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Title: Simulations on Lévy subordinators and Lévy driven contagion models
Author: Qu, Yan
ISNI:       0000 0004 7970 5598
Awarding Body: London School of Economics and Political Science (LSE)
Current Institution: London School of Economics and Political Science (University of London)
Date of Award: 2019
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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.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: QA Mathematics