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An optimal investment strategy with maximal risk aversion and its ruin probability in the presence of stochastic volatility on investments

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  • Badaoui, Mohamed
  • Fernández, Begoña

Abstract

In this paper, we study an optimal investment problem of an insurance company with a Cramér–Lundberg risk process and investments portfolio consisting of a risky asset with stochastic volatility and a money market. The asset prices are affected by a correlated economic factor, modeled as diffusion process. We prove a verification theorem, in order to show that any solution to the Hamilton–Jacobi–Bellman equation solves the optimization problem. When the insurer preferences are exponential, we prove the existence of a smooth solution, and we give an explicit form of the optimal strategy, also numerical results are presented in the case of the Scott model. Finally we use the optimal strategy to get an estimate of the ruin probability in finite horizon.

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  • Badaoui, Mohamed & Fernández, Begoña, 2013. "An optimal investment strategy with maximal risk aversion and its ruin probability in the presence of stochastic volatility on investments," Insurance: Mathematics and Economics, Elsevier, vol. 53(1), pages 1-13.
    • Handle: RePEc:eee:insuma:v:53:y:2013:i:1:p:1-13
    DOI: 10.1016/j.insmatheco.2013.04.002
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    References listed on IDEAS

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    1. Browne, S., 1995. "Optimal Investment Policies for a Firm with a Random Risk Process: Exponential Utility and Minimizing the Probability of Ruin," Papers 95-08, Columbia - Graduate School of Business.
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    Cited by:

    1. Hiroaki Hata & Shuenn-Jyi Sheu & Li-Hsien Sun, 2019. "Expected exponential utility maximization of insurers with a general diffusion factor model : The complete market case," Papers 1903.08957, arXiv.org.
    2. Mohamed Badaoui & Begoña Fernández & Anatoliy Swishchuk, 2018. "An Optimal Investment Strategy for Insurers in Incomplete Markets," Risks, MDPI, vol. 6(2), pages 1-23, April.
    3. Koch-Medina, Pablo & Moreno-Bromberg, Santiago & Ravanelli, Claudia & Šikić, Mario, 2021. "Revisiting optimal investment strategies of value-maximizing insurance firms," Insurance: Mathematics and Economics, Elsevier, vol. 99(C), pages 131-151.
    4. Xu, Lin & Zhang, Liming & Yao, Dingjun, 2017. "Optimal investment and reinsurance for an insurer under Markov-modulated financial market," Insurance: Mathematics and Economics, Elsevier, vol. 74(C), pages 7-19.
    5. Guan, Guohui & Liang, Zongxia & Feng, Jian, 2018. "Time-consistent proportional reinsurance and investment strategies under ambiguous environment," Insurance: Mathematics and Economics, Elsevier, vol. 83(C), pages 122-133.
    6. Flores, Eduardo & de Carvalho, João Vinicius França & Sampaio, Joelson Oliveira, 2021. "Impact of interest rates on the life insurance market development: Cross-country evidence," Research in International Business and Finance, Elsevier, vol. 58(C).
    7. Guan, Guohui & Liang, Zongxia, 2014. "Optimal reinsurance and investment strategies for insurer under interest rate and inflation risks," Insurance: Mathematics and Economics, Elsevier, vol. 55(C), pages 105-115.
    8. Nian Yao & Zhiming Yang, 2017. "Optimal excess-of-loss reinsurance and investment problem for an insurer with default risk under a stochastic volatility model," Papers 1704.08234, arXiv.org.

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