Optimal Insurance with Nonseparable Background Risk

2001 ◽  
Vol 68 (3) ◽  
pp. 437 ◽  
Author(s):  
James Vercammen
Keyword(s):  
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.

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.

OPTIMAL INCENTIVE-COMPATIBLE INSURANCE WITH BACKGROUND RISK

2021 ◽  
pp. 1-28
Author(s):  
Yichun Chi ◽  
Ken Seng Tan
Keyword(s):  
Critical Role ◽  
Insurance Premium ◽  
Background Risk ◽  
Risk Transfer ◽  
Optimal Insurance ◽  
Insurance Contracts ◽  
Incentive Compatible ◽  
Ex Post ◽  
Compatible Condition ◽  
Mean Variance

ABSTRACT In this paper, the optimal insurance design is studied from the perspective of an insured, who faces an insurable risk and a background risk. For the reduction of ex post moral hazard, alternative insurance contracts are asked to satisfy the principle of indemnity and the incentive-compatible condition. As in the literature, it is assumed that the insurer calculates the insurance premium solely on the basis of the expected indemnity. When the insured has a general mean-variance preference, an explicit form of optimal insurance is derived explicitly. It is found that the stochastic dependence between the background risk and the insurable risk plays a critical role in the insured’s risk transfer decision. In addition, the optimal insurance policy can often change significantly once the incentive-compatible constraint is removed.

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