OPTIMAL INVESTMENT FOR THE INSURER IN THE LEVY MARKET UNDER THE MEAN-VARIANCE CRITERION

  • Liu, Junfeng (Department of Mathematics, East China University of Science and Technology)
  • 투고 : 2009.09.10
  • 심사 : 2009.10.25
  • 발행 : 2010.05.30

초록

In this paper we apply the martingale approach, which has been widely used in mathematical finance, to investigate the optimal investment problem for an insurer under the criterion of mean-variance. When the risk and security assets are described by the L$\acute{e}$vy processes, the closed form solutions to the maximization problem are obtained. The mean-variance efficient strategies and frontier are also given.

키워드

과제정보

연구 과제 주관 기관 : National Natural Science Foundation of China

참고문헌

  1. S. Browne, Optimal investment policies for a firm with a random risk process: Exponential utility and minimizing the probability of ruin. Math. Oper. Res. 20(1995), 937-958. https://doi.org/10.1287/moor.20.4.937
  2. C. Hipp and M. Plum, Optimal investment for insurers. Insur. Math. Econ. 27(2000), 215-228. https://doi.org/10.1016/S0167-6687(00)00049-4
  3. C. Hipp, Stochastic control with application in insurance. In: Stochastic Methods in Finance. In: Lecture Notes in Mathematics, vol. 1856(2004). Springer, Berlin, pp. 127-164.
  4. C.S. Liu and H. Yang, Optimal investment for an insurer to minimize its probability of ruin. North American Actuarial Journal 8(2004), 11-31. https://doi.org/10.1080/10920277.2004.10596134
  5. H. Yang and L. Zhang, Optimal investment for insurer with jump-diffusion risk process. Insur. Math. Econ. 37(2005), 615-634.I https://doi.org/10.1016/j.insmatheco.2005.06.009
  6. N. Wang, Optimal investment for an insurer with exponential utility preference. Insur. Math. Econ. 40(2007), 77-84. https://doi.org/10.1016/j.insmatheco.2006.02.008
  7. Z. Wang, J. Xia and L. Zhang, Optimal investment for an insurer: The martingale approach. Insur. Math. Econ. 40(2007), 322-334. https://doi.org/10.1016/j.insmatheco.2006.05.003
  8. H. Markowitz, Portfolio selection. J. Finance 7(1952), 77-91. https://doi.org/10.2307/2975974
  9. R.C. Merton, An analytic derivation of the efficient frontier. J. Finance Quant. Anl. 7(1972), 1851-1872. https://doi.org/10.2307/2329621
  10. D. Li and W.L. Ng, Optimal dynamic portfolio selection: multiperiod mean-variance formulation. Math. Finance 10(2000), 387-406. https://doi.org/10.1111/1467-9965.00100
  11. D. Kramkov, W. Schachermayer, The asymptotic elasticity of utility functions and optimal investment in incomplete markets. Ann. Appl. Probab. 9(1999), 904-950. https://doi.org/10.1214/aoap/1029962818
  12. R. Cont and P. Tankov, Financial Modelling With Jump Processes. In: Chapman and Hall/CRC Financial Mathematics Series, 2003.
  13. X. Zhou and D. Li, Continuous-time mean-variance portfolio selection: a stochastic LQ framework. Appl. Math. Optim. 42(2000). 19-33. https://doi.org/10.1007/s002450010003
  14. X. Zhou and G. Yin, Markowitz mean-variance portfolio selection with regime switching: a continuous time model. SIAM J. Control Optim. 42, 1466-1482.
  15. I. Karatzas, J. P. Lehoczky, S.E. Shreve and G. L. Xu, Martingale and duality methods for utility maximization in incomplete markets. SIAM J. Control Optim. 29(1991), 702-730. https://doi.org/10.1137/0329039
  16. X. Li, X. Zhou and A.E.B. Lim, Dynamic mean-variance portfolio selection with noshorting constraints. SIAM J. Control Optim. 40(2002), 1540-1555. https://doi.org/10.1137/S0363012900378504
  17. Q. Zhou, Optimal investment for an insurer in the Levy market: The martingale approach. Statist. Probab. lett. 79(2009), 1602-1607. https://doi.org/10.1016/j.spl.2009.03.027