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Simulations on Lévy subordinators and Lévy driven contagion models

Qu, Yan (2019) Simulations on Lévy subordinators and Lévy driven contagion models. PhD thesis, The London School of Economics and Political Science (LSE).

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Abstract

Lévy subordinators have become a fundamental component to be used to construct many useful stochastic processes, which have numerous applications in finance, insurance and many other fields. However, as many applications of Lévy based stochastic models use fairly complicated analytical and probabilistic tools, it has been challenging to implement in practice. Hence, simulation-based study becomes more desirable. In this thesis, we deal with exact simulation on Lévy subordinators and Lévy driven stochastic models. In the first part, we focus on developing more efficient exact simulation schemes for Lévy subordinators with existing simulation algorithms in the literature. Besides, we also introduce a new type of Lévy subordinators, i.e. truncated Lévy subordinators. We study the path properties, develop exact simulation algorithms based on marked renewal representations, and provide relevant applications in finance and insurance. The associated results in this part are later used in the sequel. The second part of this thesis proposes a new type of point processes by generalising the classical self-exciting Hawkes processes and doubly stochastic Poisson processes with Lévy driven Ornstein-Uhlenbeck type intensities. These resulting models are analytically tractable, and intrinsically inherit the great flexibility as well as desirable features from the two original processes, including skewness, leptokurtosis, mean-reverting dynamics, and more importantly, the contagion or feedback effects. These newly constructed processes would then substantially enrich continuous-time models tailored for quantifying the contagion of event arrivals in finance, economics, insurance, queueing and many other fields. In turn, we characterise the distributional properties of this new class of point processes and design an exact simulation algorithm to generate sample paths. This is done by applying the exact distributional decomposition technique. We carry out extensive numerical implementations and tests to demonstrate the accuracy and effectiveness of our scheme and give examples of some financial applications to credit portfolio risk to show the applicability and flexibility of our new model.

Item Type: Thesis (PhD)
Additional Information: © 2019 Yan Qu
Library of Congress subject classification: Q Science > QA Mathematics
Sets: Departments > Statistics
Supervisor: Dassios, Angelos
URI: http://etheses.lse.ac.uk/id/eprint/3947

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