Mean-Variance Optimal Reinsurance Arrangements

Reinsurance reduces the risk but it also reduces the potential profit. The aim of the paper is to derive optimal, from the cedent's point of view, reinsurance arrangements balancing the risk measured by variance and expected profits under various mean-variance premium principles of the reinsurer. We find that quota share, excess of loss or combinations of excess of loss with quota share are the optimal rules according to a fixed expected gain of the cedent     

The Design of Optimal Insurance Contracts: A Topological Approach

This article deals with the optimal design of insurance contracts when the insurer faces administrative costs. If the literature provides many analyses of risk sharing with such costs, it is often assumed that these costs are linear. Furthermore, mathematical tools or initial conditions differ from one paper to another. We propose here a unified framework in which the problem is presented and solved as an infinite dimensional optimization program on a functional vector space equipped with an original norm. This general approach leads to the optimality of contracts lying on the frontier of the indemnity functions set. This frontier includes, in particular, contracts with a deductible, with total insurance and the null vector. Hence, we unify the existing results and point out some extensions.     

保险公司最优投资及再保险策略

在最大化生存概率和最大化终止时蒯期望效用准则下,通过求解相应的HJB方程,获得了最优投资策略以及最优比例再保险策略的闭式解.这一研究结果易于实时操作,对投资者的决策有直接的指导意义.     

Pricing Double-Trigger Reinsurance Contracts: Financial Versus Actuarial Approach

This article discusses various approaches to pricing double‐trigger reinsurance contracts—a new type of contract that has emerged in the area of ‘‘alternative risk transfer.’’ The potential coverage from this type of contract depends on both underwriting and financial risk. We determine the reinsurer's reservation price if it wants to retain the firm's same safety level after signing the contract, in which case the contract typically must be backed by large amounts of equity capital (if equity capital is the risk management measure to be taken). We contrast the financial insurance pricing models with an actuarial pricing model that has as its objective no lessening of the reinsurance company's expected profits and no worsening of its safety level. We show that actuarial pricing can lead the reinsurer into a trap that results in the failure to close reinsurance contracts that would have a positive net present value because typical actuarial pricing dictates the type of risk management measure that must be taken, namely, the insertion of additional capital. Additionally, this type of pricing structure forces the reinsurance buyer to provide this safety capital as a debtholder. Finally, we discuss conditions leading to a market for double‐trigger reinsurance contracts.     

Optimal Reinsurance Arrangements Under Tail Risk Measures

Regulatory authorities demand insurance companies control their risk exposure by imposing stringent risk management policies. This article investigates the optimal risk management strategy of an insurance company subject to regulatory constraints. We provide optimal reinsurance contracts under different tail risk measures and analyze the impact of regulators' requirements on risk sharing in the reinsurance market. Our results underpin adverse incentives for the insurer when compulsory Value-at-Risk risk management requirements are imposed. But economic effects may vary when regulatory constraints involve other risk measures. Finally, we compare the obtained optimal designs to existing reinsurance contracts and alternative risk transfer mechanisms on the capital market.     

最优再保险的两类定价模型

针对停止损失再保险(stop loss reinsurance)，分别运用均值一方差(mean-variance)保费定价原理及效用理论(utility theory)，在再保险人总索赔额的基础之上推导出最优再保险(optimal reinsurance)的保费定价模型。     

Optimal Proportional Reinsurance Policies in a Dynamic Setting

We consider dynamic proportional reinsurance strategies and derive the optimal strategies in a diffusion setup and a classical risk model. Optimal is meant in the sense of minimizing the ruin probability. Two basic examples are discussed.     

Optimal Bond Refunding: A Practical Approach

Although there is substantial research on optimal bond refunding, an important real-life feature is missing from the existing literature: imperfect adjustment or 'stickiness' of bond yields to short term interest rate changes. Our model takes this behavior into account, and also has the ability to handle mean reverting interest rates. The results indicate that the former has a significant effect on the optimal refunding policy (especially for longer maturities), but the latter does not. By incorporating these features, our model will hopefully offer a fairly complete and easily implementable guide to managers with regard to the bond refunding decision.     

An Extension of Arrow's Result on Optimal Reinsurance Contract

We consider the problem of finding reinsurance policies that maximize the expected utility, the stability and the survival probability of the cedent for a fixed reinsurance premium calculated according to the maximal possible claims principle. We show that the limited stop loss and the truncated stop loss are the optimal contracts.     

