We propose a general treatment of random variables aggregation accounting for the dependence among variables and bounded or unbounded support of their sum. The approach is based on the extension to the concept of convolution to dependent variables, involving copula functions. We show that some...

We consider a suitable scaling, called the slow Markov walk limit, for a risk process with shot noise Cox claim number process and reserve dependent premium rate. We provide large deviation estimates for the ruin probability. Furthermore, we find an asymptotically efficient law for the...

This paper develops a continuous-time Markov model for utility optimization of households. The household optimizes expected future utility from consumption by controlling consumption, investments and purchase of life insurance for each person in the household. The optimal controls are...

In this paper we are interested in optimizing proportional reinsurance and investment policies in a multidimensional Lévy-driven insurance model. The criterion is that of maximizing exponential utility. Solving the classical Hamilton-Jacobi-Bellman equation yields that the optimal retention...

In this paper, we assume that the surplus process of an insurance entity is represented by a pure diffusion. The company can invest its surplus into a Black-Scholes risky asset and a risk free asset. We impose investment restrictions that only a limited amount is allowed in the risky asset and...

In this paper we investigate the well-known Gerber-Shiu expected discounted penalty function in the case of dependence between the inter-claim times and the claim amounts. We set up an integral equation for it and we prove the existence and uniqueness of its solution in the set of bounded...

In actuarial practice, regression models serve as a popular statistical tool for analyzing insurance data and tariff ratemaking. In this paper, we consider classical credibility models that can be embedded within the framework of mixed linear models. For inference about fixed effects and...

Operations which form new risk measures from a collection of given (often simpler) risk measures have been used extensively in the literature. Examples include convex combination, convolution, and the worst-case operator. Here we study the risk measure that is constructed from a family of given...

In this paper, we are interested in hedging strategies which allow the insurer to reduce the risk to their portfolio of unit-linked life insurance contracts with minimum death guarantee. Hedging strategies are developed in the Black and Scholes model and in the Merton jump-diffusion model....

Correlation mixtures of elliptical copulas arise when the correlation parameter is driven itself by a latent random process. For such copulas, both penultimate and asymptotic tail dependence are much larger than for ordinary elliptical copulas with the same unconditional correlation....