Statistics and Actuarial Science - Theses, Dissertations, and other Required Graduate Degree Essays

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Pricing and dynamic hedging of segregated fund guarantees

Author: 
Date created: 
2010-11-25
Abstract: 

Guaranteed minimum maturity benefit and guaranteed minimum death benefit offered by a single premium segregated fund contract are priced. A dynamic hedging approach is used to determine the value of these guarantees. Cash flow projections are used to analyze the loss or profit to the insurance company. Optimally exercised reset options are priced by the Crank-Nicolson method. Reset options, assuming they are exercised only when the funds exceed a given threshold, are priced using simulations. Finally, we study the distribution of the loss or profit for segregated funds with reset option under a dynamic hedging strategy with an allowance for transaction costs.

Document type: 
Graduating extended essay / Research project
File(s): 
Senior supervisor: 
Cary Chi-Liang Tsai
Department: 
Science: Department of Statistics and Actuarial Science
Thesis type: 
(Project) M.Sc.

Analyzing investment return of asset portfolios with multivariate Ornstein-Uhlenbeck processes

Author: 
Date created: 
2010-12-16
Abstract: 

The investment return rates of an asset portfolio can be fitted and analyzed by one univariate Ornstein-Uhlenbeck (O-U) process (global model), several univariate O-U processes (univariate model) or one multivariate O-U process (multivariate model). The expected values, variances and covariance of the instantaneous and accumulated return rates of different asset portfolios are calculated from the three models and compared. Furthermore, we price for annuity products, optimize asset allocation strategy and compare the results. The multivariate model is the most comprehensive and complete of the three models in term of fully capturing the correlation among the assets in a single portfolio.

Document type: 
Graduating extended essay / Research project
File(s): 
Senior supervisor: 
Gary Parker
Department: 
Science: Department of Statistics and Actuarial Science
Thesis type: 
(Project) M.Sc.

Modeling uncertainty and heterogeneity in mark-recapture and occupancy experiments

Date created: 
2010-10-07
Abstract: 

Ecological data sets often present problems such as detection, heterogeneity and uncertainty. Capture-recapture and occupancy frameworks deal with issues of detection for individuals and species respectively. Although developed separately, both share commonalities that are highlighted in this thesis. We present two developments in capture-recapture and one in occupancy. In capture-recapture experiments parameter heterogeneity is often dealt with by stratifying the population in advance (e.g. by sex), but strata assignment may not always be possible. For example in the MilleLacs fishery, catachability is known to differ by sex, but sex could not be determined on all sampling occasions leaving some individuals with an “unknown” sex designation. This heterogeneity can severely bias estimates of abundance if the data are simply pooled and treated as coming from a single large population. In the first development the super-population approach is extended to handle uncertainty in strata assignments. Heterogeneity in catchability can also be result when animals do not behave in a completely independent fashion. The assumption of independence is a long-standing assumption of capture-recapture models and is known almost never to hold. We take the first steps to relaxing this assumption by modeling the dependency in capture outcomes between pair-bonded individuals. Animals in a pair-bond remain in close proximity to one another, and if one member of the pair is observed, we are also more likely to observe the other member. We estimate the “correlation” (termed rho) in capture events using simulated data, as the motivating example (a harlequin duck study) was more complicated than originally expected. In the final development we highlight the similarities between capture-recapture and occupancy models by rewriting occupancy models to use the capture-recapture multievent approach. In this development we also provide design protocols for permanent and temporary site monitoring and provide a power analysis comparing the efficiency of both protocols to detect changes in relative abundance. Finally, we provide a complicated multi-year analysis of the anuran frog data set to demonstrate the ability of the proposed framework to handle complex biological problems.

Document type: 
Thesis
File(s): 
Senior supervisor: 
Carl James Schwarz
Department: 
Science: Department of Statistics and Actuarial Science
Thesis type: 
(Thesis) Ph.D.

A comparison of location effect identification methods for unreplicated fractional factorials in the presence of dispersion effects

Author: 
Date created: 
2010-12-08
Abstract: 

Unreplicated fractional factorial designs are usually used to identify location effects and dispersion effects in screening experiments. Various methods for identifying active location effects have been proposed during last three decades. All of these methods depend on the assumption of no dispersion effects. Meanwhile most of the dispersion-identification methods rely on first identifying the correct location effect model. The presence of dispersion effects induces correlation among location effect estimates. If location-effect identification methods are sensitive to this correlation, then finding the correct location model may be more difficult in the presence of dispersion effects. The primary aim of this project is to compare the robustness of different location-identification methods - Box and Meyer (1986), Lenth (1989), Berk and Picard (1991), and Loughin and Noble (1997) - under the heteroscedastic model via simulation studies. Confounding of location and dispersion effects has also been investigated here.

