Controlling risk exposure and dividends payout schemes: Insurance company example

Mathematical Finance

Volumn 9, Issue 2, 1999, Pages 153-182

  Højgaard, Bjarne ^b   Taksar, Michael ^a  

^a STONY BROOK UNIVERSITY   (United States)

^b AALBORG UNIVERSITY   (Denmark)

Author keywords

Diffusion models; Dividends payout; HJB equation; Proportional reinsurance; Stochastic control theory

Indexed keywords

EID: 0033447426     PISSN: 09601627     EISSN: None     Source Type: Journal    
DOI: 10.1111/1467-9965.00066     Document Type: Article

References (41)

1. ASMUSSEN, S., and M. TAKSAR (1997): Controlled Diffusion Models for Optimal Dividend Pay-Out, Insurance: Math. & Economics 20, 1-15.
2. BORCH, K. (1967): The Theory of Risk, J. Royal Statist. Soc. B 29, 432-452.
3. BORCH, K. (1969): The Capital Structure of a Firm, Swedish J. Econ. 71, 1-13.
4. BROWNE, S. (1995): Optimal Investment Policies for a Firm with Random Risk Process: Exponential Utility and Minimizing the Probability of Ruin, Math. Operations Res. 20(4), 937-958.
5. BROWNE, S. (1997): Survival and Growth with Liability: Optimal Portfolio Strategies in Continuous Time, Math. Operations Res. 22(2), 468-493.
6. BÜHLMANN, H. (1970): Mathematical Methods in Risk Theory. Berlin: Springer Verlag.
7. BUZZI, R. (1974): Optimale Dividendestrategien für den Risikoprozess mit austauschbaren Zuwächsen. Ph.D. dissertation 5388, ETH Zürich.
8. CADENILLAS, A., and U. G. HAUSSMANN (1994): Stochastic Maximum Principle for a Singular Control Problem, Stoch. Stoch. Rep. 49, 211-237.
9. DAVIS, M. (1993): Markov Models and Optimization. London: Chapman and Hall.
10. DAVIS, M. H., and A. NORMAN (1990): Portfolio Selection with Transaction Costs, Math. Operations Res. 15, 676-713.
11. DAYANANDA, P. W. A. (1970): Optimal Reinsurance, J. Appl. Probab. 7, 134-156.
12. DE FINETTI, B. (1957): Su un' impostazione alternativa dell teoria collectiva del rischio. Transactions of the 15th International Congress of Actuaries, New York, 2, 433-443.
13. DELLACHERIE, C., and P-A. MEYER (1980): Probabilites et Potentiel. Theorie des Martingales. Paris: Hermann.
14. FLEMING, W. H., and R. W. RISHEL (1975): Deterministic and Stochastic Optimal Control. New York: Springer Verlag.
15. FLEMING, W. H., and H. M. SONER (1993): Controlled Markov Processes and Viscosity Solutions. New York: Springer Verlag.
16. GERBER, H. U. (1972): Games of Economic Survival with Discrete-and Continuous-Income Processes, Operations Res. 20, 37-45.
17. GERBER, H. U. (1977): An optimal cancellation of policies, ASTIN Bull. IX, 125-138.
18. GERBER, H. U. (1979): An Introduction to Mathematical Risk Theory. S. S. Huebner Foundation Monographs, University of Pennsylvania.
19. GRANDELL, J. (1990): Aspects of Risk Theory. Berlin: Springer Verlag.
20. HARRISON, J. M., and M. TAKSAR (1983): Instantaneous Control of Brownian Motion, Math. Operations Res. 8, 439-453.
21. HØJGAARD, B., and M. TAKSAR (1998): Optimal Proportional Reinsurance Policies for Diffusion Models, Scand. Actuarial J. 2, 166-180.
22. KARATZAS, I., J. P. LEHOCZKY, S. P. SETHI, and E. SHREVE (1986): Explicit Solution of a General Consumption/Investment Problem, Math. Operations Res. 11, 261-294.
23. KARATZAS, I., J. P. LEHOCZKY, and S. E. SHREVE (1987): Optimal Portfolio and Consumption Decisions for a "Small Investor" on a Finite Horizon, SIAM J. Control Optim. 25, 1557-1586.
24. KARATZAS, I., and S. E. SHREVE (1984): Connection between Optimal Stopping and Singular Stochastic Control; I. Monotone Follower Problem, SIAM J. Control Optim. 22, 856-877.
25. KARLIN, S. & H.M. TAYLOR (1981): A Second Course in Stochastic Processes. San Diego: Academic Press.
26. LEHOCZKY, J. P., and S. E. SHREVE (1986): Absolutely Continuous and Singular Stochastic Control, Stochastics 17, 91-109.
27. LIONS, P.-L., and A-S. SZNITMAN (1984): Stochastic Differential Equations with Reflecting Boundary Conditions, Comm. Pure Appl. Math. 37, 511-537.
28. MARTIN-LÖF, A. (1973): A Method for Finding the Optimal Decision Rule for a Policy Holder of an Insurance with a Bonus System, Scand. Actuarial J. 1973, 23-39.
29. MARTIN-LÖF, A. (1983): Premium Control in an Insurance System, an Approach Using Linear Control Theory, Scand. Actuarial J. 1983, 1-27.
30. MARTIN-LÖF, A. (1994): Lectures on the Use of Control Theory in Insurance, Scand. Actuarial J. 1994, 1-25.
31. MILLER, M. H., and F. MODIGLIANI (1961): Dividend Policy, Growth and Valuation of Shares, J. Business 34, 411-433.
32. ØKSENDAL, B. (1985): Stochastic Differential Equations. Berlin: Springer Verlag.
33. PAULSEN, J., and H. K. GJESSING (1997): Optimal Choice of Dividend Barriers for a Risk Process with Stochastic Return of Investment. Insurance: Math. & Economics 29, 965-985.
34. PRESMAN, E., and S. SETHI (1991): Risk Aversion Behaviour in Consumption/Investment Problems, Math. Finance 1, 100-124.
35. RADNER, R., and L. SHEPP (1996): Risk vs. Profit Potential: A Model for Corporate Strategy, J. Econ. Dynam. Control, 1373-1393.
36. SETHI, S. P. (1996): When Does the Share Price Equal the Present Value of Future Dividends? A Modified Dividend Approach, Econ. Theory 8, 307-319.
37. SETHI, S. P., N. A. DERZKO, and J. LEHOCZKY (1984): General Solution of the Stochastic Price-Dividend Integral Equation: A Theory of Financial Valuation, SIAM J. Math. Anal. 15, 1100-1113.
38. SETHI, S. P., N. A. DERZKO, and J. LEHOCZKY (1991): A Stochastic Extension of Miller Modigliani Framework, Math. Finance 1(4), 57-76.
39. SETHI, S., M. TAKSAR, and E. PRESMAN (1992): Explicit Solution of a General Consumption/Portfolio Problem with Subsistence Consumption and Bankruptcy, J. Econ. Dynam. Control 16, 747-768.
40. TAKSAR, M. (1985): Average Optimal Singular Control and a Related Stopping Problem, Math. Operations Res. 10, 63-81.
41. WHITTLE, P. (1983): Optimization over Time - Dynamic Programming and Stochastic Control, vol. II. New York: Wiley.