Optimal consumption, investment and insurance with insurable risk for an investor in a Lévy market
Numerous researchers have applied the martingale approach for models driven by Lévy processes to study optimal investment problems. The aim of this paper is to apply the martingale approach to obtain a closed form solution for the optimal investment, consumption and insurance strategies of an individual in the presence of an insurable risk when the insurable risk and risky asset returns are described by Lévy processes and the utility is a constant absolute risk aversion (CARA). The model developed in this paper can potentially be applied to absorb large insurable losses in the absence of insurance protection and to examine the level of diminishing current utility and consumption.
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- Wang, Zengwu & Xia, Jianming & Zhang, Lihong, 2007. "Optimal investment for an insurer: The martingale approach," Insurance: Mathematics and Economics, Elsevier, vol. 40(2), pages 322-334, March.
- Cox, John C. & Huang, Chi-fu, 1989. "Optimal consumption and portfolio policies when asset prices follow a diffusion process," Journal of Economic Theory, Elsevier, vol. 49(1), pages 33-83, October.
- Zhou, Qing, 2009. "Optimal investment for an insurer in the Lévy market: The martingale approach," Statistics & Probability Letters, Elsevier, vol. 79(14), pages 1602-1607, July.
- Moore, Kristen S. & Young, Virginia R., 2006. "Optimal insurance in a continuous-time model," Insurance: Mathematics and Economics, Elsevier, vol. 39(1), pages 47-68, August.
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