This paper considers the optimal investment, consumption and proportional reinsurance strategies for an insurer under model uncertainty. The surplus process of the insurer before investment and consumption is assumed to be a general jump–diffusion process. The financial market consists of one...

This paper is devoted to the study of optimization of investment, consumption and proportional reinsurance for an insurer with option type payoff at the terminal time under the criterion of exponential utility maximization. The surplus process of the insurer and the financial risky asset process...

In this paper, we propose a framework of risk measures for portfolio vectors, which is an extension of the ones introduced by Burgert and Rüschendorf (2006) and Rüschendorf (2013). Representation results for coherent and convex risk measures for portfolio vectors are provided. Applications to...

In this note, we give an estimate for the difference between the rate function for empirical measures of a stationary-dependent random sequence in [tau]-topology and the relative entropy.

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...

In this paper, we consider the optimal consumption and portfolio policies with the consumption habit constraints and the terminal wealth downside constraints, that is, here the consumption rate is greater than or equal to some nonnegative process, and the terminal wealth is no less than some...

We investigate the absolute ruin in the compound Poisson risk model with nonnegative interest and a constant dividend barrier. An integro-differential equation satisfied by the absolute ruin probability, the distribution and moments of deficit at the time to absolute ruin is derived. In the case...

Consider a discrete time risk model Un=(Un-1+Xn)(1+In)-Yn,n=1,2,..., where U0:=M0 is the initial reserve of an insurance company, Xn the total amount of premiums, Yn the total amount of claims, In the interest rate and Un the reserve at time n. The time of ruin is denoted by...

We consider the classical risk model with constant force of interest and a nonlinear dividend barrier. Lundberg-type inequalities for the ultimate ruin probabilities are derived. The results obtained carry over those of Gerber [Gerber, H.U., 1979. An Introduction to Mathematical Risk Theory. In:...