The Finite-time Ruin Probabilities of a Bidimensional risk model with Constant Interest Force and correlated Brownian Motions

We follow some recent works to study bidimensional perturbed compound Poisson risk models with constant interest force and correlated Brownian Motions. Several asymptotic formulae for three different type of ruin probabilities over a finite-time horizon are established. Our approach appeals directly to very recent developments in the ruin theory in the presence of heavy tails of unidimensional risk models and the dependence theory of stochastic processes and random vectors.Comment: 25page

Ruin models with investment income

This survey treats the problem of ruin in a risk model when assets earn investment income. In addition to a general presentation of the problem, topics covered are a presentation of the relevant integro-differential equations, exact and numerical solutions, asymptotic results, bounds on the ruin probability and also the possibility of minimizing the ruin probability by investment and possibly reinsurance control. The main emphasis is on continuous time models, but discrete time models are also covered. A fairly extensive list of references is provided, particularly of papers published after 1998. For more references to papers published before that, the reader can consult [47].Comment: Published in at http://dx.doi.org/10.1214/08-PS134 the Probability Surveys (http://www.i-journals.org/ps/) by the Institute of Mathematical Statistics (http://www.imstat.org

Two-dimensional ruin probability for subexponential claim size

We analyse the asymptotics of ruin probabilities of two insurance companies (or two branches of the same company) that divide between them both claims and premia in some specified proportions when the initial reserves of both companies tend to infinity and generic claim size is subexponential

A bivariate risk model with mutual deficit coverage

We consider a bivariate Cramer-Lundberg-type risk reserve process with the special feature that each insurance company agrees to cover the deficit of the other. It is assumed that the capital transfers between the companies are instantaneous and incur a certain proportional cost, and that ruin occurs when neither company can cover the deficit of the other. We study the survival probability as a function of initial capitals and express its bivariate transform through two univariate boundary transforms, where one of the initial capitals is fixed at 0. We identify these boundary transforms in the case when claims arriving at each company form two independent processes. The expressions are in terms of Wiener-Hopf factors associated to two auxiliary compound Poisson processes. The case of non-mutual (reinsurance) agreement is also considered