scholarly journals The Optimal Reinsurance Strategy under Conditional Tail Expectation (CTE) and Wang’s Premium Principle

2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Shaoyong Hu ◽  
Xingguo Hu ◽  
Jun Hu
Keyword(s):  
Risk Tolerance ◽  
Distortion Function ◽  
Constraint Condition ◽  
Optimal Reinsurance ◽  
Optimal Form ◽  
Tolerance Level ◽  
Insurance Contracts ◽  
General Insurance ◽  
Stop Loss ◽  
Conditional Tail Expectation

In this study, we take the conditional tail expectation (CTE) as the constraint condition and consider the optimal reinsurance issues under Wang’s premium principle in general insurance contracts. With the confidence level and the distortion function in Wang’s premium principle given by the insurer in advance, a threshold can be obtained. When the insurer’s risk tolerance level is greater than this value, the optimal reinsurance is a proportional reinsurance in which the deductible equals to this value, else the optimal form of reinsurance is a stop-loss reinsurance. Corresponding numerical examples and economic explanations are also given.

scholarly journals Optimal Limited Stop-Loss Reinsurance under VaR, TVaR, and CTE Risk Measures

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
Xianhua Zhou ◽  
Huadong Zhang ◽  
Qingquan Fan
Keyword(s):  
At Risk ◽  
Value At Risk ◽  
Risk Measures ◽  
Loss Ratio ◽  
Optimal Reinsurance ◽  
Numerical Examples ◽  
Optimal Values ◽  
Stop Loss ◽  
Conditional Tail Expectation ◽  
Reinsurance Market

This paper aims to provide a practical optimal reinsurance scheme under particular conditions, with the goal of minimizing total insurer risk. Excess of loss reinsurance is an essential part of the reinsurance market, but the concept of stop-loss reinsurance tends to be unpopular. We study the purchase arrangement of optimal reinsurance, under which the liability of reinsurers is limited by the excess of loss ratio, in order to generate a reinsurance scheme that is closer to reality. We explore the optimization of limited stop-loss reinsurance under three risk measures: value at risk (VaR), tail value at risk (TVaR), and conditional tail expectation (CTE). We analyze the topic from the following aspects: (1) finding the optimal franchise point with limited stop-loss coverage, (2) finding the optimal limited stop-loss coverage within a certain franchise point, and (3) finding the optimal franchise point with limited stop-loss coverage. We provide several numerical examples. Our results show the existence of optimal values and locations under the various constraint conditions.

Optimal Reinsurance for Variance Related Premium Calculation Principles

2010 ◽  
Vol 40 (1) ◽  
pp. 97-121 ◽  
Author(s):  
Manuel Guerra ◽  
Maria de Lourdes Centeno
Keyword(s):  
Numerical Computation ◽  
Point Of View ◽  
Adjustment Coefficient ◽  
Optimal Arrangement ◽  
Optimal Reinsurance ◽  
Optimal Form ◽  
Retention Level ◽  
Premium Calculation ◽  
Stop Loss ◽  
Increasing Function

AbstractThis paper deals with numerical computation of the optimal form of reinsurance from the ceding company point of view, when the cedent seeks to maximize the adjustment coefficient of the retained risk and the reinsurance loading is an increasing function of the variance.We compare the optimal treaty with the best stop loss policy. The optimal arrangement can provide a significant improvement in the adjustment coefficient when compared to the best stop loss treaty. Further, it is substantially more robust with respect to choice of the retention level than stop-loss treaties.

scholarly journals The Reduction of Initial Reserves Using the Optimal Reinsurance Chains in Non-Life Insurance

Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1350
Author(s):  
Galina Horáková ◽  
František Slaninka ◽  
Zsolt Simonka
Keyword(s):  
Life Insurance ◽  
Continuous Time ◽  
Ruin Probability ◽  
Proportional Reinsurance ◽  
Insurance Risk ◽  
Optimal Reinsurance ◽  
Insurance Contracts ◽  
Time Period ◽  
Different Types ◽  
Capital Injections

