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 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.

Higher-Order Risk Attitudes

2013 ◽  
pp. 41-57 ◽  
Author(s):  
Louis Eeckhoudt ◽  
Harris Schlesinger
Keyword(s):  
Higher Order ◽  
Risk Attitudes

scholarly journals Pareto-Optimal Insurance Contracts With Premium Budget and Minimum Charge Constraints

2019 ◽  
Author(s):  
Alexandru Vali Asimit ◽  
Ka Chun Cheung ◽  
Wing Fung Chong ◽  
Junlei Hu
Keyword(s):  
Pareto Optimal ◽  
Optimal Insurance ◽  
Insurance Contracts

On higher-order properties of compound geometric distributions

2002 ◽  
Vol 39 (02) ◽  
pp. 324-340 ◽  
Author(s):  
Gordon E. Willmot
Keyword(s):  
Equilibrium Distribution ◽  
Risk Model ◽  
Higher Order ◽  
Residual Lifetime ◽  
Classical Risk Model ◽  
Time Of Ruin ◽  
The Laplace Transform ◽  
The Time Of Ruin ◽  
Stop Loss ◽  
The Classical Risk Model

An explicit convolution representation for the equilibrium residual lifetime distribution of compound zero-modified geometric distributions is derived. Second-order reliability properties are seen to be essentially preserved under geometric compounding, and complement results of Brown (1990) and Cai and Kalashnikov (2000). The convolution representation is then extended to thenth-order equilibrium distribution. This higher-order convolution representation is used to evaluate the stop-loss premium and higher stop-loss moments of the compound zero-modified geometric distribution, as well as the Laplace transform of thekth moment of the time of ruin in the classical risk model.

scholarly journals OPTIMAL ASSET ALLOCATION IN LIFE INSURANCE: THE IMPACT OF REGULATION

2016 ◽  
Vol 46 (3) ◽  
pp. 605-626 ◽  
Author(s):  
An Chen ◽  
Peter Hieber
Keyword(s):  
Life Insurance ◽  
Asset Allocation ◽  
Regulatory Policy ◽  
Capital Requirements ◽  
Insurance Company ◽  
Traffic Light ◽  
Optimal Insurance ◽  
Insurance Contracts ◽  
Solvency Capital ◽  
The Impact

AbstractIn a typical equity-linked life insurance contract, the insurance company is entitled to a share of return surpluses as compensation for the return guarantee granted to the policyholders. The set of possible contract terms might, however, be restricted by a regulatory default constraint — a fact that can force the two parties to initiate sub-optimal insurance contracts. We show that this effect can be mitigated if regulatory policy is more flexible. We suggest that the regulator implement a traffic light system where companies are forced to reduce the riskiness of their asset allocation in distress. In a utility-based framework, we show that the introduction of such a system can increase the benefits of the policyholder without deteriorating the benefits of the insurance company. At the same time, default probabilities (and thus solvency capital requirements) can be reduced.

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