基于POT-GPD模型的地震巨灾风险测度

依据极值理论构建基于GPD的POT模型,对我国1969年至2013年间地震直接经济损失数据进行拟合;选取恰当的阀值,并对模型形状参数及尺度参数进行估计,以此研究地震巨灾损失的尾部特征,从而合理的对地震巨灾风险进行度量,得到损失数据的高分位数;最后,探讨了POT模型在再保险的高超额层选取及定价问题中的应用.     

Risk Measure and Premium Distribution on Catastrophe Reinsurance

In this paper, we propose a new risk measure which is based on the Orlicz premium principle to characterize catastrophe risk premium. The intention is to develop a formulation strategy for Catastrophe Fund. The logarithm equivalent form of reinsurance premium is regarded as the retention of reinsurer, and the differential earnings between the reinsurance premium and the reinsurer's retention is accumulated as a part of Catastrophe Fund. We demonstrate that the aforementioned risk measure has some good properties, which are further confirmed by numerical simulations in R environment.     

方差分保费原则下相依多险种模型的最优再保险

采用共同冲击型相依多险种模型刻画保险公司的索赔风险过程,按照方差分保费原则计算再保险费,研究最小化破产概率的再保险问题.通过扩散逼近并利用动态规划原理,得到了显式最优策略和值函数.与采用期望值分保费原则比较,发现最优分保形式和自留风险水平均不相同;与最大化期望指数效用的结果比较,发现最优分保比例除了与安全负载相关,还与索赔分布、计数过程以及直接保险费收入率c有关.最后,结合数值算例揭示了相依参数的动态影响以及最优策略与c的敏感相关性.     

Catastrophe equity put options with target variance

In this study, we consider a new class of catastrophe equity put options, whose payoff depends on the ratio of the realized variance of the stock over the life of the option and the target variance, which represents the insurance company’s expectation of the future realized variance. This kind of options could help insurance companies raise more equity capital when a large number of catastrophic events occur during the life of the option. We employ a compound doubly stochastic Poisson process with lognormal intensity to describe accumulated catastrophe losses and assume the volatility varies stochastically. Finally, numerical results are presented to investigate the values of this class of options.     

Systemic risk and optimal fee for central clearing counterparty under partial netting

We propose a novel central clearing counterparty (CCP) design for a financial network, in which the participation of banks in the CCP depends on the proportional clearing fee. We obtain the optimal fee that maximizes the CCP’s net worth. We show that partial participation of banks in the CCP at the optimal fee rate reduces banks’ aggregate shortfall and also reduces the overall systemic risk. We also carry out numerical examples to verify the theoretical results.     

Valuation of catastrophe reinsurance with catastrophe bonds

This study develops a contingent-claim framework for valuing a reinsurance contract and examines how a reinsurance company can increase the value of a reinsurance contract and reduce its default risk by issuing catastrophe (CAT) bonds. The results also show how the changes in contract values and default risk premium are related to basis risk, trigger level, catastrophe risk, interest rate risk, and the reinsurer’s capital position.     

Designing risk management support systems

The major movements emerging in the field of risk analysis over the past decades are reviewed with special emphasis placed on their treatment of non-technical issues and their relevance to risk management needs. With this background, the requirements for an effective system to support risk management activities are discussed and a user-oriented design process outlined. The Ispra Risk Management Support (IRIMS) System is briefly described.Invited for presentation at the 12th Symposium on Operations Research, University of Passau, Federal Republic of Germany, September 9–12, 1987.     

Portfolio optimization under entropic risk management

framework in the risk uniqueness In this paper, properties of the entropic risk measure are examined rigorously in a general This risk measure is then applied in a dynamic portfolio optimization problem, appearing management constraint. By considering the dual problem, we prove the existence and of the solution and obtain an analytic expression for the solution.     

Efficient option risk measurement with reduced model risk

Options require risk measurement that is also computationally efficient as it is important to derivatives risk management. There are currently few methods that are specifically adapted for efficient option risk measurement. Moreover, current methods rely on series approximations and incur significant model risks, which inhibit their applicability for risk management.In this paper we propose a new approach to computationally efficient option risk measurement, using the idea of a replicating portfolio and coherent risk measurement. We find our approach to option risk measurement provides fast computation by practically eliminating nonlinear computational operations. We reduce model risk by eliminating calibration and implementation risks by using mostly observable data, we remove internal model risk for complex option portfolios by not admitting arbitrage opportunities, we are also able to incorporate liquidity or model misspecification risks. Additionally, our method enables tractable and convex optimisation of portfolios containing multiple options. We conduct numerical experiments to test our new approach and they validate it over a range of option pricing parameters.     

Stable modeling in energy risk management

High price volatility in energy markets compels the companies to adopt and implement policies for measurement and management of the energy risk. A popular measure of risk exposure is the Value at Risk (VaR). Traditional methods of estimation of VaR used by major energy companies fail to capture the heavy tails and asymmetry of energy returns distributions. We suggest the use of stable distributions for modeling energy return distributions. The results of our study demonstrate that stable modeling captures asymmetry and heavy-tails of returns, and, therefore, provides more accurate estimates of energy VaR.     

