Optimal stopping of a risk process

Elżbieta Ferenstein; Andrzej Sierociński

Applicationes Mathematicae (1997)

  • Volume: 24, Issue: 3, page 335-342
  • ISSN: 1233-7234

Abstract

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Optimal stopping time problems for a risk process U t = u + c t - ∑ 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].

How to cite

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Ferenstein, Elżbieta, and Sierociński, Andrzej. "Optimal stopping of a risk process." Applicationes Mathematicae 24.3 (1997): 335-342. <http://eudml.org/doc/219175>.

@article{Ferenstein1997,
abstract = {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].},
author = {Ferenstein, Elżbieta, Sierociński, Andrzej},
journal = {Applicationes Mathematicae},
keywords = {risk process; optimal stopping times},
language = {eng},
number = {3},
pages = {335-342},
title = {Optimal stopping of a risk process},
url = {http://eudml.org/doc/219175},
volume = {24},
year = {1997},
}

TY - JOUR
AU - Ferenstein, Elżbieta
AU - Sierociński, Andrzej
TI - Optimal stopping of a risk process
JO - Applicationes Mathematicae
PY - 1997
VL - 24
IS - 3
SP - 335
EP - 342
AB - 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].
LA - eng
KW - risk process; optimal stopping times
UR - http://eudml.org/doc/219175
ER -

References

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  1. [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. [2] F. A. Boshuizen and J. M. Gouweleew, General optimal stopping theorems for semi-Markov processes, preprint, 1993. 
  3. [3] M. H. A. Davis, Markov Models and Optimization, Chapman & Hall, London, 1993. 
  4. [4] M. H. A. Davis, The representation of martingales of jump processes, SIAM J. Control Optim. 14 (1976), 623-638. Zbl0337.60048
  5. [5] E. Z. Ferenstein, A variation of Dynkin's stopping game, Math. Japon. 38 (1993), 371-379. Zbl0819.60049
  6. [6] E. Z. Ferenstein and E. G. Enns, A continuous-time Dynkin's stopping game: renewal processes case, to appear. Zbl0633.90106
  7. [7] R. S. Liptser and A. N. Shiryaev, Statistics of Stochastic Processes, Nauka, Moscow, 1974 (in Russian). Zbl0556.60003

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