In this paper, we consider a portfolio of n dependent risks X1,…,Xn and we study the stochastic behavior of the aggregate claim amount S=X1+⋯+Xn. Our objective is to determine the amount of economic capital needed for the whole portfolio and to compute the amount of capital to be allocated...

In insurance two major types of cycles are known: (a) regular many years long up- and down-swings referred to as underwriting cycles and (b) irregular short-range fluctuations. The key rationale of the underwriting cycles is migration of insureds triggered by the insurers’ price competition...

In this paper we model the daily average temperature via an extended version of the standard Ornstein Uhlenbeck process driven by a Levy noise with seasonally adjusted asymmetric ARCH process for volatility. More precisely, we model the disturbances with the Normal inverse Gaussian (NIG) and...

One of the major concerns of life insurers and pension funds is the increasing longevity of their beneficiaries. This paper studies the hedging problem of annuity cash flows when mortality and interest rates are stochastic. We first propose a Delta–Gamma hedging technique for mortality risk....

In this paper, we study the well-known Haezendonck–Goovaerts risk measures on their natural domain, that is on Orlicz spaces and, in particular, on Orlicz hearts. We provide a dual representation as well as the optimal scenario in such a representation and investigate the properties of the...

In actuarial theory, the Lp-metric is used to evaluate how well a probability distribution approximates another one. In the context of the distorted expectation hypothesis, the actuary replaces the original probability distribution by a distorted probability, so it makes sense to interpret the...

In the spirit of Albrecher and Hipp (2007), Albrecher et al. (2008b) and Kyprianou and Zhou (2009), we consider the reserve process of an insurance company which is governed by Rtπ=Xt−∫0tγπ(Sσ)dSσ, where X is a spectrally negative Lévy process with the usual exclusion of negative...

The distribution-free chain ladder reserving method belongs to the most frequently used approaches in general insurance. It is well known, see Mack (1993), that the estimators f̂j of the development factors are unbiased and mutually uncorrelated under some mild conditions on the mean structure...

The risk profile of an insurance company involved in annuity business is heavily affected by the uncertainty in future mortality trends. It is problematic to capture accurately future survival patterns, in particular at retirement ages when the effects of the rectangularization phenomenon and...

We present the one-year claims development result (CDR) in the paid-incurred chain (PIC) reserving model. The PIC reserving model presented in Merz and Wüthrich (2010) is a Bayesian stochastic claims reserving model that considers simultaneously claims payments and incurred losses information...