Cash Management Using Multi-Stage Stochastic Programming
Quantitative Finance, 2010, 10(2), 209-219
20 Pages Posted: 6 Sep 2007 Last revised: 1 Jul 2017
Date Written: July 1, 2008
We consider a cash management problem where a company with a given financial endowment and future cash flows minimizes the Conditional Value at Risk of final wealth using a lower bound for the expected terminal wealth. We formulate the optimization problem as a multi-stage stochastic linear program (SLP). The company can rebalance the portfolio at every stage and choose between a riskless asset (cash), several default- and option-free bonds, and an equity investment. The uncertainty is reflected in the development of interest rates and equity returns.
Our model has two new features compared to the existing literature, which uses no-arbitrage interest rate models for the scenario generation. First, we explicitly estimate a function for the market price of risk and change the underlying probability measure. Second, we simulate scenarios for equity returns with moment-matching by an extension of the interest rate scenario tree.
Keywords: Dynamic stochastic programming, Cash management, Market price of risk, Change of measure, Scenario generation
JEL Classification: C61, G11
Suggested Citation: Suggested Citation