Financial planning via multi-stage stochastic optimization

Abstract

This paper describes a framework for modeling significant financial planning problems based on multi-stage optimization under uncertainty. Applications include risk management for institutions, banks, government entities, pension plans, and insurance companies. The approach also applies to individual investors who are interested in integrating investment choices with savings and borrowing strategies. A dynamic discrete-time structure addresses realistic financial issues. The resulting stochastic program is enormous by current computer standards, but it possesses a special structure that lends itself to parallel and distributed optimization algorithms. Interior-point methods are particularly attractive. Solving these stochastic programs presents a major challenge for the computational operations research and computer science community. Scope and purpose The globalization of financial markets and the introduction of complex products such as exotic derivatives have increased volatility and risks. Strides in computer and information technology has eliminated any delays between the occurrence of an event and the impact on the markets—within the home country and internationally. Thus there is a great need for an integrative approach to financial analysis and planning that encompasses the decisional environment as well as the stochastic elements in a dynamic fashion. The financial optimization model presented here incorporates several popular approaches to the problem of investment strategies, including stochastic programming and dynamic stochastic control.