In this paper, we consider a perturbed compound Poisson risk model with two-sided jumps. The downward jumps represent the claims following an arbitrary distribution, while the upward jumps are also allowed to represent the random gains. Assuming that the density function of the upward jumps has a rational Laplace transform, the Laplace transforms and defective renewal equations for the discount...

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...

The risk modeling for determining value and decision making that we provide for you will be ultimate to give preference. This reading book is your chosen book to accompany you when in your free time, in your lonely. This kind of book can help you to heal the lonely and get or add the inspirations to be more inoperative. Yeah, book as the widow of the world can be very inspiring manners. As here...

We consider a risk model with threshold strategy, where the insurance company pays off a certain percentage of the income as dividend whenever the current surplus is larger than a given threshold. We investigate the ruin time, ruin probability and the total dividend, using methods and results from queueing theory.

We obtain stability estimates and derive analytic expansions for local solutions of multidimensional quadratic backward stochastic differential equations. We apply these results to a financial model where the prices of risky assets are quoted by a representative dealer in such a way that it is optimal to meet an exogenous demand. We show that the prices are stable under the demand process and d...

In this paper, we consider the surplus process of the classical continuous time risk model containing an independent diffusion (Wiener) process. We generalize the defective renewal equation for the expected discounted function of a penalty at the time of ruin in Garber and Landry [Insurance: Math. Econ. 22 (1998) 263]. Then an asymptotic formula for the expected discounted penalty function is p...

This paper investigates the asymptotic behavior of tail probabilities of randomly weighted sums of independent heavy-tailed random variables, where the weights form another sequence of nonnegative and arbitrarily dependent random variables. The results obtained are further applied to derive asymptotic estimates for the ruin probabilities in a discrete time risk model with dependent stochastic r...

Institutional investors and investment managers seek to better characterize the credit risk of online consumer loans. This article describes how to prepare the data and build a credit risk model that can be used for a number of applications including generating alpha, issuing protection and securitizing loans into bonds with the desired risk/reward profile. A simple example is used to provide i...

Embrechts and Veraverbeke investigated the renewal risk model and gave a tail equivalence relationship of the ruin probabilities ψ(x) under the assumption that the claim size is heavy-tailed, which is regarded as a classical result in the context of extremal value theory. In this note we extend this result to the delayed renewal risk model.