Numerical Evaluation of Continuous Time Ruin Probabilities for a Portfolio with Credibility Updated Premiums

The probability of ruin in continuous and finite time is numerically evaluated in a classical risk process where the premium can be updated according to credibility models and therefore change from year to year. A major consideration in the development of this approach is that it should be easily applicable to large portfolios. Our method uses as a first tool the model developed by Afonso et al. (2009), which is quite flexible and allows premiums to change annually. We extend that model by introducing a credibility approach to experience rating.We consider a portfolio of risks which satisfy the assumptions of the Bühlmann (1967, 1969) or Bühlmann and Straub (1970) credibility models. We compute finite time ruin probabilities for different scenarios and compare with those when a fixed premium is considered.

Calculating Continuous Time Ruin Probabilities for a Large Portfolio with Varying Premiums

In this paper we present a method for the numerical evaluation of the ruin probability in continuous and finite time for a classical risk process where the premium can change from year to year. A major consideration in the development of this methodology is that it should be easily applicable to large portfolios. Our method is based on the simulation of the annual aggregate claims and then on the calculation of the ruin probability for a given surplus at the start and at the end of each year. We calculate the within-year ruin probability assuming a translated gamma distribution approximation for aggregate claim amounts.We illustrate our method by studying the case where the premium at the start of each year is a function of the surplus level at that time or at an earlier time.

DYNAMIC MEAN-VARIANCE OPTIMIZATION UNDER CLASSICAL RISK MODEL WITH FRACTIONAL BROWNIAN MOTION PERTURBATION

In this paper, we apply the completion of squares method to study the optimal investment problem under mean-variance criteria for an insurer. The insurer's risk process is modelled by a classical risk process that is perturbed by a standard fractional Brownian motion with Hurst parameter H ∈ (1/2, 1). By virtue of an auxiliary process, the efficient strategy and efficient frontier are obtained. Moreover, when H → 1/2+ the results converge to the corresponding (known) results for standard Brownian motion.

Optimal Investment and Bounded Ruin Probability: Constant Portfolio Strategies and Mean-variance Analysis

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 the expected utility for a bounded ruin probability. The corresponding optimal strategy in various special classes of possible investment strategies will be calculated. For means of comparison we also calculate the related mean-variance optimal strategies.