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In this Master thesis, we use a singular and regular perturbation theory to derive an analytic approximation formula for the expected discounted penalty function. Our model is an extension of Cramer–Lundberg extended classical model because we consider a more general insurance risk model in which the compound Poisson risk process is perturbed by a Brownian motion multiplied by a stochastic volatility driven by two factors- which have mean reversion models. Moreover, unlike the classical model, our model allows a ruin to be caused either by claims or by surplus’ fluctuation. We compute explicitly the first terms of the asymptotic expansion and we show that they satisfy either an integro-differential equation or a Poisson equation. In addition, we derive the existence and uniqueness conditions of the risk model with two stochastic volatilities factors.

We consider weak convergence of a sequence of asset price models (Sn) to a limiting asset price model S. A typical case for this situation is the convergence of a sequence of binomial models to the Black-Scholes model, as studied by Cox, Ross, and Rubinstein. We put emphasis on two different aspects of this convergence: firstly we consider convergence with respect to the given "physical" probability measures (Pn) and secondly with respect to the "risk-neutral" measures (Qn) for the asset price processes (Sn). (In the case of non-uniqueness of the risk-neutral measures also the question of the "good choice" of (Qn) arises.) In particular we investigate under which conditions the weak convergence of (Pn) to P implies the weak convergence of (Qn) to Q and thus the convergence of prices of derivative securities. The main theorem of the present paper exhibits an intimate relation of this question with contiguity properties of the sequences of measures (Pn) with respect to (Qn) which in turn is closely connected to asymptotic arbitrage properties of the sequence (Sn) of security price processes. We illustrate these results with general homogeneous binomial and some special trinomial models. (author's abstract) / Series: Report Series SFB "Adaptive Information Systems and Modelling in Economics and Management Science"

Thesis (Ph. D.)--University of California, San Diego, 2008. / Title from first page of PDF file (viewed June 16, 2008). Available via ProQuest Digital Dissertations. Vita. Includes bibliographical references (p. 158-164).

Thesis (Ph. D.)--Ohio State University, 2004. / Title from first page of PDF file. Document formatted into pages; contains viii, 140 p.; also includes graphics. Includes bibliographical references (p. 139-140).

Thesis (Ph. D.)--Ohio State University, 2003. / Title from first page of PDF file. Document formatted into pages; contains x, 227 p.; also includes graphics Includes bibliographical references (p. 224-227). Available online via OhioLINK's ETD Center

Thesis (M.SC.) - Carleton University, 2007. / Includes bibliographical references (p. 51-52). Also available in electronic format on the Internet.

Thesis (Ph. D.)--Carleton University, 1992. / Also available in electronic format on the Internet.

Thesis (doctoral)--Universität Bonn, 1988. / Includes bibliographical references (p. 99-102).

Liu, Li. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2009. / Includes bibliographical references (leaves 41-44). / Abstract also in Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Empirical Likelihood --- p.1 / Chapter 1.2 --- Empirical Likelihood for Dependent Data --- p.4 / Chapter 1.2.1 --- Spectral Method --- p.5 / Chapter 1.2.2 --- Blockwise Method --- p.6 / Chapter 1.3 --- Edgeworth Expansions and Bartlett Correction --- p.9 / Chapter 1.3.1 --- Coverage Errors --- p.10 / Chapter 1.3.2 --- Edgeworth Expansions --- p.11 / Chapter 1.3.3 --- Bartlett Correction --- p.13 / Chapter 2 --- Bartlett Correction for EL --- p.16 / Chapter 2.1 --- Empirical Likelihood in Time Series --- p.16 / Chapter 2.2 --- Stochastic Expansions of EL in Time Series --- p.19 / Chapter 2.3 --- Edgeworth Expansions of EL in Time Series --- p.22 / Chapter 2.3.1 --- Validity of the Formal Edgeworth Expansions --- p.22 / Chapter 2.3.2 --- Cumulant Calculations --- p.24 / Chapter 2.4 --- Main Results --- p.30 / Chapter 3 --- Simulations --- p.32 / Chapter 3.1 --- Confidence Region --- p.33 / Chapter 3.2 --- Coverage Error of Confidence Regions --- p.35 / Chapter 4 --- Conclusion and Future Work --- p.38 / Bibliography --- p.41