Weak convergence approach to compound Poisson risk processes perturbed by diffusion

Sarkar, Joykrishna; Sen, Arusharka

doi:10.1016/j.insmatheco.2005.02.007

Cited by 11 publications

(6 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The results we present here extend previous work of Furrer [6], Albrecher et al [1], Tsai and Wilmott [15] and Kolkovska and Martín-González [11]. Weak approximations in risk theory have been used in Sarkar and Sen [13] in the case α = 2 and λ 2 = 0, and in Furrer et al [7] in the case λ 2 = 0 to estimate ruin probabilities within finite time horizon.…”

Section: Introductionsupporting

confidence: 82%

Path functionals of a class of Lévy insurance risk processes

Kolkovska¹,

Martín-González²

2016

COSA

View full text Add to dashboard Cite

Abstract. We study expected discounted penalty functionals for a class of Lévy processes having a component given by the difference of two independent Poisson compound processes, and a perturbation term given by an α-stable process. We obtain a formula for the Laplace transforms of the expected discounted penalty functionals, as well as explicit representations of such functionals as infinite series of convolutions of given functions. We illustrate our results in some particular examples.

show abstract

Section: Introductionsupporting

confidence: 82%

Path functionals of a class of Lévy insurance risk processes

Kolkovska¹,

Martín-González²

2016

COSA

View full text Add to dashboard Cite

show abstract

“…One should note that the diffusion perturbation W (t) in (9.1) could itself be obtained as a limit of a family of independent compound Poisson processes, see for instance Sarkar and Sen (2005).…”

Section: Perturbation By Diffusionmentioning

confidence: 99%

A Direct Approach to the Discounted Penalty Function

Albrecher

Gerber

Yang

2010

North American Actuarial Journal

View full text Add to dashboard Cite

This paper provides a new and accessible approach to establishing certain results concerning the discounted penalty function. The direct approach consists of two steps. In the first step, closed form expressions are obtained in the special case where the claim amount distribution is a combination of exponential distributions. A rational function is useful in this context. For the second step, one observes that the family of combinations of exponential distributions is dense. Hence, it suffices to reformulate the results of the first step to obtain general results. The surplus process has downward and upward jumps, modeled by two independent compound Poisson processes. If the distribution of the upward jumps is exponential, a series

show abstract

“…Our hope is to carry over results form the classical model to the diffusion model by taking limits. This idea has also been exploited by Sarkar and Sen (2005). In order to work this idea out we have to establish a limit result for the Markov-modulated model.…”

Section: Diffusion Approximationmentioning

confidence: 99%