Jingping Yang

Optimal reinsurance under distortion risk measures and expected value premium principle for reinsurer

This paper discusses optimal reinsurance strategy by minimizing insurer’s risk under one general risk measure: Distortion risk measure. The authors assume that the reinsurance premium is determined by the expected value premium principle and the retained loss of the insurer is an increasing function of the initial loss. An explicit solution of the insurer’s optimal reinsurance problem is obtained. The optimal strategies for some special distortion risk measures, such as value-at-risk (VaR) and tail value-at-risk (TVaR), are also investigated.

CreditRisk+ Model with Dependent Risk Factors

The CreditRisk+ model is widely used in industry for computing the loss of a credit portfolio. The standard CreditRisk+ model assumes independence among a set of common risk factors, a simplified assumption that leads to computational ease. In this article, we propose to model the common risk factors by a class of multivariate extreme copulas as a generalization of bivariate Fréchet copulas. Further we present a conditional compound Poisson model to approximate the credit portfolio and provide a cost-efficient recursive algorithm to calculate the loss distribution. The new model is more flexible than the standard model, with computational advantages compared to other dependence models of risk factors.

Worst-Case Range Value-at-Risk with Partial Information

In this paper, we study the worst-case scenarios of a general class of risk measures, the Range Value-at-Risk (RVaR), in single and aggregate risk models with given mean and variance, as well as symmetry and/or unimodality of each risk. For different types of partial information settings, sharp bounds for RVaR are obtained for single and aggregate risk models, together with the corresponding worst-case scenarios of marginal risks and the corresponding copula functions (dependence structure) among them. Different from the existing literature, the sharp bounds under different partial information settings in this paper are obtained via a unified method combining convex order and the recently developed notion of joint mixability. As particular cases, bounds for Value-at-Risk (VaR) and Tail Value-at-Risk (TVaR) are derived directly. Numerical examples are also provided to illustrate our results.

Jackknife empirical likelihood for parametric copulas

For fitting a parametric copula to multivariate data, a popular way is to employ the so-called pseudo maximum likelihood estimation proposed by Genest, Ghoudi, and Rivest. Although interval estimation can be obtained via estimating the asymptotic covariance of the pseudo maximum likelihood estimation, we propose a jackknife empirical likelihood method to construct confidence regions for the parameters without estimating any additional quantities such as the asymptotic covariance. A simulation study shows the advantages of the new method in case of strong dependence or having more than one parameter involved.

Shuffle of min’s random variable approximations of bivariate copulas’ realization

ABSTRACT The comonotonicity and countermonotonicity provide intuitive upper and lower dependence relationship between random variables. This paper constructs the shuffle of min’s random variable approximations for a given Uniform [0, 1] random vector. We find the two optimal orders under which the shuffle of min’s random variable approximations obtained are shown to be extensions of comonotonicity and countermonotonicity. We also provide the rate of convergence of these random vectors approximations and apply them to compute value-at-risk.