In this paper, we employ the Heston stochastic volatility model to describe the stock’s volatility and apply the model to derive and analyze trading strategies for dealers in a security market with price discovery. 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 continuously over time. Their objective is to maximize an expected profit from transactions with a penalty proportional to the variance of cumulative inventory cost. We provide an approximate, analytically tractable solution to the stochastic control problem. Numerical experiments are given to illustrate the effects of various parameters on the performances of trading strategies.

中文翻译：

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限价订单簿市场中具有随机波动性的交易策略

在本文中，我们使用Heston随机波动率模型来描述股票的波动率，并应用该模型来推导和分析具有价格发现的证券市场中交易商的交易策略。该问题被表述为随机最优控制问题，而受控状态过程就是经销商的按市值计价的财富。证券市场中的交易者可以随着时间的流逝不断地最佳地确定相关股票的要价和买价。他们的目标是最大化交易的预期利润，并与累积库存成本的方差成比例。我们为随机控制问题提供了一个近似的，易于分析处理的解决方案。数值实验表明了各种参数对交易策略绩效的影响。