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Let X denote the loss initially assumed by an insurer. In a reinsurance design, the insurer cedes part of its loss, say f (X), to a reinsurer, and thus the insurer retains a loss I f (X) = X − f (X). In return, the insurer is obligated to compensate the reinsurer for undertaking the risk by paying the reinsurance premium. Hence, the sum of the retained loss(More)
AMS subject classifications: 62E10 60E99 Keywords: Multivariate regular variation Copula Tail dependence function Multivariate subexponential distribution Multivariate long-tailed distribution a b s t r a c t The multivariate regular variation (MRV) is one of the most important tools in modeling multivariate heavy-tailed phenomena. This paper characterizes(More)
2007-02 " On the analysis of a multi-threshold Markovian risk model " , 2008-12 " Dependent risk models with bivariate phase-type distributions " , Abstract In this paper, we consider an extension of the Sparre Andersen insurance risk model by relaxing one of its well-known independence assumptions. The newly proposed dependence structure is introduced(More)
This paper establishes some asymptotic results for both finite and ultimate ruin probabilities in a discrete time risk model with constant interest rates, and individual net losses in R −α , the class of regular variation with index α > 0. The individual net losses are allowed to be generally dependent while they have zero index of upper tail dependence, so(More)
Under certain assumptions on the dependence structure of the residual lives of the in-sureds (independent, positively/negatively associated), in this paper we establish some laws of large numbers for the convex upper bounds, derived by the technique of comonotonicity, of the present value function of a homogenous portfolio composed of the whole-life(More)
2007-02 " On the analysis of a multi-threshold Markovian risk model " , Abstract In non-life insurance the traditional chain-ladder method for claims reserving is widely used and its results frequently serve as benchmark. From the actuarial point of view, reserving is a problem of estimation, or more precisely, forecasting. As in many fields the estimation(More)
2007-02 " On the analysis of a multi-threshold Markovian risk model " , Abstract. In this paper, we develop a simple and yet practically efficient simulation algorithm for derivative pricing. Our method is based on an extension of the Imai and Tan's linear transformation method which is originally proposed in the context of simulating a Gaussian process. By(More)
2007-02 " On the analysis of a multi-threshold Markovian risk model " , Abstract When analyzing catastrophic risk, traditional measures for evaluating risk, such as the probable maximum loss (PML), value at risk (VaR), tail-VaR , and others, can become practically impossible to obtain analytically in certain types of insurance, such as earthquake, and(More)