In this article, we consider an insurance risk model where the claim and premium processes follow some time series models+ We first consider the model proposed in Gerber @2,3#; then a model with dependent structure between premium and claim processes modeled by using Granger’s causal model is considered+ By using some martingale arguments, Lundberg-type upper bounds for the ruin probabilities u...

We derive a closed-form (infinite series) representation for the distribution of the ruin time for the Sparre Andersen model with exponentially distributed claims. This extends a recent result of Dickson et al. [7] for such processes with Erlang inter-claim times. We illustrate our result in the cases of gamma and mixed exponential inter-claim time distributions.

We study the continuous-time portfolio optimization problem of an insurer. The wealth of the insurer is given by a classical risk process plus gains from trading in a risky asset, modelled by a geometric Brownian motion. The insurer is not only interested in maximizing the expected utility of wealth but is also concerned about the ruin probability. We thus investigate the problem of optimizing ...

We study a family of diffusion models for compounded risk reserves, which account for the investment income earned and for the inflation experienced on claim amounts. We are interested in the models which the dividend payments are paid from the risk reserves. After defining the process of conditional probability over finite time, the classical diffusion processes results turn the nonlinear stoc...

A numerical method to approximate ruin probabilities is proposed within the frame of a compound Poisson ruin model. The defective density function associated to the ruin probability is projected in an orthogonal polynomial system. These polynomials are orthogonal with respect to a probability measure that belongs to Natural Exponential Family with Quadratic Variance Function (NEF-QVF). The meth...

This paper establishes some asymptotic formulas for the infinite-time ruin probabilities of two kinds of dependent risk models. One risk model considers the claim sizes as a modulated process, and the other deals with negatively upper orthant dependent claim sizes. In the two models, the inter-arrival times are both assumed to be negatively lower orthant dependent.

This paper investigates the moments of the surplus before ruin and the deficit at ruin in the Erlang(2) risk process. Using the integro-differential equation that we establish, we obtain some explicit expressions for the moments. Furthermore, when the claim size is exponentially and subexponentially distributed, asymptotic relationships for the moments are derived as the initial capital tends t...