Stochastic modeling has been broadly used in the financial market and actuarial industry containing certain derivative investment products. It utilizes past or present information to measure unknown future values. These models are based on Brownian motion, which is the continuous analog of random walk, and takes the randomness of future paths into account. An effective tool to analyze these models is stochastic calculus. I have read and studied some past scholars’ works, which had come up with quite many variations of stochastic models in different financial situations, such as markets involving at least one risky asset (e.g. stock) and a riskless asset (e.g. money market). However, I have noticed that more study needs to be done in incomplete markets where there exists arbitrage opportunities (i.e. riskless profit). Because in real life, when major events such as bankruptcy, financial crisis, and natural disaster happened, original pricing models based on the Black-Scholes model cannot make valuable predictions during a period of time due to the incompleteness of the market. I am trying to estimate an optimal portfolio under those circumstances by utilizing probability theories to modify the existing models. In this model, volatility of assets will be treated as random variable. By utilizing machine learning techniques, synthetic data generated by computer programs will be used to test the fit and efficiency of the model.