Optimal stopping of a risk process

• Autorzy: Elżbieta Z. Ferenstein , Andrzej Sierociński
• Języki publikacji: EN

Abstrakty

EN

Optimal stopping time problems for a risk process $U_t=u+ct-\sum_{n=0}^{N(t)}X_n$ where the number N(t) of losses up to time t is a general renewal process and the sequence of $X_i$'s represents successive losses are studied. N(t) and $X_i$'s are independent. Our goal is to maximize the expected return before the ruin time. The main results are closely related to those obtained by Boshuizen and Gouweleew [2].

Słowa kluczowe

EN

risk process; optimal stopping times

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Applicationes Mathematicae
• Rocznik: 1996-1997
• Tom: 24
• Numer: 3
• Strony: 335-342

Daty

wydano

1997

otrzymano

1996-05-30

poprawiono

1996-10-23

Twórcy

autor

Elżbieta Z. Ferenstein

• Institute of Mathematics, Warsaw University of Technology, Pl. Politechniki 1, 00-661 Warszawa, Poland

autor

Andrzej Sierociński

• Institute of Mathematics, Warsaw University of Technology, Pl. Politechniki 1, 00-661 Warszawa, Poland

Bibliografia

• [1] F. A. Boshuizen and J. M. Gouweleew, A continuous-time job search model: general renewal processes, Report 9247/A, Econometric Institute, Erasmus University Rotterdam, 1992.
• [2] F. A. Boshuizen and J. M. Gouweleew, General optimal stopping theorems for semi-Markov processes, preprint, 1993.
• [3] M. H. A. Davis, Markov Models and Optimization, Chapman & Hall, London, 1993.
• [4] M. H. A. Davis, The representation of martingales of jump processes, SIAM J. Control Optim. 14 (1976), 623-638.
• [5] E. Z. Ferenstein, A variation of Dynkin's stopping game, Math. Japon. 38 (1993), 371-379.
• [6] E. Z. Ferenstein and E. G. Enns, A continuous-time Dynkin's stopping game: renewal processes case, to appear.
• [7] R. S. Liptser and A. N. Shiryaev, Statistics of Stochastic Processes, Nauka, Moscow, 1974 (in Russian).