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.

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.

Monopoly Regulation Under Relaxed Pareto Efficiency

2017 ◽  
Vol 5 (2) ◽  
pp. 162-176
Author(s):  
Ismail Saglam
Keyword(s):  
Marginal Cost ◽  
Regulatory Environment ◽  
Pareto Dominance ◽  
Incentive Compatible ◽  
Monopoly Regulation ◽  
Dominance Relationships ◽  
Ex Post ◽  
Ex Ante ◽  
Pareto Axiom ◽  
Set Of Points

Baron and Myerson (BM; 1982, Econometrica, 50(4), 911–930) propose an incentive-compatible, individually rational and ex ante socially optimal direct-revelation mechanism to regulate a monopolistic firm with unknown costs. Their mechanism is not ex post Pareto dominated by any other feasible direct-revelation mechanism. However, there also exist an uncountable number of feasible direct-revelation mechanisms that are not ex post Pareto dominated by the BM mechanism. To investigate whether the BM mechanism remains in the set of ex post undominated mechanisms when the Pareto axiom is slightly weakened, we introduce the ∈-Pareto dominance. This concept requires the relevant dominance relationships to hold in the support of the regulator’s beliefs everywhere except for a set of points of measure ∈, which can be arbitrarily small. We show that a modification of the BM mechanism which always equates the price to the marginal cost can ∈-Pareto dominate the BM mechanism at uncountably many regulatory environments, while it is never ∈-Pareto dominated by the BM mechanism at any regulatory environment.

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

scholarly journals Dynamic Pricing of General Insurance in a Competitive Market

2007 ◽  
Vol 37 (1) ◽  
pp. 1-34 ◽  
Author(s):  
Paul Emms
Keyword(s):  
Dynamic Pricing ◽  
Insurance Premium ◽  
Objective Functions ◽  
Insurance Pricing ◽  
Terminal Wealth ◽  
Optimal Insurance ◽  
General Insurance ◽  
Discounted Utility ◽  
Strategy Changes ◽  
Wealth Generation

A model for general insurance pricing is developed which represents a stochastic generalisation of the discrete model proposed by Taylor (1986). This model determines the insurance premium based both on the breakeven premium and the competing premiums offered by the rest of the insurance market. The optimal premium is determined using stochastic optimal control theory for two objective functions in order to examine how the optimal premium strategy changes with the insurer’s objective. Each of these problems can be formulated in terms of a multi-dimensional Bellman equation.In the first problem the optimal insurance premium is calculated when the insurer maximises its expected terminal wealth. In the second, the premium is found if the insurer maximises the expected total discounted utility of wealth where the utility function is nonlinear in the wealth. The solution to both these problems is built-up from simpler optimisation problems. For the terminal wealth problem with constant loss-ratio the optimal premium strategy can be found analytically. For the total wealth problem the optimal relative premium is found to increase with the insurer’s risk aversion which leads to reduced market exposure and lower overall wealth generation.

scholarly journals A Generalised CIR Process with Externally-Exciting and Self-Exciting Jumps and Its Applications in Insurance and Finance

Risks ◽  
2019 ◽  
Vol 7 (4) ◽  
pp. 103 ◽  
Author(s):  
Angelos Dassios ◽  
Jiwook Jang ◽  
Hongbiao Zhao
Keyword(s):  
Diffusion Process ◽  
Jump Diffusion ◽  
Insurance Premium ◽  
General Process ◽  
Numerical Examples ◽  
Second Moments ◽  
Distributional Properties ◽  
The Laplace Transform ◽  
Cir Process ◽  
Mean Variance

In this paper, we study a generalised CIR process with externally-exciting and self-exciting jumps, and focus on the distributional properties and applications of this process and its aggregated process. The aim of the paper is to introduce a more general process that includes many models in the literature with self-exciting and external-exciting jumps. The first and second moments of this jump-diffusion process are used to calculate the insurance premium based on mean-variance principle. The Laplace transform of aggregated process is derived, and this leads to an application for pricing default-free bonds which could capture the impacts of both exogenous and endogenous shocks. Illustrative numerical examples and comparisons with other models are also provided.

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