Document type: 
Graduating extended essay / Research project
File(s): 
Senior supervisor: 
Thomas Loughin
Department: 
Science: Department of Statistics and Actuarial Science
Thesis type: 
(Project) M.Sc.

Analysis of variable benefit plans

Date created: 
2010-07-08
Abstract: 

The operational characteristics of a target benefit plan with fixed annual contributions and variable benefit accruals based on an aggregate funding requirement are studied both analytically and by simulation under the assumption of a constant valuation rate and log-normal returns. The distribution of the pension entitlement at retirement is compared under three different parameter sets for asset returns. The performance of the target benefit plan is then compared to a DC benchmark, both in terms of the proximity of the retirement benefits to the targeted benefit level and in terms of intergenerational equity. Finally, two practical modifications to the benefit policy are considered and their effect on performance is assessed.

Document type: 
Graduating extended essay / Research project
File(s): 
Senior supervisor: 
Gary Parker
Department: 
Science: Department of Statistics and Actuarial Science
Thesis type: 
(Project) M.Sc.

Robust estimation for differential equations, time series analysis on climate change and MCMC simulation of duration-of-load problem

Author: 
Date created: 
2010-08-11
Abstract: 

Usually we need to estimate the unknown parameters of Ordinary Differential Equations based on given data. We propose a robust method in which the parameters are estimated in two levels of optimization. Simulation studies show that the robust method gives satisfactory results. We also apply the robust method to a real ecological data set.Standard normal homogeneity test and Yao and Davis' test are two widely used methods in climate study. We generate data from four models and examine whether these two tests are sensitive to different models. We also apply these methods to the climate data of Barkerville, BC.Duration-of-load problem is of great importance in wood engineering. We present literature reviews of three papers in this field. Then we conduct Markov Chain Monte Carlo simulation to explore the empirical probability densities of the break time of lumbers under different models.

Document type: 
Graduating extended essay / Research project
File(s): 
Senior supervisor: 
Jiguo Cao
Department: 
Science: Department of Statistics and Actuarial Science
Thesis type: 
(Project) M.Sc.

Developments in computer model calibration

Date created: 
2010-08-03
Abstract: 

Computer models enable scientists to investigate real-world phenomena virtually using com- puter experiments. Recently, statistical calibration enabled scientists to incorporate field data and estimate unknown physical constants. In this thesis, we outline three new developments for the statistical calibration of computer models. The first development is a practical approach for calibrating large and non-stationary computer model output. We present a new computationally efficient approach using a criterion that measures the discrepancy between the computer model and field data. One can then construct empirical distributions for the parameters and sequentially add design points to improve these estimates. The strength of this approach is its simple computation using existing algorithms. Our method also provides good parameter estimates for large and non-stationary data. The second development deals with incorporating derivative information from the computer model into a calibration experiment. Many computer models are governed by differential equations, and including this derivative information can be helpful. Although incorporating such information has garnered a lot of attention in some areas of statistics, such as penalized regression, it has been largely ignored in computer experiments. We develop a new statistical methodology for the calibration of a computer model when derivative information is additionally available. The final development deals with extending the methodology incorporating derivatives to allow for the inclusion of possible bias in the computer model. A statistical model accounting for such bias was previously proposed, but heavily criticised as not being identifiable. We develop a model that accounts for this possible bias while simultaneously including the derivative information from the computer model in the hopes that such identifiability issues can be reduced or eliminated. Our results indicate some modest improvements over the previous approach in some experimental conditions. Proving exact conditions where such models can be identified remains interesting and challenging research to explore in future work.

Document type: 
Thesis
File(s): 
Senior supervisor: 
Derek Bingham
Department: 
Science: Department of Statistics and Actuarial Science
Thesis type: 
(Thesis) Ph.D.

