In this article, we derive the risk-neutral measures of the stock options price and volatility by incorporating a simple constrained minimization of the Kullback measure of relative information. We obtain a second-order parabolic partial differential equation, the generalized Black–Scholes equation based on the theoretical analysis when the underlying financial asset is estimated using a stochastic volatility model. Also to investigate the analytical solution of this generalized Black–Scholes equation we have used Laplace transform homotopy perturbation method.

中文翻译：

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具有随机波动率的Black-Scholes期权定价模型：一种信息理论方法

在本文中，我们通过结合相对信息的Kullback度量的简单约束最小化，得出了股票期权价格和波动率的风险中性度量。当使用随机波动率模型估算基础金融资产时，我们基于理论分析获得了二阶抛物型偏微分方程，即广义Black-Scholes方程。另外，为了研究此广义Black-Scholes方程的解析解，我们使用了Laplace变换同伦摄动方法。