Optimal proportional reinsurance and investment problem with jump-diffusion risk process under effect of inside information

Abstract

We study optimal investment and proportional reinsurance strategy in the presence of inside information. The risk process is assumed to follow a compound Poisson process perturbed by a standard Brownian motion. The insurer is allowed to invest in a risk-free asset and a risky asset as well as to purchase proportional reinsurance. In addition, it has some extra information available from the beginning of the trading interval, thus introducing in this way inside information aspects to our model. We consider two optimization problems: the problem of maximizing the expected exponential utility of terminal wealth with and without inside information, respectively. By solving the corresponding Hamilton-Jacobi-Bellman equations, explicit expressions for their optimal value functions and the corresponding optimal strategies are obtained. Finally, we discuss the effects of parameters on the optimal strategy and the effect of the inside information by numerical simulations.

Keywords

Inside information / investment / reinsurance / jump diffusion

References

[1] Bai L H, Guo J Y. Optimal proportional reinsurance and investment with multiple risky assets and no-shorting constraint. Insurance Math Econom, 2008, 42: 968-975

[2] Baltas I D, Frangos N E, Yannacopoulos A N. Optimal investment and reinsurance policies in insurance markets under the effect of inside information. Appl Stoch Models Bus Ind, 2012, 28: 506-528

[3] Browne S. Optimal investment policies for a firm with a random risk process: exponential utility and minimizing the probability of ruin. Math Oper Res, 1995, 20: 937-958

[4] Fleming W H, Soner H M. Controlled Markov Processes and Viscosity Solutions. 2nd ed. New York: Springer, 2006

[5] Hipp C, Plum M. Optimal investment for insurers. Insurance Math Econom, 2000, 27: 215-228

[6] Liang Z, Yuen K, Cheung K. Optimal reinsurance-investment problem in a constant elasticity of variance stock market for jump-diffusion risk model. Appl Stoch Models Bus Ind, 2012, 28(2): 585-597

[7] Protter P. Stochastic Integration and Stochastic Differential Equations. 2nd ed. Berlin: Springer, 2004

[8] Yang H L, Zhang L H. Optima investment for insurer with jump-diffusion risk process. Insurance Math Econom, 2005, 37: 615-634

RIGHTS & PERMISSIONS

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg