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On Optimal Cash Management under a Stochastic Volatility Model

Published online by Cambridge University Press:  28 May 2015

Na Song ,
Wai-Ki Ching ,
Tak-Kuen Siu  and
Cedric Ka-Fai Yiu
Na Song*
Affiliation:
School of Management and Economics, University of Electronic Science and Technology, Chengdu, China
Wai-Ki Ching*
Affiliation:
Advanced Modeling and Applied Computing Laboratory, Department of Mathematics, The University of Hong Kong, Pokfulam Road, Hong Kong
Tak-Kuen Siu*
Affiliation:
Cass Business School, City University London, 106 Bunhill Row, London, ECY1 8TZ, United Kingdom and Department of Applied Finance and Actuarial Studies, Faculty of Business and Economics, Macquarie University, Macquarie University, Sydney, NSW 2109, Australia
Cedric Ka-Fai Yiu*
Affiliation:
Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Hong Kong
*
Corresponding author. Email: [email protected]
Corresponding author. Email: [email protected]
Corresponding author. Email: [email protected]
Corresponding author. Email: [email protected]
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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.

Keywords

60K2568M2091A80Optimal cash managementstochastic volatilitydynamic programmingHJB equations
Type
Research Article
Information
East Asian Journal on Applied Mathematics , Volume 3 , Issue 2 , May 2013 , pp. 81 - 92
Copyright
Copyright © Global-Science Press 2013

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