Thesis (Ph. D.)--University of Texas at Austin, 2002. / Vita. Includes bibliographical references.

Thesis (M.S.)--Missouri University of Science and Technology, 2009. / Vita. The entire thesis text is included in file. Title from title screen of thesis/dissertation PDF file (viewed August 10, 2009) Includes bibliographical references.

Thesis (Ph.D.)--Ohio University, March, 2005. / Title from PDF t.p. Includes bibliographical references (p. 152-159)

This study gives a phenomenologically based stochastic model of space-time rainfall. Specifically, two random variables on the spatial rainfall, e.g., the cumulative rainfall within a season and the maximum cumulative rainfall per rainfall event within a season are considered. An approach is given to determine the cumulative distribution function (c.d.f.) of the cumulative rainfall per event, based on a particular random structure of space-time rainfall. Then the first two moments of the cumulative seasonal rainfall are derived based on a stochastic dependence between the cumulative rainfall per event and the number of rainfall events within a season. This stochastic dependence is important in the context of the spatial rainfall process. A theorem is then proved on the rate of convergence of the exact c.d.f. of the seasonal cumulative rainfall up to the iᵗʰ year, i ≥ 1, to its limiting c.d.f. Use of the limiting c.d.f. of the maximum cumulative rainfall per rainfall event up to the iᵗʰ year within a season is given in the context of determination of the 'design rainfall'. Such information is useful in the design of hydraulic structures. Special mathematical applications of the general theory are developed from a combination of empirical and phenomenological based assumptions. A numerical application of this approach is demonstrated on the Atterbury watershed in the Southwestern United States.

Ph. D, Faculty of Science, University of Witwatersrand, 2011 / Research in the area of stochastic models for actuarial use in South Africa is limited to relatively few publications. Until recently, there has been little focus on actuarial stochastic models that describe the empirical stochastic behaviour of South African financial and economic variables. A notable exception is Thomson’s (1996) proposed methodology and model. This thesis presents a collection of five papers that were presented at conferences or submitted for peer review in the South African Actuarial Journal between 1996 and 2006. References to subsequent publications in the field are also provided. Such research has implications for medium and long-term financial simulations, capital adequacy, resilience reserving and asset allocation benchmarks as well as for the immunization of short-term interest rate risk, for investment policy determination and the general quantification and management of risk pertaining to those assets and liabilities. This thesis reviews Thomson’s model and methodology from both a statistical and economic perspective, and identifies various problems and limitations in that approach. New stochastic models for actuarial use in South Africa are proposed that improve the asset and liability modelling process and risk quantification. In particular, a new Multiple Markov-Switching (MMS) model framework is presented for modelling South African assets and liabilities, together with an optimal immunization framework for nominal liability cash flows. The MMS model is a descriptive model with structural features and parameter estimates based on historical data. However, it also incorporates theoretical aspects in its design, thereby providing a balance between purely theoretical models and those based only on empirical considerations.

Cheung Ying Lok. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2004. / Includes bibliographical references (leaves 46-47). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Review on the fast mean-reverting stochastic volatility --- p.5 / Chapter 2.1 --- Estimation of mcan reversion ratc --- p.5 / Chapter 2.2 --- Methodology of pricing European option --- p.6 / Chapter 2.3 --- Capturing European smiles --- p.7 / Chapter 2.4 --- Model settings to GAO --- p.9 / Chapter 3 --- Pricing GAOs in asymptotic expansions --- p.12 / Chapter 3.1 --- Floating strike gcomctric Asian call --- p.16 / Chapter 3.2 --- Fixed strike gcomctric Asian call --- p.19 / Chapter 3.3 --- General gcomctric Asian claims --- p.21 / Chapter 4 --- Accuracy of pricing approximation --- p.24 / Chapter 5 --- Volatility smiles and calibration --- p.38 / Chapter 5.1 --- Capturing Asian smiles --- p.39 / Chapter 5.2 --- Capturing Asian and European smiles together --- p.41 / Chapter 6 --- Conclusion --- p.44 / References --- p.46 / Graphs --- p.48

