IE 524 -
In this course, basic optimization models, theory and methods of (i) linear programming, LP, (ii) nonlinear programming, NLP, (iii) conic programming, CP, (iv) piecewise linear optimization, (v) integer programming, IP, (vi) dynamic programming, DP, (vii) stochastic programming, SP, and (viii) the complementarity problems are introduced. We will discuss important applications of different types of the optimization models in financial engineering including liability matching and arbitrage detection (of LP); GARCH parameter estimation, Markowitz’s Mean-Variance portfolio Optimization, and Sharpe-Ratio maximization (of NLP); Index-tracking portfolio construction and covariance matrix adjustment (of CP); Index fund construction (of IP); American call option theorem, pricing of the American options, and Collateralized Mortgage Obligation construction (of DP); risk management (of SP); Nash game (complementarity problem). Other than the existing financial engineering applications, students are expected to formulate the given problem description into an optimization model of a suitable type. For obtaining the optimal solution by computers, the AMPL language for coding and solving the optimization model is introduced. Linking the CPLEX library with a C++ project to build a large-size optimization model will also be demonstrated. Students will practice these computer techniques in homework problems and are required to develop a group project about analyzing the market data collected by each group. Prerequisite: FIN 500 and MATH 415.