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.

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.

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.

scholarly journals Quantifying and Correcting the Bias in Estimated Risk Measures

2007 ◽  
Vol 37 (2) ◽  
pp. 365-386 ◽  
Author(s):  
Joseph Hyun Tae Kim ◽  
Mary R. Hardy
Keyword(s):  
At Risk ◽  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Value At Risk ◽  
Risk Measures ◽  
Bootstrap Techniques ◽  
Practical Guideline ◽  
Estimated Risk ◽  
Conditional Tail Expectation

In this paper we explore the bias in the estimation of the Value at Risk and Conditional Tail Expectation risk measures using Monte Carlo simulation. We assess the use of bootstrap techniques to correct the bias for a number of different examples. In the case of the Conditional Tail Expectation, we show that application of the exact bootstrap can improve estimates, and we develop a practical guideline for assessing when to use the exact bootstrap.

Optimal Reinsurance Revisited – A Geometric Approach

2010 ◽  
Vol 40 (1) ◽  
pp. 221-239 ◽  
Author(s):  
Ka Chun Cheung
Keyword(s):  
At Risk ◽  
Minimization Problem ◽  
Value At Risk ◽  
Geometric Approach ◽  
Risk Exposure ◽  
Total Risk ◽  
Optimal Reinsurance ◽  
Conditional Tail Expectation

AbstractIn this paper, we reexamine the two optimal reinsurance problems studied in Cai et al. (2008), in which the objectives are to find the optimal reinsurance contracts that minimize the value-at-risk (VaR) and the conditional tail expectation (CTE) of the total risk exposure under the expectation premium principle. We provide a simpler and more transparent approach to solve these problems by using intuitive geometric arguments. The usefulness of this approach is further demonstrated by solving the VaR-minimization problem when the expectation premium principle is replaced by Wang's premium principle.

OPTIMAL REINSURANCE DESIGN WITH DISTORTION RISK MEASURES AND ASYMMETRIC INFORMATION

2021 ◽  
pp. 1-23
Author(s):  
Tim J. Boonen ◽  
Yiying Zhang
Keyword(s):  
At Risk ◽  
Asymmetric Information ◽  
Value At Risk ◽  
Functional Form ◽  
Risk Measures ◽  
Risk Measure ◽  
Incentive Compatibility ◽  
Optimal Reinsurance ◽  
Net Profit ◽  
Distortion Risk Measures

ABSTRACT This paper studies a problem of optimal reinsurance design under asymmetric information. The insurer adopts distortion risk measures to quantify his/her risk position, and the reinsurer does not know the functional form of this distortion risk measure. The risk-neutral reinsurer maximizes his/her net profit subject to individual rationality and incentive compatibility constraints. The optimal reinsurance menu is succinctly derived under the assumption that one type of insurer has a larger willingness to pay than the other type of insurer for every risk. Some comparative analyses are given as illustrations when the insurer adopts the value at risk or the tail value at risk as preferences.

scholarly journals Quantifying and Correcting the Bias in Estimated Risk Measures

2007 ◽  
Vol 37 (02) ◽  
pp. 365-386 ◽  
Author(s):  
Joseph Hyun Tae Kim ◽  
Mary R. Hardy
Keyword(s):  
At Risk ◽  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Value At Risk ◽  
Risk Measures ◽  
Bootstrap Techniques ◽  
Practical Guideline ◽  
Estimated Risk ◽  
Conditional Tail Expectation

In this paper we explore the bias in the estimation of the Value at Risk and Conditional Tail Expectation risk measures using Monte Carlo simulation. We assess the use of bootstrap techniques to correct the bias for a number of different examples. In the case of the Conditional Tail Expectation, we show that application of the exact bootstrap can improve estimates, and we develop a practical guideline for assessing when to use the exact bootstrap.

scholarly journals PENGUKURAN RISIKO PADA RETENSI OPTIMAL UNTUK REASURANSI STOP LOSS DENGAN VALUE AT RISK

2012 ◽  
Vol 4 (1) ◽  
Author(s):  
Agustina Sunarwatiningsih ◽  
Yuciana Wilandari ◽  
Agus Rusgiyono
Keyword(s):  
At Risk ◽  
Value At Risk ◽  
Stop Loss
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