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A risk model driven by Lévy processes
Author(s) -
Morales Manuel,
Schoutens Wim
Publication year - 2003
Publication title -
applied stochastic models in business and industry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.413
H-Index - 40
eISSN - 1526-4025
pISSN - 1524-1904
DOI - 10.1002/asmb.492
Subject(s) - aggregate (composite) , econometrics , asset (computer security) , mathematical economics , economics , lévy process , relevance (law) , risk model , function (biology) , risk premium , process (computing) , systematic risk , computer science , mathematics , materials science , computer security , evolutionary biology , political science , law , composite material , biology , operating system
We present a general risk model where the aggregate claims, as well as the premium function, evolve by jumps. This is achieved by incorporating a Lévy process into the model. This seeks to account for the discrete nature of claims and asset prices. We give several explicit examples of Lévy processes that can be used to drive a risk model. This allows us to incorporate aggregate claims and premium fluctuations in the same process. We discuss important features of such processes and their relevance to risk modeling. We also extend classical results on ruin probabilities to this model. Copyright © 2003 John Wiley & Sons, Ltd.