Insurance with multiple insurers: A game-theoretic approach

Abstract

This paper studies the set of Pareto optimal insurance contracts and the core of an insurance game. Our setting allows multiple insurers with translation invariant preferences. We characterise the Pareto optimal contracts, which determines the shape of the indemnities. Closed-form and numerical solutions are found for various preferences that the insurance players might have. Determining associated premiums with any given optimal Pareto contract is another problem for which economic-based arguments are further discussed. We also explain how one may link the recent fast growing literature on risk-based optimality criteria to the Pareto optimality criterion and we show that the latter is much more general than the former one, which according to our knowledge, has not been pointed out by now. Further, we extend some of our results when model risk is included, i.e. there is some uncertainty with the risk model and/or the insurance players make decisions based on divergent beliefs about the underlying risk. These robust optimal contracts are investigated and we show how one may find robust and Pareto efficient contracts, which is a key decision-making problem under uncertainty.

Resilience and learning from insurance firms: Dataset on British long-term insurance market performance

“…Previous studies that used industry data for insurance and risk management analysis can be found in Refs. [1] , [2] , [3] , [4] , [5] , [6] , [7] , [8] , [9] , [10] , [11] , [12] , [13] , [14] , [15] . Details on other researched works on the subject and relevant literature can be found in Refs.…”

“…Details on other researched works on the subject and relevant literature can be found in Refs. [1] , [2] , [3] , [4] , [5] , [6] , [7] , [8] , [9] , [10] , [11] , [12] , [13] , [14] , [15] , [16] , [17] , [18] , [19] , [20] , [21] , [22] . There are several lessons other businesses can learn from insurance sector dataset especially in terms of business continuity, business resilience, strategic innovation, and sustainable survival during the global financial crisis.…”

Risky business: Data on trading results for UK general insurance firms during and after the global financial crisis

“…Likewise, the data analysis can allow for measurement of insurance firms competitiveness and detect systemic risk which may disrupt the financial industry. Research questions can be posed as in previous studies [1] , [2] , [3] , [4] , [5] , [6] , [7] , [8] , [9] , [10] , [11] , [12] , [13] , [14] , [15] , [16] , [17] , [18] , [19] , [20] , which in turn can lead to inferential statistics, which when interpreted can inform the development of policies and strategic actions for the competitiveness and innovation of insurance industry. The uniqueness of this data is its focus on insurance business as risky which is an area where Solvency II concentrates on as a risk-based approach to prevent the failure of insurance firms.…”

Weighted Comonotonic Risk Sharing Under Heterogeneous Beliefs

“…If we remove the assumption of comonotonicity, it will be challenging to find an explicit optimal allocation even with value at risk (VaR) and for identical weights under heterogeneous beliefs; see Embrechts et al (2018b). See Boonen et al (2018), Asimit andZhuang et al (2016) for more discussions on the use of comonotonic allocations in risk-sharing games and insurance. Under the assumption of comonotonicity, we are able to find optimal allocations for risk sharing with general distortion risk measures and characterize the set of Pareto-optimal allocations.…”