Equilibrium Loss Reporting for a Risk-Averse Insured of Deductible Insurance

24 Pages Posted: 23 Aug 2023

See all articles by Jingyi Cao

Jingyi Cao

York University

Dongchen Li

York University

V.R. Young

University of Michigan at Ann Arbor - Department of Mathematics

Bin Zou

University of Connecticut - Department of Mathematics

Abstract

We consider a risk-averse insured who purchases a deductible insurance contract and follows a barrier strategy to decide whether she should report a loss. The insurer adopts a bonus-malus system with two rate classes, and the insured will move to or stay in the more expensive class if she reports a loss. When the deductibles are exogenously given, we establish a sufficient and necessary condition under which the insured will underreport losses, and obtain her equilibrium barrier strategy in semi-closed form. Next, we allow the insured to choose the deductibles of her insurance contract and numerically show that the equilibrium deductibles are strictly positive, suggesting that full insurance, often assumed in related literature, is not optimal. Our study justifies the prevalent phenomenon of underreporting losses across non-life insurance sectors.

Keywords: moral hazard, underreporting losses, deductible insurance, bonus-malus system, Nash equilibrium

Suggested Citation

Cao, Jingyi and Li, Dongchen and Young, Virginia R. and Zou, Bin, Equilibrium Loss Reporting for a Risk-Averse Insured of Deductible Insurance. Available at SSRN: https://ssrn.com/abstract=4549720 or http://dx.doi.org/10.2139/ssrn.4549720

Jingyi Cao

York University ( email )

4700 Keele Street
Toronto, M3J 1P3
Canada

Dongchen Li

York University ( email )

4700 Keele Street
Toronto, M3J 1P3
Canada

Virginia R. Young (Contact Author)

University of Michigan at Ann Arbor - Department of Mathematics ( email )

2074 East Hall
530 Church Street
Ann Arbor, MI 48109-1043
United States
734-764-7227 (Phone)

Bin Zou

University of Connecticut - Department of Mathematics ( email )

341 Mansfield Road U1009
Department of Mathematics
Storrs, CT 06269-1069
United States

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