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The Estimation of Stochastic Models in Finance with Volatility and Jump Intensity
(University of Waterloo, 2018-10-26)
This thesis covers the parametric estimation of models with stochastic volatility, jumps, and stochastic jump intensity, by FFT. The first primary contribution is a parametric minimum relative entropy optimal Q-measure ...
On the Extrema of Functions in the Takagi Class
(University of Waterloo, 2019-01-23)
The Takagi class is a class of fractal functions on the unit interval generalizing the celebrated Takagi function. In this thesis, we study the extrema of these functions. This is a problem that goes back to J.-P. Kahane ...
Estimation and Assessment of Markov Multistate Models with Intermittent Observations on Individuals
(Springer, 2015-04)
Multistate models provide important methods of analysis for many life history processes, and this
is an area where John Klein made numerous contributions. When individuals in a study group are
observed continuously so ...
Matrix analytic methods for computations in risk theory
(University of Waterloo, 2019-01-15)
The introduction of matrix analytic methods in risk theory has marked a significant progress in computations in risk theory. Matrix analytic methods have proven to be powerful computational tools for numerically analyzing ...
Analysis of Time Dependent Aggregate Claims
(University of Waterloo, 2016-07-22)
Estimation of aggregate claim amounts is a fundamental task in Actuarial science, based on which risk theory, ruin theory and reinsurance theory can be studied. Properties, including moments, Laplace transforms, and ...
Estimation of Finite Population Duration Distributions from Longitudinal Survey Panels with Intermittent Followup
(Springer, 2013)
We consider survival or duration times associated with spells (sojourns in some state) or events experienced
by individuals in a population over a specified time period. Duration distributions can be
estimated from data ...
Multiply Robust Empirical Likelihood Inference for Missing Data and Causal Inference Problems
(University of Waterloo, 2019-06-06)
Missing data are ubiquitous in many social and medical studies. A naive complete-case (CC) analysis by simply ignoring the missing data commonly leads to invalid inferential results. This thesis aims to develop statistical ...
A Statistical Response to Challenges in Vast Portfolio Selection
(University of Waterloo, 2019-07-04)
The thesis is written in response to emerging issues brought about by an increasing number of assets allocated in a portfolio and seeks answers to puzzling empirical findings in the portfolio management area. Over the ...
Event History Analysis in Longitudinal Cohort Studies with Intermittent Inspection Times
(University of Waterloo, 2016-01-20)
Event history studies based on disease clinic data often face several complications. Specifically, patients visit the clinic irregularly, and the intermittent inspection times depend on the history of disease-related ...
Compatibility Problems of Probability Measures for Stochastic Processes
(University of Waterloo, 2018-07-27)
In this thesis, we address three topics in the area of compatibility for probability measures. By "compatibility", we mean the problems concerning the existence of random variables/stochastic processes which generate certain ...