Credit risk optimization using factor models

We study portfolio credit risk management using factor models, with a focus on optimal portfolio selection based on the tradeoff of expected return and credit risk. We begin with a discussion of factor models and their known analytic properties, paying particular attention to the asymptotic limit of a large, finely grained portfolio. We recall prior results on the convergence of risk measures in this “large portfolio approximation” which are important for credit risk optimization. We then show how the results on the large portfolio approximation can be used to reduce significantly the computational effort required for credit risk optimization. For example, when determining the fraction of capital to be assigned to particular ratings classes, it is sufficient to solve the optimization problem for the large portfolio approximation, rather than for the actual portfolio. This dramatically reduces the dimensionality of the problem, and the amount of computation required for its solution. Numerical results illustrating the application of this principle are also presented. JEL Classification G11     

Signed graphs for portfolio analysis in risk management

We introduce the notion of structural balance for signed graphsin the context of portfolio analysis. A portfolio of securitiescan be represented as a signed graph with the nodes denotingthe securities and the edges representing the correlation betweenthe securities. With signed graphs, the characteristics of aportfolio from a risk management perspective can be uncoveredfor analysis purposes. It is shown that a portfolio characterizedby a signed graph of positive and negative edges that is structurallybalanced is characteristically more predictable. Investors whoundertake a portfolio position with all positively correlatedsecurities do so with the intention to speculate on the upside(or downside). If the portfolio consists of negative edges andis balanced, then it is likely that the position has a hedgingdisposition within it. On the other hand, an unbalanced signedgraph is representative of an investment portfolio which ischaracteristically unpredictable.     

Multi-period defined contribution pension funds investment management with regime-switching and mortality risk

Using mean–variance criterion, we investigate a multi-period defined contribution pension fund investment problem in a Markovian regime-switching market. Both stochastic wage income and mortality risk are incorporated in our model. In a regime-switching market, the market mode changes among a finite number of regimes, and the market state process is modeled by a Markov chain. The key parameters, such as the bank interest rate, or expected returns and covariance matrix of stocks, will change according to the market state. By virtue of Lagrange duality technique, dynamic programming approach and matrix representation method, we derive expressions of efficient investment strategy and its efficient frontier in closed-form. Also, we study some special cases of our model. Finally, a numerical example based on real data from the American market sheds light on our theoretical results.     

Optimal dividend payout for classical risk model with risk constraint

In this paper we consider the problem of maximizing the total discounted utility of dividend payments for a Cramér-Lundberg risk model subject to both proportional and fixed transaction costs.We assume that dividend payments are prohibited unless the surplus of insurance company has reached a level b.Given fixed level b,we derive a integro-differential equation satisfied by the value function.By solving this equation we obtain the analytical solutions of the value function and the optimal dividend strategy when claims are exponentially distributed.Finally we show how the threshold b can be determined so that the expected ruin time is not less than some T.Also,numerical examples are presented to illustrate our results.     

Optimal pension fund management under multi-period risk minimization

In this paper, a multi-period stochastic optimization model for solving a problem of optimal selection of a pension fund by a pension plan member is presented. In our model, members of the pension plan are given a possibility to switch periodically between J types of funds with different risk profiles and so actively manage their risk exposure and expected return. Minimization of a multi-period average value-at-risk deviation measure under expected return constraint leads to a large-scale linear program. A theoretical framework and a solution for the case of the pension system of Slovak Republic are presented.     

Optimal risk and dividend control of an insurance company with exponential premium principle and liquidation value

Assume that an insurer can control it’s surplus by paying dividends, purchasing reinsurance and injecting capital. The exponential premium principle is used when pricing insurance contract instead of the expected value principle. Under the objective of maximizing the company’s value, we identify the optimal strategies with liquidation value and transaction costs. The results illustrate that the insurer should buy less reinsurance when the surplus increases, capital injection should be considered if and only if the transaction costs and the liquidation value are relatively low, dividends are paid according to barrier strategy if the dividend rate is unrestricted or threshold strategy if the dividend rate is bounded.     

保费率-巨灾索赔相依的风险模型的破产概率

进一步推广Sparre Andersen风险模型,考虑有意外巨额赔付情况下得到保险公司的破产概率,并得到尾等价式,此结果反映了特殊的巨额索赔对破产的影响程度.另外,当有巨灾索赔发生的时候,模型会对保险费率做出相应的调整.     

Consistent modeling of risk averse behavior with spectral risk measures

This paper clarifies the relation between decisions of a risk-averse decision maker, based on expected utility theory on the one hand, and spectral risk measures on the other.     

Markov调节中基于时滞和相依风险模型的最优再保险与投资

本文研究保险公司在Markov调节下基于时滞及相依风险模型的最优再保险与最优投资问题,其中市场被划分为有限个状态,一些重要的参数随着市场状态的转换而变化.假设保险公司的盈余过程由复合Poisson过程描述,而风险资产的价格过程由几何跳扩散模型刻画,并且假设这两个跳过程是相依的.以最大化终端财富值的均值-方差效用为目标,...     

User-model interaction in decision support systems for risk management

This paper describes and evaluates three different approaches to building decision support systems: the Operations Research/Management Science approach, the Decision Analysis/Multiattribute Utility approach, and the Artificial Intelligence/Expert Systems approach. It evaluates the usefulness of the three approaches for risk management. In particular, it defines evaluation objectives of risk analysts, risk managers, and laypeople and provides a subjective assessment how the three approaches stack up against their objectives. The paper concludes that for most risk management applications a combination of the three approaches would be most desirable.This paper was written under contract No. 2709-85-05 ED ISP D of the European Atomic Energy Community, Commission of the European Communities, Joint Research Centre, Ispra Establishment, Ispra, Italy to the Gemeinschaft für Entscheidungs- und Risikoanalyse, Berlin, West Germany. It was prepared for presentation at the Conference on Operations Research and Multiattribute Decision Analysis held in Passau, April 20–26, 1986. The views and opinions expressed in this paper are solely those of the author.