A diffusion model for optimal dividend distribution for a company with constraints on risk control

SIAM Journal on Control and Optimization

Volumn 41, Issue 6, 2003, Pages 1946-1979

  Choulli, Tahir ^a   Taksar, Michael ^b   Zhou, Xun Yu ^c  

^a UNIVERSITY OF ALBERTA   (Canada)

^b UNIVERSITY OF MISSOURI   (United States)

^c CHINESE UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

Diffusion model; Dividend distribution; HJB equation; Optimal stochastic control; Risk control; Skorohod problem; Viscosity solution

Indexed keywords

BUSINESS POLICY; RISK CONTROL; VISCOSITY SOLUTION;

BROWNIAN MOVEMENT; DIFFUSION; OPTIMIZATION; RISK ASSESSMENT;

STOCHASTIC CONTROL SYSTEMS;

EID: 0347214936     PISSN: 03630129     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0363012900382667     Document Type: Article

References (19)

1. S. ASMUSSEN, B. HØJGAARD, AND M. TAKSAR (2000), Optimal risk control and dividend distribution policies. Example of excess-of loss reinsurance, Finance Stoch., 4, pp. 299-324.
2. S. ASMUSSEN AND M. TAKSAR (1997), Controlled diffusion models for optimal dividend pay-out, Insurance Math. Econom., 20, pp. 1-15.
3. P. BOYLE, R. J. ELLIOTT, AND H. YANG (1998), Controlled Diffusion Models of an Insurance Company, preprint, Department of Statistics, The University of Hong Kong.
4. T. CHOULLI, M. TAKSAR, AND X. Y. ZHOU (2001), Excess-of-loss reinsurance for a company with debt liability and constraints on risk reduction, Quantitative Finance, 1, pp. 573-596.
5. C. DELLACHERIE AND P. A. MEYER (1980), Probabilité et potentiels: Théorie des martingales, Hermann, Paris.
6. W. H. FLEMING AND R. W. RISHEL (1975), Deterministic and Stochastic Optimal Control, Springer-Verlag, Berlin-New York.
7. W. H. FLEMING AND H. M. SONER (1993), Controlled Markov Processes and Viscosity Solutions, Springer-Verlag, New York.
8. B. HØJGAARD AND M. TAKSAR (1998a), Optimal proportional reinsurance policies for diffusion models with transaction costs, Insurance Math. Econom., 22, pp. 41-51.
9. B. HØJGAARD AND M. TAKSAR (1998b), Optimal proportional reinsurance policies for diffusion models, Scand. Actuar. J., 2, pp. 166-168.
10. B. HØJGAARD AND M. TAKSAR (1999), Controlling risk exposure and dividends pay-out schemes: Insurance company example, Math. Finance, 2, pp. 153-182.
11. M. JEANBLANC-PICQUE AND A. N. SHIRYAEV (1995), Optimization of the flow of dividends, Russian Math. Surveys, 50, pp. 257-277.
12. P.-L. LIONS AND A.-S. SZNITMAN (1984), Stochastic differential equations with reflecting boundary conditions, Comm. Pure Appl. Math., 37, pp. 511-537.
13. J. PAULSEN AND H. K. GJESSING (1997), Optimal choice of dividend barriers for a risk process with stochastic return on investments, Insurance Math. Econom., 20, pp. 215-223.
14. D. REVUZ AND M. YOR (1999), Continuous Martingales and Brownian Motion, 3rd ed., Springer-Verlag, Berlin.
15. H. L. ROYDEN (1988), Real Analysis, 3rd ed., Prentice-Hall, Upper Saddle River, NJ.
16. R. RADNER AND L. SHEPP (1996), Risk vs. profit potential: A model for corporate strategy, J. Econ. Dynam. Control, 20, pp. 1373-1393.
17. M. TAKSAR (2000), Optimal risk and dividend distribution control models for an insurance company, Math. Methods Oper. Res., 51, pp. 1-42.
18. M. TAKSAR AND X. Y. ZHOU (1998), Optimal risk and dividend control for a company with a debt liability, Insurance Math. Econom., 22, pp. 105-122.
19. J. YONG AND X. Y. ZHOU (1999), Stochastic Controls: Hamiltonian Systems and HJB Equations, Springer-Verlag, New York.