The aim of the paper is to propose, and give an example of, a strategy for managing insurance risk in continuous time to protect a portfolio of non-life insurance contracts against unwelcome surplus fluctuations. The strategy combines the characteristics of the ruin probability and the values VaR and CVaR. It also proposes an approach for reducing the required initial reserves by means of capital injections when the surplus is tending towards negative values, which, if used, would protect a portfolio of insurance contracts against unwelcome fluctuations of that surplus. The proposed approach enables the insurer to analyse the surplus by developing a number of scenarios for the progress of the surplus for a given reinsurance protection over a particular time period. It allows one to observe the differences in the reduction of risk obtained with different types of reinsurance chains. In addition, one can compare the differences with the results obtained, using optimally chosen parameters for each type of proportional reinsurance making up the reinsurance chain.

Identification and prioritization of factors influencing organization risk tolerance level

2019 ◽  
Vol 16 (4) ◽  
pp. 417-435
Author(s):  
Mohammad Khalilzadeh ◽  
Shiba Masoumi ◽  
Isa Masoumi
Keyword(s):  
Decision Making ◽  
Risk Tolerance ◽  
Project Manager ◽  
Validity And Reliability ◽  
Statistical Population ◽  
Content Type ◽  
Tolerance Level ◽  
Factors Influencing ◽  
Critical Issues ◽  
Decision Making Model

Purpose Identifying and prioritizing the risks are considered as critical issues in risk management; otherwise, non-considering the risks will lead to the problems such as delays in project implementation, increased costs, loss of reputation, loss of clients, reduced revenue and liquidity and even bankruptcy. The paper aims to discuss these issues. Design/methodology/approach In this paper, the factors influencing the organization risk tolerance level were identified. Then, the factors increasing and decreasing the risk tolerance level were determined by a decision-making model. Finally, a comprehensive model was considered for risk measuring and preparing a risk failure structure chart, in order to determine the factors influencing it as well as the measurement criteria and then they were ranked using the taxonomy method. In this study, the size of the statistical population was 130 (six small and medium manufacturer and service provider companies). Based on Cochran’s sample size formula, 97 questionnaires containing 30 questions were randomly distributed among the population. Validity and reliability of the questionnaire were confirmed. The data were analyzed by SPSS 22. Findings Given the hypotheses of this study, the first hypothesis was rejected and the other hypotheses were accepted. The final ranking was done using the taxonomy method; the personality of the project manager was ranked at first; income, credit and capital were ranked second and the number of personnel was ranked third. Moreover, the TOPSIS method was used for ranking to compare the results. Originality/value In this research, the identification and ranking of these factors have taken place in several small- and medium-sized organizations; in addition, the rankings are conducted using the taxonomy decision-making method.

scholarly journals On Optimal Reinsurance

1966 ◽  
Vol 4 (1) ◽  
pp. 29-38 ◽  
Author(s):  
H. G. Verbeek
Keyword(s):  
Optimization Problem ◽  
General Setting ◽  
Loss Of Stability ◽  
Optimal Reinsurance ◽  
Degree Of Stability ◽  
Potential Loss ◽  
Stop Loss

In this paper an attempt is made to find an answer to the question, “What is the most advantageous size for the retention limit of a risk portfolio, given the fact that a certain stability requirement is to be satisfied?”This problem will be approached from the viewpoint of an insurer who wishes to obtain a certain degree of stability at lowest cost.It is assumed that in his choice of reinsurance methods, the insurer restricts himself to either a surplus treaty, a stop loss treaty or a combination of both these types.Moreover it is assumed that “stability” can be adequately measured by the variance of the risks retained for own account.We start to consider a reinsurance policy based on the surplus system where the amount of risk in excess of a retention limit u is ceded.By thus limiting the potential loss on each risk individually, the variance is kept at a certain level, but at the expense of an amount of premium payable to a reinsurer.The insurer could, of course, reduce the reinsurance cost by increasing his retention but he then is bound to incur a higher variance in his portfolio, which would mean a loss of stability.One might ask, however, whether a suitably chosen stop loss coverage could bring the variance down again to the proper level at lesser cost than the profit obtained by taking a higher retention. A reduction in reinsurance cost would then have been effected.The question leads to an optimization problem, which in a more general setting, has been discussed by K. Borch.

scholarly journals An optimal multi-layer reinsurance policy under conditional tail expectation

