On Optimal Cash Management under a Stochastic Volatility Model

On Optimal Cash Management under a Stochastic Volatility Model

Year:    2013

East Asian Journal on Applied Mathematics, Vol. 3 (2013), Iss. 2 : pp. 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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/eajam.070313.220413a

East Asian Journal on Applied Mathematics, Vol. 3 (2013), Iss. 2 : pp. 81–92

Published online:    2013-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    12

Keywords:    Optimal cash management stochastic volatility dynamic programming HJB equations.

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