scholarly journals Pareto-Optimal Reinsurance Revisited: A Two-Stage Optimisation Procedure Approach

2020 ◽  
Vol 2020 ◽  
pp. 1-16
Author(s):  
Ying Fang ◽  
Lu Wang ◽  
Zhongfeng Qu ◽  
Wenguang Yu
Keyword(s):  
Value At Risk ◽  
Integral Form ◽  
Expected Value ◽  
Value Premium ◽  
Pareto Optimal ◽  
Two Stage ◽  
Optimal Reinsurance ◽  
Incentive Compatible ◽  
Ex Post ◽  
Optimisation Procedure

In this paper, based on the Tail-Value-at-Risk (TVaR) measure, we revisit the Pareto-optimal reinsurance policies for the insurer and the reinsurer via a two-stage optimisation procedure. To reduce ex-post moral hazard, we assume that reinsurance contracts satisfy the principle of indemnity and the incentive compatible constraint which have been advocated by Huberman et al. (1983). We show that the Pareto-optimal reinsurance policy exists if the reinsurance premiums can be expressed as an integral form. The proposed class of premium principles encompasses the net premium principle, expected value premium principle, TVaR premium principle, generalized percentile premium principle, and so on. We further use the TVaR premium principle and the expected value premium principle as examples to illustrate the two-stage optimisation procedure by deriving explicitly the Pareto-optimal reinsurance policies. We extend the results by Cai et al. (2017) when the expected value premium principle is replaced by the TVaR premium principle.

OPTIMAL REINSURANCE FROM THE PERSPECTIVES OF BOTH AN INSURER AND A REINSURER

2015 ◽  
Vol 46 (3) ◽  
pp. 815-849 ◽  
Author(s):  
Jun Cai ◽  
Christiane Lemieux ◽  
Fangda Liu
Keyword(s):  
Wide Class ◽  
Value At Risk ◽  
Risk Measures ◽  
Convex Combination ◽  
Expected Value ◽  
Point Of View ◽  
The Other ◽  
Optimal Reinsurance ◽  
Optimal Form ◽  
Conflicting Interests

AbstractOptimal reinsurance from an insurer's point of view or from a reinsurer's point of view has been studied extensively in the literature. However, as two parties of a reinsurance contract, an insurer and a reinsurer have conflicting interests. An optimal form of reinsurance from one party's point of view may be not acceptable to the other party. In this paper, we study optimal reinsurance designs from the perspectives of both an insurer and a reinsurer and take into account both an insurer's aims and a reinsurer's goals in reinsurance contract designs. We develop optimal reinsurance contracts that minimize the convex combination of the Value-at-Risk (VaR) risk measures of the insurer's loss and the reinsurer's loss under two types of constraints, respectively. The constraints describe the interests of both the insurer and the reinsurer. With the first type of constraints, the insurer and the reinsurer each have their limit on the VaR of their own loss. With the second type of constraints, the insurer has a limit on the VaR of his loss while the reinsurer has a target on his profit from selling a reinsurance contract. For both types of constraints, we derive the optimal reinsurance forms in a wide class of reinsurance policies and under the expected value reinsurance premium principle. These optimal reinsurance forms are more complicated than the optimal reinsurance contracts from the perspective of one party only. The proposed models can also be reduced to the problems of minimizing the VaR of one party's loss under the constraints on the interests of both the insurer and the reinsurer.

scholarly journals Equilibrium reinsurance-investment strategy with a common shock under two kinds of premium principles

2021 ◽  
Author(s):  
Junna Bi ◽  
Danping Li ◽  
Nan Zhang
Keyword(s):  
Investment Strategy ◽  
Expected Value ◽  
Value Premium ◽  
Equilibrium Strategy ◽  
Model Parameters ◽  
Optimal Reinsurance ◽  
Investment Problem ◽  
Common Shock ◽  
Game Theoretic ◽  
Hamilton Jacobi Bellman

This paper investigates the optimal mean-variance reinsurance-investment problem for an insurer with a common shock dependence under two kinds of popular premium principles: the variance premium principle and the expected value premium principle. We formulate the optimization problem within a game theoretic framework and derive the closed-form expressions of the equilibrium reinsurance-investment strategy and equilibrium value function under the two different premium principles by solving the extended Hamilton-Jacobi-Bellman system of equations. We find that under the variance premium principle, the proportional reinsurance is the optimal reinsurance strategy for the optimal reinsurance-investment problem with a common shock, while under the expected value premium principle, the excess-of-loss reinsurance is the optimal reinsurance strategy. In addition, we illustrate the equilibrium reinsurance-investment strategy by numerical examples and discuss the impacts of model parameters on the equilibrium strategy.

