TY - JOUR
T1 - Optimal insurance with background risk
T2 - An analysis of general dependence structures
AU - Chi, Yichun
AU - Wei, Wei
N1 - Funding Information:
Chi’s work was supported by grants from National Natural Science Foundation of China (No. 11971505), the MOE (China) Project of the Key Research Institute of Humanities and Social Sciences at Universities (No. 16JJD790061) and the 111 Project of China (No. B17050). Wei acknowledges the financial support from the Research and Creative Activities Support (AAC2253) of the University of Wisconsin-Milwaukee.
Publisher Copyright:
© 2020, Springer-Verlag GmbH Germany, part of Springer Nature.
PY - 2020/10/1
Y1 - 2020/10/1
N2 - 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.
AB - 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.
KW - Background risk
KW - General dependence structures
KW - Mossin’s theorem
KW - No-sabotage condition
KW - Optimal insurance design
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U2 - 10.1007/s00780-020-00429-0
DO - 10.1007/s00780-020-00429-0
M3 - Article
AN - SCOPUS:85087900645
SN - 0949-2984
VL - 24
SP - 903
EP - 937
JO - Finance and Stochastics
JF - Finance and Stochastics
IS - 4
ER -