2 April 2008

ORIS Research Seminar

Friday April 4^th 2008

12:00 noon

Mechanical Building, 5 King’s College Road, Room MC331

Stochastic Mixed-Integer Programming Approach to Money Management Problems

Stephen James Stoyan

Ph.D. Candidate

Department of Mechanical and Industrial Engineering

All students and faculty welcome

Abstract: In this presentation we show two money management problems where the solution involves a Stochastic Mixed-Integer Programming (SMIP) approach. We first consider the problem of tracking a target portfolio or index under uncertainty. Due to an embedded NP-hard subproblem, many of the current index tracking models only consider a small number of important portfolio elements such as transaction costs, number of securities to hold, rebalancing, etc. We formulate a tracking portfolio model that includes a comprehensive set of real world portfolio elements, one of which involves uncertainty. Due to the size and complexity of the stochastic problem, the SMIP model is decomposed into subproblems and an iterative algorithm is developed that exploits the decomposition. A two-stage SMIP is solved and the results are compared with actual index values. In the second problem, an Asset and Liability Management (ALM) model is defined whose assets meet a terminal financial obligation while upholding a number of important maintenance characteristics. The numerous sources of uncertainty are captured in a SMIP approach, where a Goal Program (GP) is used to handle some of the portfolio objectives.