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

See all articles by Robert Ferstl

Robert Ferstl

Oesterreichische Nationalbank (OeNB)

Alex Weissensteiner

Free University of Bolzano Bozen

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

Ferstl, Robert and Weissensteiner, Alex, Cash Management Using Multi-Stage Stochastic Programming (July 1, 2008). Quantitative Finance, 2010, 10(2), 209-219, Available at SSRN:

Robert Ferstl (Contact Author)

Oesterreichische Nationalbank (OeNB) ( email )

Otto-Wagner-Platz 3, PO Box 61
1010 Vienna, A-1011

Alex Weissensteiner

Free University of Bolzano Bozen ( email )

Universitätsplatz 1
Bolzano, 39100
+39 0471 013496 (Phone)

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