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Cash management using multi-stage stochastic programming

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  • Robert Ferstl
  • Alex Weissensteiner

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.

Suggested Citation

  • Robert Ferstl & Alex Weissensteiner, 2010. "Cash management using multi-stage stochastic programming," Quantitative Finance, Taylor & Francis Journals, vol. 10(2), pages 209-219.
    • Handle: RePEc:taf:quantf:v:10:y:2010:i:2:p:209-219
    DOI: 10.1080/14697680802637908
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    Cited by:

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    3. Schroeder, Pascal & Kacem, Imed, 2020. "Competitive difference analysis of the cash management problem with uncertain demands," European Journal of Operational Research, Elsevier, vol. 283(3), pages 1183-1192.
    4. Robert Ferstl & Alexander Weissensteiner, 2011. "Backtesting Short-Term Treasury Management Strategies Based on Multi-Stage Stochastic Programming," Palgrave Macmillan Books, in: Gautam Mitra & Katharina Schwaiger (ed.), Asset and Liability Management Handbook, chapter 19, pages 469-494, Palgrave Macmillan.
    5. Libo Yin & Liyan Han, 2020. "International Assets Allocation with Risk Management via Multi-Stage Stochastic Programming," Computational Economics, Springer;Society for Computational Economics, vol. 55(2), pages 383-405, February.
    6. Geyer, Alois & Hanke, Michael & Weissensteiner, Alex, 2010. "No-arbitrage conditions, scenario trees, and multi-asset financial optimization," European Journal of Operational Research, Elsevier, vol. 206(3), pages 609-613, November.
    7. Havran, Dániel, 2008. "Pénzgazdálkodási szokások hatása a működőtőkére. A Magyar Posta példája [The effect of financial management habits on operating capital. The example of the Hungarian Post Office]," Közgazdasági Szemle (Economic Review - monthly of the Hungarian Academy of Sciences), Közgazdasági Szemle Alapítvány (Economic Review Foundation), vol. 0(10), pages 907-926.

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