Asymptotic analysis of dependent risks and extremes in insurance and finance

Liu, Jiajun (2015) Asymptotic analysis of dependent risks and extremes in insurance and finance. PhD thesis, University of Liverpool.

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Abstract

In this thesis, we are interested in the asymptotic analysis of extremes and risks. The heavy-tailed distribution function is used to model the extreme risks, which is widely applied in insurance and is gradually penetrating in finance as well. We also use various tools such as copula, to model dependence structures, and extreme value theorem, to model rare events. We focus on modelling and analysing of extreme risks as well as demonstrate how the derived results that can be used in practice. We start from a discrete-time risk model. More concretely, consider a discrete-time annuity-immediate risk model in which the insurer is allowed to invest its wealth into a risk-free or a risky portfolio under a certain regulation. Then the insurer is said to be exposed to a stochastic economic environment that contains two kinds of risk, the insurance risk and financial risk. The former is traditional liability risk caused by insurance loss while the later is the asset risk resulting from investment. Within each period, the insurance risk is denoted by a real-valued random variable $X$, and the financial risk $Y$ as a positive random variable fulfils some constraints. We are interested in the ruin probability and the tail behaviour of maximum of the stochastic present values of aggregate net loss with Sarmanov or Farlie-Gumbel-Morgenstern (FGM) dependent insurance and financial risks. We derive asymptotic formulas for the finite-ruin probability with lighted-tailed or moderately heavy-tailed insurance risk for both risk-free investment and risky investment. As an extension, we improve the result for extreme risks arising from a rare event, combining simulation with asymptotics, to compute the ruin probability more efficiently. Next, we consider a similar risk model but a special case that insurance and financial risks following the least risky FGM dependence structure with heavy-tailed distribution. We follow the study of Chen (2011) that the finite-time ruin probability in a discrete-time risk model in which insurance and financial risks form a sequence of independent and identically distributed random pairs following a common bivariate FGM distribution function with parameter $-1\leq \theta \leq 1$ governing the strength of dependence. For the subexponential case, when $-1

Item Type:	Thesis (PhD)
Additional Information:	Date: 2015-07 (completed)
Subjects:	?? HA ?? ?? HB ?? ?? HG ?? ?? Q1 ?? ?? QA ??
Divisions:	Faculty of Science and Engineering > School of Physical Sciences
Depositing User:	Symplectic Admin
Date Deposited:	01 Sep 2016 10:54
Last Modified:	17 Dec 2022 02:27
DOI:	10.17638/02042999
URI:	https://livrepository.liverpool.ac.uk/id/eprint/2042999