2017 ◽  
Vol 12 (1) ◽  
pp. 130-146
Author(s):  
Amir T. Payandeh Najafabadi ◽  
Ali Panahi Bazaz
Keyword(s):  
Optimality Criterion ◽  
Risk Measure ◽  
Insurance Companies ◽  
Total Risk ◽  
Unknown Parameters ◽  
Practical Applications ◽  
Simulation Based ◽  
Cartesian Coordinate ◽  
Stop Loss ◽  
Conditional Tail Expectation

AbstractAn usual reinsurance policy for insurance companies admits one or two layers of the payment deductions. Under optimality criterion of minimising the Conditional Tail Expectation (CTE) risk measure of the insurer’s total risk, this article generalises an optimal stop-loss reinsurance policy to an optimal multi-layer reinsurance policy. To achieve such optimal multi-layer reinsurance policy, this article starts from a given optimal stop-loss reinsurance policy f(⋅). In the first step, it cuts down the interval [0, ∞) into intervals [0, M1) and [M1, ∞). By shifting the origin of Cartesian coordinate system to (M1, f(M1)), and showing that under the CTE criteria $$f\left( x \right)I_{{[0,M_{{\rm 1}} )}} \left( x \right){\plus}\left( {f\left( {M_{{\rm 1}} } \right){\plus}f\left( {x{\minus}M_{{\rm 1}} } \right)} \right)I_{{[M_{{\rm 1}} ,{\rm }\infty)}} \left( x \right)$$ is, again, an optimal policy. This extension procedure can be repeated to obtain an optimal k-layer reinsurance policy. Finally, unknown parameters of the optimal multi-layer reinsurance policy are estimated using some additional appropriate criteria. Three simulation-based studies have been conducted to demonstrate: (1) the practical applications of our findings and (2) how one may employ other appropriate criteria to estimate unknown parameters of an optimal multi-layer contract. The multi-layer reinsurance policy, similar to the original stop-loss reinsurance policy is optimal, in a same sense. Moreover, it has some other optimal criteria which the original policy does not have. Under optimality criterion of minimising a general translative and monotone risk measure ρ(⋅) of either the insurer’s total risk or both the insurer’s and the reinsurer’s total risks, this article (in its discussion) also extends a given optimal reinsurance contract f(⋅) to a multi-layer and continuous reinsurance policy.

ON SOME PROPERTIES OF TWO VECTOR-VALUED VAR AND CTE MULTIVARIATE RISK MEASURES FOR ARCHIMEDEAN COPULAS

2014 ◽  
Vol 44 (3) ◽  
pp. 613-633 ◽  
Author(s):  
Werner Hürlimann
Keyword(s):  
Value At Risk ◽  
Integral Transform ◽  
Risk Measures ◽  
Usual Sense ◽  
Translation Invariance ◽  
Archimedean Copulas ◽  
Coherent Risk ◽  
Multivariate Risk Measures ◽  
Stop Loss ◽  
Conditional Tail Expectation

AbstractWe consider the multivariate Value-at-Risk (VaR) and Conditional-Tail-Expectation (CTE) risk measures introduced in Cousin and Di Bernardino (Cousin, A. and Di Bernardino, E. (2013) Journal of Multivariate Analysis, 119, 32–46; Cousin, A. and Di Bernardino, E. (2014) Insurance: Mathematics and Economics, 55(C), 272–282). For absolutely continuous Archimedean copulas, we derive integral formulas for the multivariate VaR and CTE Archimedean risk measures. We show that each component of the multivariate VaR and CTE functional vectors is an integral transform of the corresponding univariate VaR measures. For the class of Archimedean copulas, the marginal components of the CTE vector satisfy the following properties: positive homogeneity (PH), translation invariance (TI), monotonicity (MO), safety loading (SL) and VaR inequality (VIA). In case marginal risks satisfy the subadditivity (MSA) property, the marginal CTE components are also sub-additive and hitherto coherent risk measures in the usual sense. Moreover, the increasing risk (IR) or stop-loss order preserving property of the marginal CTE components holds for the class of bivariate Archimedean copulas. A counterexample to the (IR) property for the trivariate Clayton copula is included.

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.

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