Uniform asymptotic estimates for ruin probabilities of renewal risk models with exponential Lévy process investment returns and dependent claims

2012 ◽  
Vol 29 (3) ◽  
pp. 295-313 ◽  
Author(s):  
Fenglong Guo ◽  
Dingcheng Wang
Keyword(s):  
Lévy Process ◽  
Levy Process ◽  
Ruin Probabilities ◽  
Asymptotic Estimates ◽  
Risk Models ◽  
Investment Returns ◽  
Exponential Lévy Process ◽  
Renewal Risk

scholarly journals Uniform Asymptotics for Discounted Aggregate Claims in Dependent Risk Models

2014 ◽  
Vol 51 (3) ◽  
pp. 669-684 ◽  
Author(s):  
Yang Yang ◽  
Kaiyong Wang ◽  
Dimitrios G. Konstantinides
Keyword(s):  
Lévy Process ◽  
Tail Probability ◽  
Levy Process ◽  
Insurance Company ◽  
Risk Models ◽  
Heavy Tailed Distributions ◽  
Discounted Aggregate Claims ◽  
Aggregate Claims ◽  
Heavy Tailed ◽  
Renewal Risk

In this paper we consider some nonstandard renewal risk models with some dependent claim sizes and stochastic return, where an insurance company is allowed to invest her/his wealth in financial assets, and the price process of the investment portfolio is described as a geometric Lévy process. When the claim size distribution belongs to some classes of heavy-tailed distributions and a constraint is imposed on the Lévy process in terms of its Laplace exponent, we obtain some asymptotic formulae for the tail probability of discounted aggregate claims and ruin probabilities holding uniformly for some finite or infinite time horizons.

Uniform Asymptotics for Discounted Aggregate Claims in Dependent Risk Models

2014 ◽  
Vol 51 (03) ◽  
pp. 669-684 ◽  
Author(s):  
Yang Yang ◽  
Kaiyong Wang ◽  
Dimitrios G. Konstantinides
Keyword(s):  
Lévy Process ◽  
Tail Probability ◽  
Levy Process ◽  
Insurance Company ◽  
Risk Models ◽  
Heavy Tailed Distributions ◽  
Discounted Aggregate Claims ◽  
Aggregate Claims ◽  
Heavy Tailed ◽  
Renewal Risk

In this paper we consider some nonstandard renewal risk models with some dependent claim sizes and stochastic return, where an insurance company is allowed to invest her/his wealth in financial assets, and the price process of the investment portfolio is described as a geometric Lévy process. When the claim size distribution belongs to some classes of heavy-tailed distributions and a constraint is imposed on the Lévy process in terms of its Laplace exponent, we obtain some asymptotic formulae for the tail probability of discounted aggregate claims and ruin probabilities holding uniformly for some finite or infinite time horizons.

scholarly journals Applications of factorization embeddings for Lévy processes

2006 ◽  
Vol 38 (03) ◽  
pp. 768-791 ◽  
Author(s):  
A. B. Dieker
Keyword(s):  
Lévy Process ◽  
Joint Distribution ◽  
Lévy Processes ◽  
Levy Processes ◽  
Levy Process ◽  
Tail Asymptotics ◽  
Lévy Measure ◽  
Risk Models ◽  
General Properties ◽  
Phase Type

We give three applications of the Pecherskii-Rogozin-Spitzer identity for Lévy processes. First, we find the joint distribution of the supremum and the epoch at which it is ‘attained’ if a Lévy process has phase-type upward jumps. We also find the characteristics of the ladder process. Second, we establish general properties of perturbed risk models, and obtain explicit fluctuation identities in the case that the Lévy process is spectrally positive. Third, we study the tail asymptotics for the supremum of a Lévy process under different assumptions on the tail of the Lévy measure.

First exit from an open set for a matrix-exponential Lévy process

2017 ◽  
Vol 127 ◽  
pp. 104-110
Author(s):  
Yu-Ting Chen ◽  
Yu-Tzu Chen ◽  
Yuan-Chung Sheu
Keyword(s):  
Lévy Process ◽  
Matrix Exponential ◽  
Levy Process ◽  
Open Set ◽  
Exponential Lévy Process
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