Optimal proportional reinsurance and investment problem for insurers with loss aversion

SUN Qingya, RONG Ximin, ZHAO Hui

Systems Engineering - Theory & Practice ›› 2020, Vol. 40 ›› Issue (2) : 284-297.

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Systems Engineering - Theory & Practice ›› 2020, Vol. 40 ›› Issue (2) : 284-297. DOI: 10.12011/1000-6788-2018-1484-14

Optimal proportional reinsurance and investment problem for insurers with loss aversion

  • SUN Qingya, RONG Ximin, ZHAO Hui
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Abstract

This paper introduces the concept of loss aversion in behavioral finance, and studies an optimal reinsurance and investment problem for a loss-averse insurer. Most investors are risk-averse towards gains, but they will change to be risk-seeking when they suffer from losses, so we assume that the insurer's goal is to chose the optimal strategy to maximize the expected S-shaped utility from the terminal wealth. The surplus process of the insurer is assumed to follow a classical Cramér-Lundberg model and the insurer is allowed to purchase proportional reinsurance. Moreover, the insurer can invest in a risk-free asset and a risky asset. By martingale approach and lagrange dual theory, we derive the optimal strategy. Finally, numerical examples are provided to illustrate the effects of model parameters on the optimal terminal wealth and the optimal strategy.

Key words

loss aversion / proportional reinsurance / martingale approach / S-shaped utility / optimal strategy

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SUN Qingya , RONG Ximin , ZHAO Hui. Optimal proportional reinsurance and investment problem for insurers with loss aversion. Systems Engineering - Theory & Practice, 2020, 40(2): 284-297 https://doi.org/10.12011/1000-6788-2018-1484-14

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Funding

National Natural Science Foundation of China (11871052, 71102118)
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