Credits 3. 3 Lecture Hours.

Advanced linear algebra, orthogonality and projections, eigenvalue and SV decomposition, pseudoinverse, least squares and minimum norm solutions, hyperplane separation theorem; applications to Mean-Variance portfolio analysis and capital asset pricing model, arbitrage and fundamental theorem of asset pricing, 1-period asset replication in incomplete markets; optimization and calculus of variations; Lagrange multipliers, dynamical programming, numerical methods; applications to utility theory, multi-period asset replication in incomplete markets; application of probability topics including conditional expectations, Markov chains and Martingales, extreme value theory; applications in optional stopping theorem and trading strategies, Markov Chains in credit risk modeling.
Prerequisite: MATH 251 and MATH 411, or equivalent, or approval of instructor.