Prelim Courses - Ph.D. in Actuarial Science
This is not necessarily the official description for the courses. For the official descriptions, consult the 2008 - 2009 graduate catalog.
Description: Lebesgue measure and integration, differentiation,
Lp-spaces. Banach spaces, general theory of measure and integration.
Prerequisites: MATH 5110
Offered: Spring
Credits: 3
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Description: This class is an introduction to complex analysis at the graduate level. A practical purpose of the class is to prepare students to take the qualifying exams. Highlights of the course will be (not an exclusive list) analytic functions, meromorphic functions, the Cauchy Integral Formula, residues, maximum principle and the Schwartz Lemma.
For prelims, check out the Complex Analysis Study Guide.
Prerequisites: MATH 5110
Credits: 3
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Description: Convergence of random variables and their probability laws, maximal inequalities, series of independent random variables and laws of large numbers, central limit theorems, martingales, Brownian motion. Contemporary theory of stochastic processes, including stopping times, stochastic integration, stochastic differential equations and Markov processes, Gaussian processes, and empirical and related processes with applications in asymptotic statistics.
Prerequisites: MATH 5111
Credits: 3
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Description: Banach spaces, linear operator theory and application to differential equations, nonlinear operators, compact sets on Banach spaces, the adjoint operator on Hilbert space, linear compact operators, Fredholm alternative, fixed point theorems and application to differential equations, spectral theory, distributions.
Credits: 3
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Description: The study of convergence, numerical stability, roundoff error, and discretization error arising from the approximation of differential and integral operators.
Prerequisites: MATH 5110, which may be taken concurrently.
Offered: Fall
Credits: 3
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Description: Individual and collective risk theory, distribution theory, ruin theory, stoploss, reinsurance and Monte Carlo methods. Emphasis is on problems in insurance.
Offered: Fall
Credits: 3
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