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     

Robust bootstrap procedures for the chain-ladder method

Insurers are faced with the challenge of estimating the future reserves needed to handle historic and outstanding claims that are not fully settled. A well-known and widely used technique is the chain-ladder method, which is a deterministic algorithm. To include a stochastic component one may apply generalized linear models to the run-off triangles based on past claims data. Analytical expressions for the standard deviation of the resulting reserve estimates are typically difficult to derive. A popular alternative approach to obtain inference is to use the bootstrap technique. However, the standard procedures are very sensitive to the possible presence of outliers. These atypical observations, deviating from the pattern of the majority of the data, may both inflate or deflate traditional reserve estimates and corresponding inference such as their standard errors. Even when paired with a robust chain-ladder method, classical bootstrap inference may break down. Therefore, we discuss and implement several robust bootstrap procedures in the claims reserving framework and we investigate and compare their performance on both simulated and real data. We also illustrate their use for obtaining the distribution of one year risk measures.     

Parameter risk in time-series mortality forecasts

The projection of mortality rates is an essential part of valuing liabilities in life insurance portfolios and pension schemes. An important tool for risk management and solvency purposes is a stochastic projection model. We show that ARIMA models can be better representations of mortality time-series than simple random-walk models. We also consider the issue of parameter risk in time-series models from the point of view of an insurer using them for regulatory risk reporting – formulae are given for decomposing overall risk into undiversifiable trend risk (parameter uncertainty) and diversifiable volatility. Particular attention is given to the contrasts in how academic researchers might view these models and how insurance regulators and practitioners in life offices might use them. Using a bootstrap method we find that, while certain kinds of parameter risk are negligible, others are too material to ignore. We also find that an objective model selection criterion, such as goodness of fit to past data, can result in the selection of a model with unstable parameter values. While this aspect of the model is superficially undesirable, it also leads to slightly higher capital requirements and thus makes the model of keen interest to regulators. Our conclusions have relevance to insurers using value-at-risk capital assessments in the European Union under Solvency II, but also territories using conditional tail expectations such as Australia, Canada and Switzerland.     

中国非寿险业法定偿付能力额度标准的合理性分析与实证分析

在综合分析我国非寿险保险公司最低偿付能力额度标准的理论根源的基础上,该文探讨了现行标准存在的缺陷及其原因,并利用我国非寿险市场的统计数据,重新计算了以净保费为计算基础的计算比率,对现行标准的不足进行了修正.     

Stress scenario generation for solvency and risk management

We derive worst-case scenarios in a life insurance model in the case where the interest rate and the various transition intensities are mutually dependent. Examples of this dependence are that (a) surrender intensities and interest rates are high at the same time, (b) mortality intensities of a policyholder as active and disabled, respectively, are low at the same time, and (c) mortality intensities of the policyholders in a portfolio are low at the same time. The set from which the worst-case scenario is taken reflects the dependence structure and allows us to relate the worst-case scenario-based reserve, qualitatively, to a Value-at-Risk-based calculation of solvency capital requirements. This brings out perspectives for our results in relation to qualifying the standard formula of Solvency II or using a scenario-based approach in internal models. Our results are powerful for various applications and the techniques are non-standard in control theory, exactly because our worst-case scenario is deterministic and not adapted to the stochastic development of the portfolio. The formalistic results are exemplified in a series of numerical studies.     

总分行制度下基于Delta-EVT模型的操作风险度量研究

总分行制度下制度设计缺陷及人员管理等方面的失误是商业银行操作风险产生的重要原因之一.在操作风险损失数据不完全的情况下,首先将损失进行分类,并选取总行对分行管理人员配备的误差、机构内部人员的组合误差、员工素质问题、分行出现问题后向总行报告的时间延误和总行及时处理问题分行的能力等特定的风险因子,继而借助Delta-EVT模型,采用Delta方法计算由以上风险因子导致的操作损失.通过计算,由于控制失效或外部事件引起的超额损失,再利用门槛值将两者结合起来,用EVT方法可以较准确地估算出在分行经营过程中和在向总行传递信息过程中由于制度设计不合理导致的操作风险.     

总分行制度下基于Delta-EVT模型的操作风险度量研究

总分行制度下制度设计缺陷及人员管理等方面的失误是商业银行操作风险产生的重要原因之一。在操作风险损失数据不完全的情况下，首先将损失进行分类，并选取总行对分行管理人员配备的误差、机构内部人员的组合误差、员工素质问题、分行出现问题后向总行报告的时间延误和总行及时处理问题分行的能力等特定的风险因子，继而借助Delta-EVT模型，采用Delta方法计算由以上风险因子导致的操作损失。通过计算，由于控制失效或外部事件引起的超额损失，再利用门槛值将两者结合起来，用EVT方法可以较准确地估算出在分行经营过程中和在向总行传递信息过程中由于制度设计不合理导致的操作风险。     

On the optimality of proportional reinsurance

Proportional reinsurance is often thought to be a very simple method of covering the portfolio of an insurer. Theoreticians are not really interested in analysing the optimality properties of these types of reinsurance covers. In this paper, we will use a real-life insurance portfolio in order to compare four proportional structures: quota share reinsurance, variable quota share reinsurance, surplus reinsurance and surplus reinsurance with a table of lines.     

Mathematical foundation of the replicating portfolio approach

In the last few years, the first theoretical foundations for replicating portfolios – probably the most prevailing technique for risk capital calculation in life insurance – have been given in a series of papers by Beutner, Pelsser and Schweizer. In these papers, the asymptotic behaviour of replicating portfolios concerning the approximation of the terminal value (TVL) and the fair value distribution of the liabilities (FVL) has been investigated in detail. We complement this line of research by providing results on approximations based on a finite number of replicating instruments. We do so by providing the link between the approximation error of the TVL distribution, the FVL distribution and the error in the resulting risk capital figure, either value at risk or some coherent risk measure. We further allow for a variety of practically relevant formulations of the replication problem, including cash flow matching approaches. In contrast to the existing literature, all our results apply to approaches both under the risk-neutral and the real-world measure. Our strongest bounds are due to the observation that in discrete time, the measure change from the real-world to the risk-neutral measure can be both bounded below and above by a suitable constant in the first period.