  In this paper, we employ the Heston stochastic volatility model to describe
the stock's volatility and apply the model to derive and analyze the optimal
trading strategies for dealers in a security market. We also extend our study
to option market making for options written on stocks in the presence of
stochastic volatility. Mathematically, the problem is formulated as a
stochastic optimal control problem and the controlled state process is the
dealer's mark-to-market wealth. Dealers in the security market can optimally
determine their ask and bid quotes on the underlying stocks or options
continuously over time. Their objective is to maximize an expected profit from
transactions with a penalty proportional to the variance of cumulative
inventory cost.
