Prevention efforts, insurance demand and price incentives under coherent risk measures

Sarah Bensalem (), Nicolás Hernández Santibáñez and Nabil Kazi-Tani ()
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Sarah Bensalem: LSAF - Laboratoire de Sciences Actuarielle et Financière - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon
Nabil Kazi-Tani: LSAF - Laboratoire de Sciences Actuarielle et Financière - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon

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Abstract: This paper studies an equilibrium model between an insurance buyer and an insurance seller, where both parties' risk preferences are given by convex risk measures. The interaction is modeled through a Stackelberg type game, where the insurance seller plays first by offering prices, in the form of safety loadings. Then the insurance buyer chooses his optimal proportional insurance share and his optimal prevention effort in order to minimize his risk measure. The loss distribution is given by a family of stochastically ordered probability measures, indexed by the prevention effort. We give special attention to the problems of self-insurance and self-protection. We prove that the formulated game admits a unique equilibrium, that we can explicitly solve by further specifying the agents criteria and the loss distribution. In self-insurance, we consider also an adverse selection setting, where the type of the insurance buyers is given by his loss probability, and study the screening and shutdown contracts. Finally, we provide case studies in which we explicitly apply our theoretical results.

Keywords: Prevention; Self-insurance; Self-protection; Coherent risk measures; Stackelberg game (search for similar items in EconPapers)
Date: 2020-07
Note: View the original document on HAL open archive server: https://hal.science/hal-01983433v1
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Published in Insurance: Mathematics and Economics, 2020, 93, pp.369-386. ⟨10.1016/j.insmatheco.2020.05.006⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-01983433

DOI: 10.1016/j.insmatheco.2020.05.006

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