Investment Portfolio Strategy Based on Geometric Brownian Motion and Backward Stochastic Differential Equations

In this paper, we expound an investment model based on Geometric Brownian Motion and Backward Stochastic Differential Equations, which can help to solve the investment portfolio strategy problem in a financial market consisting of one single stock and one single bond. This challenging investment analysis problem in the field of financial mathematics has only been discussed for recent three decades, and decision-makers seldom combine it with Geometric Brownian Motion. This paper proposes our study framework based on the assumption that the volatility of stock prices can be simulated using Geometric Brownian Motion, and offers a specific algorithm to solve the equations in the model. Moreover, we present an empirical analysis in which we discuss a variety of cases and work out the optimal strategy for each situation. Overall, the application of Backward Stochastic Differential Equations is vital for further research in investment risk aversion in financial markets.