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In the paper we solve a problem of optimal stopping of a risk process in two alternative settings. We assume that the main characteristics of the risk process change according to unobservable random variable. In the first model we assume that the post-disorder distributions are not known a'priori and are randomly chosen from a finite set of admissible distributions. The second model concentrates on a situation when more than one disorder is possible. For both models optimal stopping rules with respect to given utility function are constructed using dynamic programming methodology.
Wydawca
Czasopismo
Rocznik
Tom
Strony
435--454
Opis fizyczny
Bibliogr. 25 poz.
Twórcy
autor
autor
- Faculty Of Mathematics And Information Science Warsaw University Of Technology Pl. Politechniki 1 00-661 Warszawa, Poland, efer@mini.pw.edu.pl
Bibliografia
- [1] N. Bäuerle, U. Rieder, Markov Decision Processes with Applications to Finance, Springer, Berlin 2011.
- [2] E. Bayraktar, S. Dayanik, I. Karatzas, Adaptive Poisson disorder problem, Ann. Appl. Probab. 16 (2006), 1190–1261.
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- [9] E. Ferenstein, A. Pasternak-Winiarski, Optimal stopping of a risk process with disruption and interest rates, in: Advances in Dynamic Games: Theory, Applications,and Numerical Methods for Differential and Stochastic Games, M. Breton, K. Szajowski (eds.), 2010, 489–508, Birkhäuser, Boston.
- [10] E. Ferenstein, A. Sierocinski, Optimal stopping of a risk process, Appl. Math. 24 (1997), 335–342.
- [11] L. I. Galchuk, B. L. Rozovskii, The disorder problem for a Poisson process, Theory Probab. Appl. 16 (1971), 729–734.
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- [14] A. Karpowicz, K. Szajowski, Double optimal stopping of a risk process, Stoch.: Int. J. Probab. Stoch. Process. 79 (2007), 155–167.
- [15] K. Kuratowski, C. Ryll-Nardzewski, A general theorem on selectors, Bull. Acad. Polon Sci. 13 (1965), 397–403.
- [16] B. K. Muciek, Optimal stopping of a risk process: model with interest rates, J. Appl. Probab. 39 (2002), 261–270.
- [17] B. K. Muciek, K. Szajowski, Optimal stopping of a risk process when claims are covered immediately, in: Mathematical Economics, Toru Maruyama (ed.), RIMS Kyoto University, Kôkyuroku 1557 (2007), 132–139.
- [18] G. Peskir, A. Shiryayev, Solving the Poisson disorder problem, in: Advances in Finance and Stochastics (2002), 295–312.
- [19] T. Rolski, H. Schmidli, V. Schmidt, J. Teugels, Stochastic Processes for Insurance and Finance, John Wiley and Sons, Chichester, 1999.
- [20] W. Sarnowski, K. Szajowski, On-line detection of a part of a sequence with unspecified distribution, Statist. Probab. Lett. 78 (2008), 2511–2516.
- [21] A. Schöttl, Optimal stopping of a risk reserve process with interest and cost rates, J. Appl. Probab. 35 (1998), 115–123.
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- [23] K. Szajowski, A two-disorder detection problem, Appl. Math. 24 (1996), 231–241.
- [24] K. Szajowski, On a random number of disorders, Probab. Math. Statist. 31 (2011).
- [25] C. Zhu, Optimal control of the risk process n a regime-switching environment, Automatica 47 (2011), 1570–1579.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-PWA4-0034-0037