The Study on the Penalty Function of the Insurance Company When the Stock Price Follows Exponential Lévy Process

2009 ◽  
pp. 187-190
Author(s):  
Zhao Wu ◽  
Wang Ding-cheng ◽  
Zeng Yong
Keyword(s):  
Penalty Function ◽  
Stock Price ◽  
Lévy Process ◽  
Levy Process ◽  
Insurance Company ◽  
Exponential Lévy Process

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

scholarly journals Property Claim Services by Compound Poisson Process And Inhomogeneous Levy Process

2018 ◽  
Vol 6 (1) ◽  
pp. 32
Author(s):  
Muhammed A. S. Murad
Keyword(s):  
Poisson Process ◽  
Lévy Process ◽  
Compound Poisson Process ◽  
Levy Process ◽  
Arrival Process ◽  
Compound Poisson ◽  
Process Factor ◽  
Before And After ◽  
Exponential Lévy Process ◽  
Loss Index

In this paper, stochastic compound Poisson process is employed to value the catastrophic insurance options and model the claim arrival process for catastrophic events, which were written in the loss period , during which the catastrophe took place. Here, a time compound process gives the underlying loss index before and after  whose losses are revaluated by inhomogeneous exponential Levy process factor. For this paper, an exponential Levy process is used to evaluate the well-known European call option in order to price Property Claim Services catastrophe insurance based on catastrophe index.

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.

scholarly journals Finite-time ruin probability with an exponential Lévy process investment return and heavy-tailed claims

2009 ◽  
Vol 41 (1) ◽  
pp. 206-224 ◽  
Author(s):  
C. C. Heyde ◽  
Dingcheng Wang
Keyword(s):  
Finite Time ◽  
Lévy Process ◽  
Financial Risk ◽  
Risk Model ◽  
Levy Process ◽  
Insurance Risk ◽  
Total Risk ◽  
Investment Return ◽  
Exponential Lévy Process ◽  
Heavy Tailed

By expressing the discounted net loss process as a randomly weighted sum, we investigate the finite-time ruin probabilities for the Poisson risk model with an exponential Lévy process investment return and heavy-tailed claims. It is found that in finite time, however, the extreme of insurance risk dominates the extreme of financial risk, but, for the case of dangerous investment (see Klüppelberg and Kostadinova (2008) for an accurate definition of dangerous investment), the extreme of financial risk has more and more of an effect on the total risk, and as time passes, the extreme of financial risk finally dominates the extreme of insurance risk.

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