Optimal insurance with background risk: An analysis of general dependence structures

Yichun Chi and Wei Wei ()
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Wei Wei: University of Wisconsin-Milwaukee

Finance and Stochastics, 2020, vol. 24, issue 4, No 3, 903-937

Abstract: Abstract In this paper, we consider an optimal insurance problem from the perspective of a risk-averse individual who faces an insurable risk as well as some background risk and wants to maximise the expected utility of his/her final wealth. To reduce ex post moral hazard, we follow Huberman et al. (Bell J. Econ. 14:415–426 1983) to assume that alternative insurance contracts satisfy the principle of indemnity and the no-sabotage condition. When the insurance premium is calculated by the expected value premium principle, a necessary and sufficient condition for the optimality of an insurance contract is established under a general dependence structure between insurable and background risks. By virtue of this condition, some qualitative properties of optimal contracts are developed, a scheme is provided to improve any suboptimal insurance strategy, and optimal insurance forms are derived explicitly for some dependence structures of interest. These forms are not always piecewise linear.

Keywords: Background risk; General dependence structures; Mossin’s theorem; No-sabotage condition; Optimal insurance design; 91B30; 91G99 (search for similar items in EconPapers)
JEL-codes: C61 D81 G22 (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (14)

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DOI: 10.1007/s00780-020-00429-0

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