Linear Programming Approach to American Option Pricing
We solve the variational inequality (VI) from American option pricing problem by linear programming (LP) approach. We approximate its solution by a combination of basis functions. The objective is to minimize the absolute error of the solution and the max operator in VI is converted into linear constraints of LP. We discuss its convergence, and compare our results with Longstaff-Schwartz least-square approach and numerical partial differential equation (PDE) approach.