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ON THE OPTIMALITY OF A STRAIGHT DEDUCTIBLE UNDER BELIEF HETEROGENEITY

Published online by Cambridge University Press:  22 November 2018

Yichun Chi
Yichun Chi*
Affiliation:
China Institute for Actuarial Science, Central University of Finance and Economics, Beijing 100081, China E-Mail: yichun@cufe.edu.cn
*
E-Mail: yichun@cufe.edu.cn
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Abstract

This article attempts to extend Arrow’s theorem of the deductible to the case of belief heterogeneity, which allows the insured and the insurer to have different beliefs about the distribution of the underlying loss. Like Huberman et al. [(1983) Bell Journal of Economics14(2), 415–426], we preclude ex post moral hazard by asking both parties in the insurance contract to pay more for a larger realization of the loss. It is shown that, ceteris paribus, full insurance above a constant deductible is always optimal for any chosen utility function of a risk-averse insured if and only if the insurer appears more optimistic about the conditional loss given non-zero loss than the insured in the sense of monotone hazard rate order. We derive the optimal deductible level explicitly and then examine how it is affected by the changes of the insured’s risk aversion, the insurance price and the degree of belief heterogeneity.

Keywords

Arrow’s theorem of the deductibledeductible insuranceex post moral hazardheterogeneous beliefsmonotone hazard rate order
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 49 , Issue 1 , January 2019 , pp. 243 - 262
Copyright
Copyright © Astin Bulletin 2018 

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