We consider a rm that is faced with an uncontrollable stochastic cash ow, or random risk process. There is one investment opportunity, a risky stock, and we study the optimal investment decision for such rms. There is a fundamental incompleteness in the market, in that the risk to the investor of going bankrupt can not be eliminated under any investment strategy, since the random risk process e...

In this paper we study orders of pairs of ruin probabilities resulting from two claim severity random variables X and Y for a continuous time surplus process perturbed by diffusion, each of which is the underlying risk Z with or without a deductible and/or a policy limit imposed, called a layer of Z. The deductibles and policy limits for X and Y could be the same or different. Under some condit...

In this paper we consider a risk process in which claim inter-arrival times have an Erlang(2) distribution. We consider the in…nite time survival probability as a compound geometric random variable and give expressions from which both the survival probability from initial surplus zero and the ladder height distribution can be calculated. We consider explicit solutions for the survival/ruin prob...

It is well-known in ruin theory that the expected present value of penalty at ruin satisfies a defective renewal equation in the Erlang-n renewal risk model. This paper presents a new matrix operator approach to derive a parallel defective renewal equation for the expected present value of total operating costs in a phase-type renewal risk model and hence provides explicit matrix analytic solut...

In this paper we consider an extension of the Sparre Andersen insurance risk model by relaxing one of its independence assumptions. The newly proposed dependence structure is introduced through the premise that the joint distribution of the interclaim time and the subsequent claim size is bivariate phase-type (see, e.g. Assaf et al. (1984) and Kulkarni (1989)). Relying on the existing connectio...