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Volume 3, Issue 2
On Optimal Cash Management under a Stochastic Volatility Model

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

DOI: 10.4208/eajam.070313.220413a

East Asian J. Appl. Math., 3 (2013), pp. 81-92.

Published online: 2018-02

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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

Optimal cash management, stochastic volatility, dynamic programming, HJB equations.

  • AMS Subject Headings

60K25, 68M20, 91A80

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-3-81, author = {Na Song, Wai-Ki Ching, Tak-Kuen Siu and Cedric Ka-Fai Yiu}, title = {On Optimal Cash Management under a Stochastic Volatility Model}, journal = {East Asian Journal on Applied Mathematics}, year = {2018}, volume = {3}, number = {2}, pages = {81--92}, 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.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.070313.220413a}, url = {http://global-sci.org/intro/article_detail/eajam/10848.html} }
TY - JOUR T1 - On Optimal Cash Management under a Stochastic Volatility Model AU - Na Song, Wai-Ki Ching, Tak-Kuen Siu & Cedric Ka-Fai Yiu JO - East Asian Journal on Applied Mathematics VL - 2 SP - 81 EP - 92 PY - 2018 DA - 2018/02 SN - 3 DO - http://doi.org/10.4208/eajam.070313.220413a UR - https://global-sci.org/intro/article_detail/eajam/10848.html KW - Optimal cash management, stochastic volatility, dynamic programming, HJB equations. AB -

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.

Na Song, Wai-Ki Ching, Tak-Kuen Siu and Cedric Ka-Fai Yiu. (2018). On Optimal Cash Management under a Stochastic Volatility Model. East Asian Journal on Applied Mathematics. 3 (2). 81-92. doi:10.4208/eajam.070313.220413a
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