Optimal Insurance Design Under Rank‐dependent Expected Utility

Bernard, Carole; He, Xue Dong; Yan, Jiajie; Zhou, Xun Yu

doi:10.1111/mafi.12027

Cited by 116 publications

(114 citation statements)

References 55 publications

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“…As described in Yaari [6] and Bernard et al [7], this framework fails to explain various phenomena that are observed in practice, for instance, that financial agents prefer to purchase extended insurance cover for relatively small claims over buying protection against disastrous large claims. Bernard et al [7] modify the original framework by introducing a probability distortion which tries to describe human behavior more appropriately.…”

Section: Introductionmentioning

confidence: 99%

Demand of Insurance under the Cost-of-Capital Premium Calculation Principle

Merz

Wüthrich

2014

Risks

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Abstract:We study the optimal insurance design problem. This is a risk sharing problem between an insured and an insurer. The main novelty in this paper is that we study this optimization problem under a risk-adjusted premium calculation principle for the insurance cover. This risk-adjusted premium calculation principle uses the cost-of-capital approach as it is suggested (and used) by the regulator and the insurance industry.

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Section: Introductionmentioning

confidence: 99%

Demand of Insurance under the Cost-of-Capital Premium Calculation Principle

Merz

Wüthrich

2014

Risks

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“…6 All necessary background material about capacities and Choquet integration is given in Appendix A. 7 Since the Choquet integral is only positively homogeneous (Proposition A.6 (3)), the premium constraint cannot be written as R ě ş Y dν.…”

Section: Insurance Demand With Insurer Ambiguitymentioning

confidence: 99%

“…Young [46] and Bernard et al [6] examine the case where the insured is a Rank-Dependent Expected-Utility maximizer [37,45]. Doherty and Eeckhoudt [15] study the optimal level of deductible under Yaari's Dual Theory [45].…”

Section: Introductionmentioning

confidence: 99%

Ambiguity on the insurer’s side: The demand for insurance

Amarante

Ghossoub

Phelps

2015

Journal of Mathematical Economics

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Abstract. Empirical evidence suggests that ambiguity is prevalent in insurance pricing and underwriting, and that often insurers tend to exhibit more ambiguity than the insured individuals (e.g., [23]). Motivated by these findings, we consider a problem of demand for insurance indemnity schedules, where the insurer has ambiguous beliefs about the realizations of the insurable loss, whereas the insured is an expected-utility maximizer. We show that if the ambiguous beliefs of the insurer satisfy a property of compatibility with the non-ambiguous beliefs of the insured, then there exist optimal monotonic indemnity schedules. By virtue of monotonicity, no ex-post moral hazard issues arise at our solutions (e.g., [25]). In addition, in the case where the insurer is either ambiguity-seeking or ambiguity-averse, we show that the problem of determining the optimal indemnity schedule reduces to that of solving an auxiliary problem that is simpler than the original one in that it does not involve ambiguity. Finally, under additional assumptions, we give an explicit characterization of the optimal indemnity schedule for the insured, and we show how our results naturally extend the classical result of Arrow [5] on the optimality of the deductible indemnity schedule.

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“…12 A number of papers have studied portfolio theory, risk-sharing and insurance contracting in the RDEU framework; see Bernard, He, Yan, and Zhou (2013) for a detailed review.…”

Section: Choquet Expected Utility Theorymentioning

confidence: 99%

Diversification preferences in the theory of choice

Giorgi

Mahmoud

2016

Decisions Econ Finan

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Diversification represents the idea of choosing variety over uniformity. Within the theory of choice, desirability of diversification is axiomatized as preference for a convex combination of choices that are equivalently ranked. This corresponds to the notion of risk aversion when one assumes the von-Neumann-Morgenstern expected utility model, but the equivalence fails to hold in other models. This paper analyzes axiomatizations of the concept of diversification and their relationship to the related notions of risk aversion and convex preferences within different choice theoretic models. Implications of these notions on portfolio choice are discussed. We cover model-independent diversification preferences, preferences within models of choice under risk, including expected utility theory and the more general rank-dependent expected utility theory, as well as models of choice under uncertainty axiomatized via Choquet expected utility theory. Remarks on interpretations of diversification preferences within models of behavioral choice are given in the conclusion.

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Optimal Insurance Design Under Rank‐dependent Expected Utility

Cited by 116 publications

References 55 publications

Demand of Insurance under the Cost-of-Capital Premium Calculation Principle

Demand of Insurance under the Cost-of-Capital Premium Calculation Principle

Ambiguity on the insurer’s side: The demand for insurance

Diversification preferences in the theory of choice

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