On a solution of the optimal stopping problem for processes with independent increments. (English) Zbl 1114.60035
Summary: 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 Lévy 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.
MSC:
| 60G40 | Stopping times; optimal stopping problems; gambling theory |
| 60G51 | Processes with independent increments; Lévy processes |
References:
| [1] | DOI: 10.1080/07474949808836404 · Zbl 0913.62078 · doi:10.1080/07474949808836404 |
| [2] | DOI: 10.1214/aoms/1177728798 · Zbl 0055.37002 · doi:10.1214/aoms/1177728798 |
| [3] | Borovkov A.A., Stochastic Processes in Queueing Theory (1976) · Zbl 0319.60057 |
| [4] | Chow Y.S., Probability Theory: Independence, Interchangeability, Martingales (1997) |
| [5] | DOI: 10.1214/aoms/1177692491 · Zbl 0244.60037 · doi:10.1214/aoms/1177692491 |
| [6] | DOI: 10.1214/aoms/1177698978 · Zbl 0158.17201 · doi:10.1214/aoms/1177698978 |
| [7] | Kyprianou A.E., Electronic Communications in Probability 10 pp 146– (2005) |
| [8] | Novikov A.A., Teor. Veroyatn. Primen. 20 pp 13– (1975) |
| [9] | Novikov A.A., Teor. Veroyatn. Primen. 49 pp 373– (2004) |
| [10] | Schoutens W., Stochastic Processes and Orthogonal Polynomials (2000) · Zbl 0960.60076 |
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