A Numerical Study of a Parabolic Monge-Ampere Equation in Mathematical Finance

摘要

We propose iterative algorithms for solving finite difference schemes approximating an initial value problem of a parabolic Monge-Ampere equation, arising from the optimal investment of mathematical finance theory. We investigate positivity and convexity preserving properties of the numerical solution. Convergence results are also given. Numerical experiments demonstrate the efficiency of the algorithms and verify theoretical statements.