We introduce a new option pricing equation with noise in a frictional financial market, which is fully different from the classical option pricing equation, and arrive at the existence of martingale solutions of this option pricing equation regardless of incompressibility. Furthermore, we also discuss the uniqueness of martingale solutions.

中文翻译：

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含噪声期权定价方程鞅解的存在唯一性

我们在摩擦性金融市场中引入了一个新的带有噪声的期权定价方程，它与经典的期权定价方程完全不同，并且无论不可压缩性如何，都得出该期权定价方程的鞅解的存在性。此外，我们还讨论了鞅解的唯一性。