On discrete-time dynamic programming in insurance: Exponential utility and minimizing the ruin probability

Scandinavian Actuarial Journal

Volumn 2004, Issue 3, 2004, Pages 189-210

  Schäl, Manfred ^a  

^a UNIVERSITY OF BONN   (Germany)

Author keywords

Howard improvement; Investment; Markov decision processes; Reinsurance; Verification theorem

Indexed keywords

EID: 21244503317     PISSN: 03461238     EISSN: 16512030     Source Type: Journal    
DOI: 10.1080/03461230110106507     Document Type: Article

References (34)

1. Bellman, R. (1957). Dynamic programming. Princeton Univ. Press, New Jersey.
2. Bertsekas, D. (1974). Necessary and sufficient conditions for existence of an optimal portfolio. J. Econ. Theory 8, 235-247.
3. Bertsekas, D. & Shreve, S. E. (1978). Stochastic optimal control: the discrete-time case. Academic Press, New York.
4. Brown, L. D. & Purves, R. (1973). Measurable selections of extrema. Ann. Statist. 1, 902-912.
5. Browne, S. (1995). Optimal investment policies for a firm with a random risk process: exponential utility and minimizing the probability of ruin. Math. Oper. Res. 20, 937-958.
6. Dickson, D. C. M. & Waters, H. R. (1996). Reinsurance and ruin. Insurance: Mathematics and Economics 19, 61-80.
7. Dubins, L. E. & Savage L. J. (1965, 1976). How to gamble if you must: Inequalities for stochastic processes. Dover, New York.
8. Ferguson, T. (1965). Betting systems which minimize the probability of ruin. J. SIAM 13, 795-818.
9. Goovaerts, M. J., Kaas, R., van Heerwaarden, A. E. & Bauwelincks, T. (1990). Effective actuarial methods. North-Holland, Amsterdam.
10. Grandell, J. (1991). Aspects of risk theory. Springer, Berlin.
11. Harrison, J. M. & Kreps, D. M. (1979). Martingales and arbitrage in multiperiod securities markets. J. Economic Theory 20, 381-408.
12. Hipp, C. & Plum, M. (2000). Optimal investment for insurers. Insurance: Mathematics and Economics 27, 215-228.
13. Hipp, C., Vogt, M. (2001). Optimal XL insurance. Technical report, Univers. Karlsruhe.
14. Hojgaard, B. & Taksar, M. (1998a). Optimal proportional reinsurance policies for diffusion models. Scand. Actuarial J. 2, 166-180.
15. Hojgaard, B. & Taksar, M. (1998b). Optimal proportional reinsurance policies for diffusion models with transaction costs. Insurance: Mathematics and Economics 22, 41-51.
16. Jacod, J. & Shiryaev, A. N. (1998). Local martingales and the fundamental asset pricing theorems in the discrete-time case. Finance Stochast. 3, 259-273.
17. Martin-Lof, A. (1994). Lectures on the use of control theory in insurance. Scand. Actuarial J. 1, 1-25.
18. Merton, R. C. (1990). Continuous-time finance. Blackwell, Cambridge, MA.
19. Pliska, S. R. (1997). Introduction to mathematical finance. Blackwell Publisher, Malden, USA, Oxford, UK.
20. Porteus, E. L. (1975). On the optimality of structured policies in countable stage decision processes. Management Science 22, 148-157.
21. Rockafeller, R. T. (1970). Convex analysis. Princeton Univ. Press, Princeton, N.J.
22. Rogers, L. C. G. (1994). Equivalent martingale measures and no-arbitrage. Stochastics and Stochastic Reports 51, 41-49.
23. Scarf, H. (1960). The optimality of (s.S) policies in the dynamic inventory problem. In: Arrow, K. J., Karlin, S. & Suppes, P. (eds.). Mathematical methods in the social science. Stanford University Press, Stanford.
24. Schal, M. (1975). Conditions for optimality in dynamic programming and for the limit of n-stage optimal policies to be optimal. Z. Wahrscheinlichkeitstheorie verw. Gebiete 32, 179-196.
25. Schal, M. (1998). On piecewise deterministic Markov control processes: Control of jumps and of risk processes in insurance. Insurance: Mathematics and Economics 22, 75-91.
26. Schal, M. (2000a). Portfolio optimization and martingale measures. Mathematical Finance 10, 289- 304. Schal, M. (2000b). Price systems constructed by optimal dynamic portfolios. Math. Methods Op. Res. 51, 375-397.
27. Schal, M. (2001). Markov decision processes in finance and dynamic options. In: Shwartz, A. & Feinberg, E. (eds.). Markov decision processes. Kluwer.
28. Schal, M. (2002). On the first order Bellman equation in reinsurance and investment control problems. Working paper. Univ. Bonn, Inst. Angew. Math.
29. Schmidli, H. (1999). Lecture notes on risk theory. Dept. of Theoretical Statistics and Operations Research, University of Aarhus.
30. Schmidli, H. (2001a). Optimal proportional reinsurance policies in a dynamic setting. Scand. Actuarial J. 55-68.
31. Schmidli, H. (2001b). On minimizing the ruin probability by investment and reinsurance. Working paper No. 175, Laboratory of Actuarial Mathematics, University of Copenhagen.
32. Strauch, R. E. (1966). Negative dynamic programming. Ann. Math. Statist. 37, 871-890.
33. Taksar, M. I., Markusson, C. (2002). Optimal dynamic reinsurance policies for large insurance portfolios. Working paper.
34. Waters, H. R. (1983). Some mathematical aspects of reinsurance. Insurance: Mathematics and Economics 2, 17-26.