Optimal risk and dividend distribution control models for an insurance company

Mathematical Methods of Operations Research

Volumn 51, Issue 1, 2000, Pages 1-42

  Taksar, Michael I ^a  

^a USA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0002516587     PISSN: 14322994     EISSN: None     Source Type: Journal    
DOI: 10.1007/s001860050001     Document Type: Article

References (62)

1. Asmussen S (1984) Approximations for the probability of ruin within finite time. Scandinavian Actuarial Journal 84:31-57
2. Asmussen S, Højgaard B, Taksar M (1999) Optimal risk control and dividend distribution olicies. Example of Excess-of Loss Reinsurance. to appear in Finance and Stochastics
3. Asmussen S, Taksar M (1997) Controlled diffusion models for optimal dividend pay-out. Insurance: Mathematics and Economics 20:1-15
4. Bachelier L (1900) Theorie de la speculation. Paris Thesis
5. Black F, Scholes MJ (1973) The pricing of options and corporate liabilities. J. Political Econom. 81:637-654
6. Bernis G (1999) Reinsurance of a life-insurance company. working paper, CERMSEM, Universite Paris
7. Borch K (1967) The theory of risk. Journal of the Royal Statistical Society. Series B, 29:432-452
8. Borch K (1969) The capital structure of a firm. Swedish Journal of Economics 71:1-13
9. Boyle P, Elliott RJ, Yang H (1998) Controlled diffusion models of an insurance company. preprint, Department of Statistics, The University of Hong Kong
10. Browne S (1995) Optimal investment policies for a firm with a random risk process: Exponential utility and minimizing the probability of ruin. Math. of Oper. Res. 20:937-958
11. Browne S (1997) Survival and growth with liability: Optimal portfolio strategies in continuous time. Math. of Oper. Res. 22:468-492
12. Bühlmann H (1970) Mathematical methods in risk Theory. Springer-Verlag, Berlin
13. Buzzi R (1974) Optimale Dividendstrategien fur den Risikoprozess mit austauschbaren Zuwachsen. Ph.D Dissertation 5388, ETH Zurch
14. Cox J, Huang C-F (1989) Optimal consumption and portfolio policies when asset prices follow a diffusion process. Journal of Economic Theory 49:33-83
15. de Finetti B (1957) Su un'Impostazione Alternativa dell Teoria Colletiva del Rischio. Transactions of the 15th International Congress of Actuaries. New York, 2:433-443
16. Delbaen F, Haezendonck J (1987) Classical risk theory in an economic environment. Insurance: Mathematics and Economics 6:85-116
17. Elliott RJ (1982) Stochastic calculus and applications. Applications of Mathematics 18: Springer-Verlag, Berlin
18. Emanuel DC, Harrison JM, Taylor AJ (1975) A diffusion approximation for the ruin probability with compounding assets. Scandinavian Actuarial Journal 75:37-45
19. Fleming WH, Rishel RW (1975) Deterministic and stochastic optimal control. Springer-Verlag
20. Fleming WH, Soner HM (1993) Controlled Markov processes and viscosity solutions. Springer-Verlag
21. Fleming WH, Zariphopoulou T (1991) An optimal investment/consumption model with borrowing. Math. Oper. Res. 16:802-822
22. Garrido J (1989) Stochastic differential equations for compounded risk reserves. Insurance: Mathematics and Economics 8:165-173
23. Garrido J (1988) Diffusion premiums for claim severities subject to inflation. Insurance: Mathematics and Economics 7:123-129
24. Gerber HU (1969) Entscheidungskriterien für den zusammengesetzten Poissonprozess. Mitteilungen der Schweizer Versicherungsmathematiker: 185-228
25. Gerber HU (1972) Games of economic survival with discrete and continuous income processes. Operations Research. 20:37-45
26. Gerber HU (1979) An introduction to mathematical risk theory. S.S. Huebner Foundation Monographs, University of Pennsylvania
27. Grandell J (1977) A class of approximations of ruin probabilmies. Scandinavian Actuarial Journal, Suppl.: 37-52
28. Grandell J (1978) A remark on 'A class of approximations of ruin probabilmies'. Scandinavian Actuarial Journal 78:77-78
29. Grandell J (1990) Aspects of risk theory. Springer-Verlag
30. Harrison JM (1977) Ruin problems with compounding assets. Stochastic Proc, Their Appl. 5:67-79
31. Harrison JM (1985) Brownian motion and stochastic flow systems. Wiley, New York
