Mathematical methods for portfolio management

Abstract

Portfolio Management is the process of allocating an investor's wealth to in­ vestment opportunities over a given planning period. Not only should Portfolio Management be treated within a multi-period framework, but one should also take into consideration the stochastic nature of related parameters.

After a short review of key concepts from Finance Theory, e.g. utility function, risk attitude, Value-at-rusk estimation methods, a.nd mean-variance efficiency, this work describes a framework for the formulation of the Portfolio Management problem in a Stochastic Programming setting. Classical solution techniques for the resolution of the resulting Stochastic Programs (e.g. L-shaped Decompo­ sition, Approximation of the probability function) are presented. These are discussed within both the two-stage and the multi-stage case with a special em­ phasis on the former. A description of how Importance Sampling and EVPI are used to improve the efficiency of classical methods is presented. Postoptimality Analysis, a sensitivity analysis method, is also described.