MATH 405 - Stochastic Analysis I

3 units (fi 6)(FIRST, 3-0-0)

Discrete-time stochastic analysis: Stochastic basis, filtration, stochastic sequences. Absolute continuity of probability measures and conditional expectations. Martingale-like and predictable stochastic sequences. Doob's decomposition and inequalities. Stopping times and related properties. Uniformly integrable stochastic sequences. Limit behaviour of martingales, including the Law of Large Numbers and the Central Limit Theorem. Transition from discrete-time to continuous-time stochastic analysis. Introduction to stochastic integration with respect to Brownian motion. Prerequisite: STAT 371 or STAT 281 or MATH 467 or consent of the Department.

MATH 505 - Stochastic Analysis I

3 units (fi 6)(FIRST, 3-0-0)

Discrete-time stochastic analysis: Stochastic basis, filtration, stochastic sequences. Absolute continuity of probability measures and conditional expectations. Martingale-like and predictable stochastic sequences. Doob's decomposition and inequalities. Stopping times and related properties. Uniformly integrable stochastic sequences. Limit behaviour of martingales, including the Law of Large Numbers and the Central Limit Theorem. Transition from discrete-time to continuous-time stochastic analysis. Introduction to stochastic integration with respect to Brownian motion. Prerequisites: STAT 371 or STAT 281 or MATH 467 or consent of the Department. Note: Credit cannot be obtained in both MATH 405 and MATH 505.

STAT 453 - Risk Theory

3 units (fi 6)(EITHER, 3-0-0)

Classical ruin theory, individual risk models, collective risk models, models for loss severity: parametric models, tail behavior, models for loss frequency, mixed Poisson models; compound Poisson models, convolutions and recursive methods, probability and moment generating functions. Prerequisite: One of STAT 371 or STAT 281.

STAT 553 - Risk Theory

3 units (fi 6)(EITHER, 3-0-0)

Classical ruin theory, individual risk models, collective risk models, models for loss severity: parametric models, tail behavior, models for loss frequency, mixed Poisson models; compound Poisson models, convolutions and recursive methods, probability and moment generating functions. Prerequisite: STAT 371 or equivalent. Note: Cannot be used for credit towards a thesis-based graduate program in the Department of Mathematical and Statistical Sciences.