Impact of abolishment of mandatory retirement on BC employment income

Author: 
Date created: 
2011-12-15
Abstract: 

Amendments to the provincial Human Rights Code effectively abolished mandatory retirement in BC in 2008. Additionally, the Canadian population is aging. The seniors, 65 years of age or older, constitute the fastest growing population group. These facts are expected to have an impact on the insurance and pension industry as well as on social programs. In this project, we study the total employment income in BC. The total income in BC is projected, first, using pre-legislation retirement rates and secondly, using post-legislation retirement rates that are based on a survey of Canadian workers. The workforce is projected using a two-decrement model, with death and retirement as the two causes of decrement. Average annual salaries by age are then applied to the projected workforces to get the total income in BC. Prediction intervals are calculated and sensitivity analysis is performed for some of the key assumptions.

Document type: 
Graduating extended essay / Research project
File(s): 
Senior supervisor: 
Gary Parker
Department: 
Science: Department of Statistics and Actuarial Science
Thesis type: 
(Project) M.Sc.

Models and methods for spatial data: applications in epidemiological, environmental and ecological studies

Author: 
Date created: 
2011-08-24
Abstract: 

This thesis develops new methodologies for applied problems using smoothing techniques for spatial or spatial temporal data. We investigate Bayesian ranking methods for identifying high risk areas in disease mapping, assessing these particularly withregard their performance in isolating emerging unusual and extreme risks in small areas. We build on information obtained through mapping multivariate outcomes by developing models which investigate if the multivariate spatial outcomes share the same underlying spatial structure. We develop a general framework for joint modeling of multivariate spatial outcomes for count and zero-inflated count data using a common spatial factor model. We also study spatial exposure measures, motivated by an analysis of Comandra blister rust infection on lodgepole pine trees from British Columbia. We contrast nearest distance with other, more general, exposure measures and consider the impact of mis-specification of exposure measures in a semiparametric generalized additive modeling framework including a spatial residual term modeled as thin plate regression spline. An appealing feature of the new spatial exposure measures considered is that they can be easily adapted to other problems, such as investigation of the association of asthma incidence to traffic exposures. A common theme in the thesis is the use of functional data analysis, and we specifically adapt such methods for assessing spatial and temporal variation of Cadmium concentration in Pacific oysters from British Columbia. The methodologies developed in these projects widen the toolbox for spatial analysis in applications in epidemiology, and in environmental and ecological studies.

Document type: 
Thesis
File(s): 
Senior supervisor: 
Charmaine Dean
Department: 
Science: Department of Statistics and Actuarial Science
Thesis type: 
(Thesis) Ph.D.

Survival models for data arising from multiphase hazards, latent subgroups or subject to time-dependent treatment effects

Date created: 
2011-08-24
Abstract: 

Studies of time-to-event outcomes are among the most common in many areas of scientific research, particularly medicine. Ubiquitous in subject-area literature for this research, is the Cox model; a model which assumes that the instantaneous risk of failure is proportional for different groups of people with similar covariate values. The Cox model has become so pervasive in communicating results that the verification of this assumption is rarely mentioned in subject-area literature and alternative methods are even more rarely attempted. Unfortunately, the mechanisms leading to violation of this assumption can often be accounted for with alternative models yielding only slightly more complex interpretation than the standard Cox model. Motivated by a dataset capturing survival following coronary artery bypass graft surgery and another containing longitudinal tree growth and mortality, this thesis will describe, compare/contrast and provide interpretations of several models addressing specific pathologies which lead to violation of the proportional hazards assumption. In these models, the proportional hazards structure will be maintained in part, but be augmented to accommodate specific situations. Interpretations of these augmented proportional-hazards models will be a key element of the comparisons. Three different pathologies will be investigated, including complex (ie: multi-phase) hazard functions, latent mixtures of individuals subject to distinct hazards, and effects of covariates which change over time either through a direct erosion of the effect or indirectly through complex longitudinal mechanisms. Additional scientific questions related to inference on duration of different risk phases or latent group membership will be enabled by these models. Related to these questions, a novel procedure incorporating covariate information into risk-phase durations will be presented. Further, through connections to the rapidly evolving field of joint modeling of longitudinal and time-to-event data, the utility of joint models to fully characterize the mechanisms underlying an overall, possibly time-dependent treatment effect will be explored. An application of joint models to interval-censored survival data including a novel, recursive, event-time imputation method exploiting the relationship between longitudinal data and the failure mechanism will be described.

Document type: 
Thesis
File(s): 
Senior supervisor: 
Charmaine Dean
Department: 
Science: Department of Statistics and Actuarial Science
Thesis type: 
(Thesis) Ph.D.