Optimal Insurance with Background Risk and Incentive Compatibility

2015 ◽  
Author(s):  
Yichun Chi
Keyword(s):  
Incentive Compatibility ◽  
Background Risk ◽  
Optimal Insurance

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

2018 ◽  
Vol 48 (3) ◽  
pp. 1025-1047 ◽  
Author(s):  
Yichun Chi ◽  
Wei Wei
Keyword(s):  
Higher Order ◽  
Background Risk ◽  
Risk Attitudes ◽  
Positive Dependence ◽  
Optimal Insurance ◽  
Insurance Contracts ◽  
Retention Level ◽  
Initial Wealth ◽  
Stop Loss ◽  
Dependence Structures

AbstractIn 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.

MEAN–VARIANCE INSURANCE DESIGN WITH COUNTERPARTY RISK AND INCENTIVE COMPATIBILITY

2021 ◽  
pp. 1-23
Author(s):  
Tim J. Boonen ◽  
Wenjun Jiang
Keyword(s):  
Compatibility Condition ◽  
Default Risk ◽  
Incentive Compatibility ◽  
Limited Liability ◽  
Counterparty Risk ◽  
Optimal Insurance ◽  
Ex Post ◽  
Function Formulation ◽  
The Mean ◽  
Mean Variance

Abstract This paper studies the optimal insurance design from the perspective of an insured when there is possibility for the insurer to default on its promised indemnity. Default of the insurer leads to limited liability, and the promised indemnity is only partially recovered in case of a default. To alleviate the potential ex post moral hazard, an incentive compatibility condition is added to restrict the permissible indemnity function. Assuming that the premium is determined as a function of the expected coverage and under the mean–variance preference of the insured, we derive the explicit structure of the optimal indemnity function through the marginal indemnity function formulation of the problem. It is shown that the optimal indemnity function depends on the first and second order expectations of the random recovery rate conditioned on the realized insurable loss. The methodology and results in this article complement the literature regarding the optimal insurance subject to the default risk and provide new insights on problems of similar types.

Optimal insurance design under background risk with dependence

2018 ◽  
Vol 80 ◽  
pp. 15-28 ◽  
Author(s):  
Zhiyi Lu ◽  
Shengwang Meng ◽  
Leping Liu ◽  
Ziqi Han
Keyword(s):  
Background Risk ◽  
Optimal Insurance

scholarly journals The Solution of the Optimal Insurance Problem with Background Risk

2019 ◽  
Vol 2019 ◽  
pp. 1-5 ◽  
Author(s):  
Yulian Fan
Keyword(s):  
Explicit Form ◽  
Existence And Uniqueness ◽  
Optimal Solution ◽  
Background Risk ◽  
Optimal Insurance ◽  
Uniqueness Of The Solution

This paper proves the existence and uniqueness of the solution of the optimal insurance problem with background risk and presents the explicit form of the optimal solution.

scholarly journals Optimal insurance under rank-dependent utility and incentive compatibility

2018 ◽  
Vol 29 (2) ◽  
pp. 659-692 ◽  
Author(s):  
Zuo Quan Xu ◽  
Xun Yu Zhou ◽  
Sheng Chao Zhuang
Keyword(s):  
Incentive Compatibility ◽  
Optimal Insurance ◽  
Rank Dependent Utility
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