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 - <p style="text-align: justify;">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.</p>