Browse > Article
http://dx.doi.org/10.7858/eamj.2011.27.1.091

ON STOCHASTIC OPTIMAL REINSURANCE AND INVESTMENT STRATEGIES FOR THE SURPLUS UNDER THE CEV MODEL  

Jung, Eun-Ju (Department of Mathematics Pusan National University)
Kim, Jai-Heui (Department of Mathematics Pusan National University)
Publication Information
East Asian mathematical journal / v.27, no.1, 2011 , pp. 91-100 More about this Journal
Abstract
It is important to find an optimal strategy which maximize the surplus of the insurance company at the maturity time T. The purpose of this paper is to give an explicit expression for the optimal reinsurance and investment strategy, under the CEV model, which maximizes the expected exponential utility of the final value of the surplus at T. To do this optimization problem, the corresponding Hamilton-Jacobi-Bellman equation will be transformed a linear partial differential equation by applying a Legendre transform.
Keywords
Reinsurance; surplus process; CEV model; stochastic optimal control; exponential utility function; HJB equation; Legendre transform;
Citations & Related Records
연도 인용수 순위
  • Reference
1 S. Luo, M. Taksar and A. Tsoi, On reinsurance and investment for large insurance portfolios, Insurance Math. Econom 42 (2007), 434-444.
2 B. Oksendal, Stochastic Differential Equations, Springer-Verlag Berlin Heidelberg (1998).
3 H. Schmidli, Optimal proportional reinsurance policies in a dynamic setting, Scan. Actuarial J. (2001), No.1, 55-68.
4 M. Taksar and C. Markussen, Optimal dynamic reinsurance policies for large insurance portfolios, Finance and Stochastics 7 (2003), 97-121.   DOI   ScienceOn
5 M. Gu, Y. Yang, S. Li and J. Zhang, Constant elasticity of variance model for proportional reinsurance and investment strategies, Insuance Math. Econom 46 (2010), 580-587.   DOI   ScienceOn
6 C. Hipp and M. Plum, Optimal investment for insurers, Insurance Math. Econom 27 (2000), 215-228.   DOI   ScienceOn
7 T. Bjork, Arbitrage Theory in Continuous Time, Oxford Univ. Press (1998).
8 B. Hojgaad and M. Taksar, Optimal proportional reinsurance policies for diffusion models with transaction costs, Insuance Math. Econom 22 (1998), 41-51.   DOI   ScienceOn
9 M. Jonsson and R. Sircar, Optimal investment problems and volatility homogenization approximations, NATO Science Series II, Vol.75, Kluwer (2002), 255-281.
10 J. H. Kim and E. S. Lee, On stochastic ptimal proportional reinsurance and investment strategies for the surplus, Korean J. Math. 16 (2008), 145-156.
11 P. Devolder, M.B. Princep and I.D. Fabian, Stochastic optimal control of annuity contracts, Insurance Math. Econom. 33 (2003), 227-238.   DOI   ScienceOn
12 J. Gao, Optimal investment strategy for annuity contracts under the constant elasticity of variance (CEV) model, Insuance Math. Econom 45 (2009), 9-18.   DOI   ScienceOn