Solving American option optimal control problems in financial markets using a novel neural network

In this paper, we introduce a novel neural network (NN) for solving optimal control problems associated with American options in financial markets. American options provide holders with the flexibility to exercise the option before expiration, thereby affecting potential profitability. This paper focuses on determining the optimal exercise strategy and option price to maximize the payoff by solving a class of American option optimal control problems. We reformulate the optimal control problem into a linear complementarity problem(LCP). Subsequently, we employ the penalty approach and smoothing method to convert the LCP into a bi-nonlinear system with a set of partial differential equations (PDEs). By solving the reformulated PDE equations with the proposed method, we obtain numerical solutions that yield the optimal exercise strategy and option price. Numerical examples of American call and put options demonstrate the efficiency and usefulness of the proposed methods.