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Cash management using multi-stage stochastic programming

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Ferstl, Robert; Weissensteiner, Alex

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Abstract We consider a cash management problem where a company with a given financial endowment and given 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 choose between a riskless asset (cash), several default- and option-free bonds, and an equity investment, and rebalances the portfolio at every stage. The uncertainty faced by the company 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.
Classification Financial Planning, Accountancy; Economic Statistics, Econometrics, Business Informatics
Free Keywords Dynamic stochastic programming; Stochastic linear programming; Cash management; Market price of risk; Change of measure; Scenario generation
Document language English
Publication Year 2010
Page/Pages p. 209-219
Journal Quantitative Finance, 10 (2010) 2
Status Postprint; reviewed
Licence PEER Licence Agreement (applicable only to documents from PEER project)