Ruin probabilities and optimal investment when the stock price follows an exponential Lévy process

2015 ◽  
Vol 259 ◽  
pp. 1030-1045
Author(s):  
Ping Li ◽  
Wu Zhao ◽  
Wei Zhou
Keyword(s):  
Stock Price ◽  
Lévy Process ◽  
Optimal Investment ◽  
Levy Process ◽  
Ruin Probabilities ◽  
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.

Ruin probabilities for competing claim processes

2004 ◽  
Vol 41 (03) ◽  
pp. 679-690 ◽  
Author(s):  
Miljenko Huzak ◽  
Mihael Perman ◽  
Hrvoje Šikić ◽  
Zoran Vondraček
Keyword(s):  
Ruin Probability ◽  
Lévy Process ◽  
Risk Process ◽  
Levy Process ◽  
Ruin Probabilities ◽  
Classical Risk Process ◽  
Risk Processes

Let C 1, C 2,…,C m be independent subordinators with finite expectations and denote their sum by C. Consider the classical risk process X(t) = x + ct - C(t). The ruin probability is given by the well-known Pollaczek–Khinchin formula. If ruin occurs, however, it will be caused by a jump of one of the subordinators C i . Formulae for the probability that ruin is caused by C i are derived. These formulae can be extended to perturbed risk processes of the type X(t) = x + ct - C(t) + Z(t), where Z is a Lévy process with mean 0 and no positive jumps.

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