The Expected Value Premium

CFA Digest ◽  
2008 ◽  
Vol 38 (3) ◽  
pp. 35-36
Author(s):  
Michael Kobal
Keyword(s):  
Expected Value ◽  
Value Premium

Crime and Punishment

2017 ◽  
Author(s):  
Richard Adelstein
Keyword(s):  
Criminal Liability ◽  
Court Case ◽  
Efficient Allocation ◽  
Two Stage ◽  
Crime And Punishment ◽  
The Past ◽  
Ex Post ◽  
Ex Ante ◽  
Supreme Court Case

This chapter elaborates the operation of criminal liability by closely considering efficient crimes and the law’s stance toward them, shows how its commitment to proportional punishment prevents the probability scaling that systemically efficient allocation requires, and discusses the procedures that determine the actual liability prices imposed on offenders. Efficient crimes are effectively encouraged by proportional punishment, and their nature and implications are examined. But proportional punishment precludes probability scaling, and induces far more than the systemically efficient number of crimes. Liability prices that match the specific costs imposed by the offender at bar are sought through a two-stage procedure of legislative determination of punishment ranges ex ante and judicial determination of exact prices ex post, which creates a dilemma: whether to price crimes accurately in the past or deter them accurately in the future. An illustrative Supreme Court case bringing all these themes together is discussed in conclusion.

OPTIMAL REINSURANCE FROM THE VIEWPOINTS OF BOTH AN INSURER AND A REINSURER UNDER THE CVAR RISK MEASURE AND VAJDA CONDITION

2021 ◽  
pp. 1-29
Author(s):  
Yanhong Chen
Keyword(s):  
Loss Function ◽  
Value At Risk ◽  
Numerical Study ◽  
Risk Measure ◽  
Convex Combination ◽  
Weighting Factor ◽  
Loss Functions ◽  
Conditional Value At Risk ◽  
Optimal Reinsurance ◽  
The Impact

ABSTRACT In this paper, we study the optimal reinsurance contracts that minimize the convex combination of the Conditional Value-at-Risk (CVaR) of the insurer’s loss and the reinsurer’s loss over the class of ceded loss functions such that the retained loss function is increasing and the ceded loss function satisfies Vajda condition. Among a general class of reinsurance premium principles that satisfy the properties of risk loading and convex order preserving, the optimal solutions are obtained. Our results show that the optimal ceded loss functions are in the form of five interconnected segments for general reinsurance premium principles, and they can be further simplified to four interconnected segments if more properties are added to reinsurance premium principles. Finally, we derive optimal parameters for the expected value premium principle and give a numerical study to analyze the impact of the weighting factor on the optimal reinsurance.

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 Optimal reinsurance: a reinsurer’s perspective

2017 ◽  
Vol 12 (1) ◽  
pp. 147-184 ◽  
Author(s):  
Fei Huang ◽  
Honglin Yu
Keyword(s):  
At Risk ◽  
Closed Form ◽  
Value At Risk ◽  
Optimality Criteria ◽  
Total Loss ◽  
Optimal Reinsurance ◽  
Numerical Examples ◽  
Dependency Structure ◽  
Closed Form Solutions

AbstractIn this paper, the optimal safety loading that the reinsurer should set in the reinsurance pricing is studied, which is novel in the literature. It is first assumed that the insurer will choose the form of the reinsurance contract by following the results derived in Cai et al. Different optimality criteria from the reinsurer’s perspective are then studied, such as maximising the expectation of the profit, maximising the utility of the profit and minimising the value-at-risk of the reinsurer’s total loss. By applying the concept of comonotonicity, the problem in which the reinsurer is facing two risks with unknown dependency structure is also solved. Closed-form solutions are obtained when the underlying losses are zero-modified exponentially distributed. Finally, numerical examples are provided to illustrate the results derived.

Optimal Reciprocal Reinsurance under VaR or TVaR Constraint

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Hung-Hsi Huang ◽  
Ching-Ping Wang
Keyword(s):  
At Risk ◽  
Risk Management ◽  
Moral Hazard ◽  
Value At Risk ◽  
Incentive Compatibility ◽  
Regular Form ◽  
Optimal Reinsurance ◽  
The Common ◽  
Risk Constraint ◽  
Management Requirement

Abstract Most existing researches on optimal reinsurance contract are based on an insurer’s viewpoint. However, the optimal reinsurance contract for an insurer is not necessarily to be optimal for a reinsurer. Hence, this study aims to develop the optimal reciprocal reinsurance which satisfies the benefits of both the insurer and reinsurer. Additionally, due to legislative restriction or risk management requirement, the wealth of insurer and reinsurer are frequently imposed upon a VaR (Value-at-Risk) or TVaR (Tail Value-at-Risk) constraint. Therefore, this study develops an optimal reciprocal reinsurance contract which maximizes the common benefits (evaluated by weighted addition of expected utilities) of the insurer and reinsurer subject to their VaR or TVaR constraints. Furthermore, for avoiding moral hazard problem, the developed contract is additionally restricted to a regular form or incentive compatibility (both indemnity schedule and retained loss schedule are continuously nondecreasing).

Sign in / Sign up

Export Citation Format

Share Document