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Option pricing models and their application to insurance and financial risks. Discrete-time models. Black-Scholes-Merton model. Market-making, option Greeks, and hedging. Exotic options. Economic scenario generators. Students with credit for ACMA 340 or RISK 441 may not take this course for further credit.

Advanced models and methods used in the valuation and management of long-term insurance coverages. Topics include cash-flow based profit analysis of modern life insurance products (universal life insurance, equity-linked insurance, and contracts with embedded options), stochastic pricing and reserving, and stochastic longevity models. Corequisite: RISK 801. Students with credit for RISK 412 may not take this course for further credit.

Risk measures. Extreme value theory: models and applications. Aggregate models for claims. Regression-based approaches to claims modeling: generalized linear models, linear mixed models. Students with credit for RISK (or ACMA) 421 may not take this course for further credit.

Economic perspectives on risk and insurance. Multivariate risk models, copulas and dependence. Risk aggregation and capital allocation. Risk management in practice. Students with credit for ACMA 832 may not take this course for further credit.

Students with credit for ACMA 850 may not take this course for further credit.

The statistical theory that supports modern statistical methodologies. Distribution theory, methods for construction of tests, estimators, and confidence intervals with special attention to likelihood and Bayesian methods. Properties of the procedures including large sample theory will be considered. Consistency and asymptotic normality for maximum likelihood and related methods (e.g., estimating equations, quasi-likelihood), as well as hypothesis testing and p-values. Additional topics may include: nonparametric models, the bootstrap, causal inference, and simulation. Prerequisite: STAT 450 or permission of the instructor. Students with credit for STAT 801 may not take this course for further credit.

Advanced mathematical statistics for PhD students. Topics in probability theory including densities, expectation and random vectors and matrices are covered. The theory of point estimation including unbiased and Bayesian estimation, conditional distributions, variance bounds and information. The theoretical framework of hypothesis testing is covered. Additional topics that may be covered include modes of convergence, central limit theorems for averages and medians, large sample theory and empirical processes. Prerequisite: STAT 830 or permission from the instructor.

An introduction to smoothing and modelling of functional data. Basis expansion methods, functional regression models and derivative estimation are covered. Prerequisite: STAT 830 or permission of the instructor.

A modern approach to normal theory for general linear models including models with random effects and "messy" data. Topics include experimental units, blocking, theory of quadratic forms, linear contrasts, analysis of covariance, heterogeneous variances, factorial treatment structures, means comparisons, missing data, multi-unit designs, pseudoreplication, repeated measures mixed model formulation and estimation and inference. Prerequisite: STAT 350 or equivalent.

The theory and application of statistical methodology for analyzing non-normal responses. Special emphasis on contingency tables, logistic regression, and log-linear models. Other topics can include mixed-effects models and models for overdispersed data. Prerequisite: STAT 830 and STAT 850 or permission of instructor.

An advanced treatment of modern methods of multivariate statistics and non-parametric regression. Topics may include: (1) dimension reduction techniques such as principal component analysis, multidimensional scaling and related extensions; (2) classification and clustering methods; (3) modern regression techniques such as generalized additive models, Gaussian process regression and splines. Prerequisite: STAT 830 and STAT 853 or permission of instructor.

An introduction to computational methods in applied statistics. Topics can include: the bootstrap, Markov Chain Monte Carlo, EM algorithm, as well as optimization and matrix decompositions. Statistical applications will include frequentist and Bayesian model estimation, as well as inference for complex models. The theoretical motivation and application of computational methods will be addressed. Prerequisite: STAT 830 or equivalent or permission of instructor.

Statistical methodology used in analysing failure time data. Likelihoods under various censoring patterns. Inference using parametric regression models including the exponential, Weibull, lognormal, generalized gamma distributions. Goodness-of-fit tests. The proportional hazards family, and inference under the proportional hazards model. Stratification and blocking in proportional hazards models. Time dependent covariates. Regression methods for grouped data. Prerequisite: STAT 450. Students with credit for STAT 806 may not take this course for further credit.

Methods for the analysis of repeated measures, correlated outcomes and longitudinal data, including unbalanced and incomplete data sets, characteristic of biomedical research are covered. Topics include covariance pattern models, random or mixed-effects models, multilevel models, generalized estimating equations, inference for multistate processes and counting processes, and methods for handling missing data. Prerequisite: STAT 450 or permission of the instructor.

Students are required to submit and successfully defend a project based on a statistical analysis problem or on the development of new statistical methodology. The project is examined as a thesis and must be submitted to the library. Graded on a satisfactory/unsatisfactory basis.