Practical Financial Optimization: Decision Making for Financial Engineers

Chapter 6

Dynamic Portfolio Optimization with Stochastic Programming

A dynamic theory would unquestionably be more complete and therefore preferable.

J. von Neumann and O. Morgenstern

Theory of Games and Economic Behavior

6.1 Preview

In this chapter we model the optimization of dynamic trading strategies. Investors dynamically rebalance their portfolio at some discrete trading dates in the future in response to new information. Simple decision rules for portfolio rebalancing are introduced first. Stochastic dedication is then formulated as a simple model for optimizing dynamic strategies of short-term borrowing and lending decisions. Stochastic linear programming is finally presented as a versatile tool for formulating a wide range of financial planning models. Stochastic programming models optimize dynamic strategies of borrowing, lending, and portfolio rebalancing.

6.2 Setting the Stage for Dynamic Models

Many financial decision making problems involve liability streams that extend well into the future. For example, the planning horizon for most insurance products extends beyond a decade; for pension funds it is more than 30 years; and for social security plans it may go up to 50. It is reasonable in such settings to inquire about optimal dynamic strategies that allow portfolio managers to rebalance their portfolio at some discrete trading dates in the future, in response to new information. The discrete time, discrete scenario setting is well suited to the modeling of dynamic ...