On optimal cash management under a stochastic volatility model

Na Song, Wai Ki Ching, Tak Kuen Siu, Ka Fai Cedric Yiu

Research output: Journal article publicationJournal articleAcademic researchpeer-review

8 Citations (Scopus)

Abstract

We discuss a mathematical model for optimal cash management. A firm wishes to manage cash to meet demands for daily operations, and to maximize terminal wealth via bank deposits and stock investments that pay dividends and have uncertain capital gains. A Stochastic Volatility (SV) model is adopted for the capital gains rate of a stock, providing a more realistic way to describe its price dynamics. The cash management problem is formulated as a stochastic optimal control problem, and solved numerically using dynamic programming. We analyze the implications of the heteroscedasticity described by the SV model for evaluating risk, by comparing the terminal wealth arising from the SV model to that obtained from a Constant Volatility (CV) model.
Original languageEnglish
Pages (from-to)81-92
Number of pages12
JournalEast Asian Journal on Applied Mathematics
Volume3
Issue number2
DOIs
Publication statusPublished - 1 May 2013

Keywords

  • Dynamic programming
  • HJB equations
  • Optimal cash management
  • Stochastic volatility

ASJC Scopus subject areas

  • Applied Mathematics

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