Optimal Risk Transfer: A Numerical Optimization Approach

Capital efficiency and asset/liability management are part of the Enterprise Risk Management Process of any insurance/reinsurance conglomerate and serve as quantitative methods to fulfill the strategic planning within an insurance organization. A considerable amount of work has been done in this ample research field, but invariably one of the last questions is whether or not, numerically, the method is practically implementable, which is our main interest. The numerical issues are dependent on the traits of the optimization problem, and therefore we plan to focus on the optimal reinsurance design, which has been a very dynamic topic in the last decade. The existing literature is focused on finding closed-form solutions that are usually possible when economic, solvency, and other constraints are not included in the model. Including these constraints, the optimal contract can be found only numerically. The efficiency of these methods is extremely good for some well-behaved convex problems, such as Second-Order Conic Problems. Specific numerical solutions are provided to better explain the advantages of appropriate numerical optimization methods chosen to solve various risk transfer problems. The stability issues are also investigated together with a case study performed for an insurance group that aims capital efficiency across the entire organization.     

The Design of Private Reinsurance Contracts

This article examines the effect of asymmetric information on the trading of underwriting risk between insurers and reinsurers and how it is mitigated in a context of long-term relationships. It begins by explaining how information problems affect the efficiency of the allocation of risk between insurers and reinsurers and how long-term implicit contracts allow the inclusion of new information in the pricing of reinsurance coverage. A key feature of these relationships is the reliance on loss-contingent rebates and commissions in the pricing of reinsurance coverage. We argue that when information is revealed only over time, long-term implicit contracts between insurers and reinsurers allow the inclusion of new information into reinsurance pricing. Because of this feature, the allocation of risk between insurers and reinsurers is more efficient. Specifically, such arrangements lead to more reinsurance coverage, higher insurer profits, and lower expected distress in the industry. Journal of Economic Literature Classification Numbers: G22, G13, L15, D81.     

VAR and CTE Criteria for Optimal Quota-Share and Stop-Loss Reinsurance

Abstract

It is well known that reinsurance can be an effective risk management tool for an insurer to minimize its exposure to risk. In this paper we provide further analysis on two optimal reinsurance models recently proposed by Cai and Tan. These models have several appealing features including (1) practicality in that the models could be of interest to insurers and reinsurers, (2) simplicity in that optimal solutions can be derived in many cases, and (3) integration between banks and insurance companies in that the models exploit explicitly some of the popular risk measures such as value-at-risk and conditional tail expectation. The objective of the paper is to study and analyze the optimal reinsurance designs associated with two of the most common reinsurance contracts: the quota share and the stop loss. Furthermore, as many as 17 reinsurance premium principles are investigated. This paper also highlights the critical role of the reinsurance premium principles in the sense that, depending on the chosen principles, optimal quota-share and stop-loss reinsurance may or may not exist. For some cases we formally establish the sufficient and necessary (or just sufficient) conditions for the existence of the nontrivial optimal reinsurance. Numerical examples are presented to illustrate our results.     

A Generalisation of the Mean-Variance Analysis

In this paper we consider a decision maker whose utility function has a kink at the reference point with different functions below and above this reference point. We also suppose that the decision maker generally distorts the objective probabilities. First we show that the expected utility function of this decision maker can be approximated by a function of mean and partial moments of distribution. This 'mean-partial moments' utility generalises not only mean-variance utility of Tobin and Markowitz, but also mean-semivariance utility of Markowitz. Then, in the spirit of Arrow and Pratt, we derive an expression for a risk premium when risk is small. Our analysis shows that a decision maker in this framework exhibits three types of aversions: aversion to loss, aversion to uncertainty in gains, and aversion to uncertainty in losses. Finally we present a solution to the optimal capital allocation problem and derive an expression for a portfolio performance measure which generalises the Sharpe and Sortino ratios. We demonstrate that in this framework the decision maker's skewness preferences have first-order impact on risk measurement even when the risk is small.     

Keynesian Inefficiency and Optimal Policy: A New Monetarist Approach

A simple model of monetary/labor search is constructed to study Keynesian indeterminacy and optimal policy. In the model, economic agents have trouble splitting the surplus from exchange appropriately, and we consider monetary and fiscal policies that correct this Keynesian inefficiency. A Taylor rule neither implies determinacy, nor does it support an efficient outcome. An optimal policy yields an efficient and determinate allocation of resources, but equilibrium policy actions, wages, and prices are indeterminate at the optimum.     

Organization Design — A Set Theoretic Decision Model for the Reinsurance Enterprise

The aim of the paper is to support reinsurance executives who have to decide about an organizational framework structure for their enterprises. To provide the support a decision model is constructed that relieves the decision-makers of parts of their own modelling tasks. The model is formulated in set theoretic terms to connect it to the methodological basis of the structuralist philosophy of science and to prepare the ground for computer simulation. The central assumption of the model is that the quality of coordination is influenced by disruptive factors associated, most notably, with interdependencies between organizational units and the competence-based splitting of markets and resources. The utility creation of an organizational structure is consequently determined by its degree of success in alleviating these disruptive factors — since they cannot be avoided altogether. The outcome of the study is that critical attributes of the disruptive factors are identified and recommendations are formulated as to the organizational actions that should be taken in order to safeguard the desired attributes of these factors.