32. Harrison JM, Taksar M (1983) Instantaneous control of brownian motion. Math. Oper. Res. 8:439-453
33. Hesselager O (1990) Some results on optimal reinsurance in terms of the adjustment coefficient. Scandinavian Actuarial Journal 90:80-95
34. Hipp C, Taksar M (1999) Stochastic control for optimal new business. working paper, Department of Economics, Karlruhe University
35. Højgaard B, Taksar M (1998) Optimal proportional reinsurance policies for diffusion models with transaction costs. Insurance: Mathematics and Economics 22:41-51
36. Højgaard B, Taksar M (1998) Optimal proportional reinsurance policies for diffusion models. Scandinavian Actuarial Journal 2:166-168
37. Højgaard B, Taksar M (1999) Controlling risk exposure and dividends pay-out schemes: Insurance company example. Mathematical Finance 2:153-182
38. Iglehart DL (1969) Diffusion approximations in collective risk theory. Journal of Applied Probability 6:285-292
39. Jeanblanc-Picque M, Shiryaev AN (1995) Optimization of the flow of dividends. Russian Math. Surveys 50:257-277
40. Karatzas I, Lehoczky J, Shreve S (1987) Optimal portfolio and consumption decisions for a small investor on a finite horizon. SIAM J. Control and Optim. 25:1557-1586
41. Karatzas I, Lehoczky J, Sethi S, Shreve S (1986) Explicit solution of a general consumption/ investment problem. Math. Oper. Research 11:261-294
42. Lions P-L, Sznitman A-S (1984) Stochastic differential equations with reflecting boundary conditions. Comm. Pure Appl. Math. 37:511-537
43. Lundberg F (1909) Über die Theorie der Rückversicherung. Transactions of the VI International Congress of Actuaries 1:877-995
44. Martin-Löf A (1994) Lectures on the use of control theory in insurance. Scandinavian Actuarial Journal 94:1-25
45. Merton RC (1971) Optimal consumption and portfolio rules in a continuous-time model. J. Economic Theory 3:373-413; Erratum (1973) J. Economic Theory 6:213-214
46. Merton RC (1990) Continuous-time finance. Basil Blackwell, Cambridge, MA
47. Meyer P-A (1976) Un cours sur les integrales stochastiques. Seminare de Probabilites X. Lecture notes in Mathematics 511, Springer-Verlag, New York
48. Møller CM (1994) Point processes and martingales in risk theory. PhD Thesis, Laboratory of Insurance Mathematics, University of Copenhagen
49. Paulsen J, Gjessing H (1998) Ruin theory with stochastic returns on investments. Technical report, Department of Mathematics, University of Bergen, Norway
50. Paulsen J, Gjessing H (1997) Optimal choice of dividend barriers for a risk process with stochastic return on investments. Insurance: Mathematics and Economics 29:965-985
51. Radner R, Shepp L (1996) Risk vs. profit potential: A model for corporate strategy. J. Econ. Dynam. Control
52. Schmidli H (1992) A general insurance risk model. PhD Thesis 9881, ETH Zürich
53. Schmidli H (1994) Diffusion approximations for a risk process with the possibility of borrowing and interest. Comm. Statist. Stochastic Models 10:365-388
54. Sondermann D (1991) Reinsurance in arbitrage free markets. Insurance: Mathematics and Economics 10:191-202
55. Sethi S (1997) Optimal consumption and investment with bankruptcy (with a foreword by Harry M. Markowitz). Kluwer Academic Publishers, Norwell, MA
56. Sethi S, Taksar M (1988) A note on Merton's optimum consumption and portfolio rules in a continuous-time model. J. Econom. Theory 46:395-401
57. Sethi S, Taksar M (1992) Infinite-horizon investment consumption model with a nonterminal bankruptcy. J. Optim. Theory Appl. 74:333-346
58. Sundt B, Teugels JL (1995) Ruin estimates under interest force. Insurance: Mathematics and Economics 16:7-22
59. Takeuchi K (1962) A remark on economic survival games. J. Operations Res. Soc. Japan 4:114-121
60. Taksar M (1998) Incorporating the value of bankruptcy into the optimal risk/dividend control of a financial corporation. Proceedings of the 4th International Conference on Optimization: Techniques and Applications. Perth, Australia, pp. 1247-1254
61. Taksar M, Zhou X (1998) Optimal risk and dividend control for a company with a debt liability. Insurance: Mathematics and Economics 22:105-122
62. Whittle P (1983) Optimization over time - dynamic programming and stochastic control. Vol II. Wiley, New York