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.

Censored symmetric Lévy-type processes

2019 ◽  
Vol 31 (6) ◽  
pp. 1351-1368
Author(s):  
Vanja Wagner
Keyword(s):  
Lévy Process ◽  
Boundary Behavior ◽  
Levy Process ◽  
Green Functions ◽  
Trace Theorem ◽  
Scale Invariant ◽  
Open Set ◽  
Type Spaces ◽  
Complete Bernstein Functions ◽  
Besov Type Spaces

AbstractWe examine three equivalent constructions of a censored symmetric purely discontinuous Lévy process on an open set D; via the corresponding Dirichlet form, through the Feynman–Kac transform of the Lévy process killed outside of D and from the same killed process by the Ikeda–Nagasawa–Watanabe piecing together procedure. By applying the trace theorem on n-sets for Besov-type spaces of generalized smoothness associated with complete Bernstein functions satisfying certain scaling conditions, we analyze the boundary behavior of the corresponding censored Lévy process and determine conditions under which the process approaches the boundary {\partial D} in finite time. Furthermore, we prove a stronger version of the 3G inequality and its generalized version for Green functions of purely discontinuous Lévy processes on κ-fat open sets. Using this result, we obtain the scale invariant Harnack inequality for the corresponding censored process.

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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