Consider two insurance companies (or two branches of the same company) that divide between them both claims and premia in some specified proportions. We model the occurrence of claims according to a renewal process. One ruin problem considered is that when the corresponding two-dimensional risk process first leaves the positive quadrant; another is that of entering the negative quadrant. When t...

The contribution of this paper is two-fold. First, we show that mutual fund theorems hold when minimizing the probability of lifetime ruin (that is, wealth reaching zero before death), as Merton (1971) does when maximizing the utility of consumption. Bayraktar and Young (2007a) determine when the investment strategies are identical under the two problems of maximizing utility of consumption or ...

The paper investigates a discrete time Binomial risk model with different types of polices and shock events may influence some the claim sizes. It is shown that this can be considered as particular case classical compound model. As far we work parallel counting processes in infinite time, if consider them independent, probability event they to have at least once simultaneous jumps would equal o...

This paper presents an explicit characterization for the joint probability density function of the surplus immediately prior to ruin and the deficit at ruin for a general risk process, which includes the Sparre-Andersen risk model with phase-type inter-claim times and claim sizes. The model can also accommodate a Markovian arrival process which enables claim sizes to be correlated with the inte...

We consider a discrete-time insurance risk model, in which the financial risks constitute a stationary process with finite dimensional distributions of Farlie–Gumbel–Morgenstern type. We obtain an exact asymptotic formula for the ruin probability, reflecting the impact of this kind of association structure among the financial risks. r 2007 Elsevier B.V. All rights reserved.

We discuss the uniformly asymptotic estimate of the finite-time ruin probability for all times in a generalized compound renewal risk model, where the interarrival times of successive accidents and all the claim sizes caused by an accident are two sequences of random variables following a wide dependence structure. This wide dependence structure allows random variables to be either negatively d...

At retirement, most individuals face a choice between voluntary annuitization and discretionary management of assets with systematic withdrawals for consumption purposes. Annuitization— buying a life annuity from an insurance company—assures a lifelong consumption stream that cannot be outlived, but it is at the expense of a complete loss of liquidity. On the other hand, discretionary managemen...