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OPTIMUM INSURANCE CONTRACTS WITH BACKGROUND RISK AND HIGHER-ORDER RISK ATTITUDES

Published online by Cambridge University Press:  25 April 2018

Yichun Chi  and
Wei Wei
Yichun Chi
Affiliation:
China Institute for Actuarial Science, Central University of Finance and Economics, Beijing 100081, China E-mail: [email protected]
Wei Wei*
Affiliation:
Department of Mathematical Sciences, University of Wisconsin-Milwaukee, Milwaukee, WI, 53211, USA
*
E-mail: [email protected]
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Abstract

In this paper, we study an optimal insurance problem in the presence of background risk from the perspective of an insured with higher-order risk attitudes. We introduce several useful dependence notions to model positive dependence structures between the insurable risk and background risk. Under these dependence structures, we compare insurance contracts of different forms in higher-order risk attitudes and establish the optimality of stop-loss insurance form. We also explicitly derive the optimal retention level. Finally, we carry out a comparative analysis and investigate how the change in the insured's initial wealth or background risk affects the optimal retention level.

Keywords

Background riskhigher-order risk attitudesstochastically increasingright tail increasingstop-loss insurance
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 48 , Issue 3 , September 2018 , pp. 1025 - 1047
Copyright
Copyright © Astin Bulletin 2018 

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