令B{U+209C}表示一個平面布朗運動。我們把C \B[0, 1] 的無界連通分支的邊界稱爲B[0; 1] 的外邊界。在本文中，我們將討論如何計算B[0,1] 的外邊界的Hausdorff 維數。 / 我們將在第二章討論Lawler早期的工作[7]。他定義了一個常數ζ(所謂的不聯通指數） 。利用能量的方法， 他證明了 B[0,1]的外邊界的Hausdorff維數是2(1 - ζ)概率大於零， 然後0-1律可以明這個概率就是1。但是用他的方法我們不能算出ζ的準確值。 / Lawler, Schramm and Werner 在一系列文章[10]，[11] 和[13] 中研究了SLE{U+2096}和excursion 測度。利用SLE6 和excursion 測度的共形不變性，他們可以計算出了布朗運動的相交指數ξ (j; λ )。因此ζ = ξ (2; 0)/2 = 1/3，由此可以知道B[0, 1] 的外邊界的Hausdorff 維數就是4/3。從而可以說完全證明了著名的Mandelbrot 猜想。 / Let B{U+209C} be a Brownian motion on the complex plane. The frontier of B[0; 1] is defined to be the boundary of the unbounded connected component of C\B[0; 1].In this thesis, we will review the calculation of the Hausdorff dimension of the frontier of B[0; 1]. / We first dissuss the earlier work of Lawler [7] in Chapter 2. He defined a constant ζ (so called the dimension of disconnection exponent). By using the energy method, he proved that with positive probability the Hausdorff dimension of the frontier of B[0; 1] is 2(1 -ζ ), then zero-one law show that the probability is one. But we can not calculate the exact value of ζ in this way. / In the series of papers by Lawler, Schramm and Werner [10], [11] and [13], they studied the SLE{U+2096} and excursion measure. By using the conformal invariance of SLE₆ and excursion measure, they can calculate the exact value of the Brownian intersection exponents ξ(j, λ). Consequently, ζ = ξ(2, 0)/2 = 1/3, and the Hausdorff dimension of the frontier of B [0,1] is 4/3 almost surely. This answers the well known conjecture by Mandelbrot positively. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Zhang, Pengfei. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2012. / Includes bibliographical references (leaves 53-55). / Abstracts also in Chinese. / Chapter 1 --- Introduction --- p.6 / Chapter 2 --- Hausdorff dimension of the frontier of Brownian motion --- p.11 / Chapter 2.1 --- Preliminaries --- p.11 / Chapter 2.2 --- Hausdorff dimension of Brownian frontier --- p.13 / Chapter 3 --- Stochastic Loewner Evolution --- p.24 / Chapter 3.1 --- Definitions --- p.24 / Chapter 3.2 --- Continuity and Transience --- p.26 / Chapter 3.3 --- Locality property of SLE₆ --- p.30 / Chapter 3.4 --- Crossing exponent for SLE₆ --- p.32 / Chapter 4 --- Brownian intersection exponents --- p.37 / Chapter 4.1 --- Half-plane exponent --- p.37 / Chapter 4.2 --- Whole-plane exponent --- p.41 / Chapter 4.3 --- Proof of Theorem 4.6 and Theorem 4.7 --- p.44 / Chapter 4.4 --- Proof of Theorem 1.2 --- p.47 / Chapter A --- Excursion measure --- p.48 / Chapter A.1 --- Metric space of curves --- p.48 / Chapter A.2 --- Measures on metric space --- p.49 / Chapter A.3 --- Excursion measure on K --- p.49 / Bibliography --- p.53

Thesis (M. Phil.)--University of Hong Kong, 2006. / Title proper from title frame. Also available in printed format.

Thesis (Ph. D.)--Rutgers University, 2008. / "Graduate Program in Mathematics." Includes bibliographical references (p. 147-153).

Thesis (Ph.D.)--University of Texas at Arlington, 2008.