root of the Appell function associated with the maximum of the underlying process.

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References

1976Stochastic Processes in Queueing Theory 1972Optimal Stopping for Partial Sums

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2012Optimal stopping of strong Markov processes 2011Optimal stopping, Appell polynomials, and Wiener–Hopf factorization 2013On the solution of general impulse control problems using superharmonic functions 2009Optimal Stopping for Processes with Independent Increments, and Applications

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