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The Malliavin calculus is an especially promising tool for solving the pricing problem of American options under a constant volatility, and also when the volatility is stochastic. Using the Malliavin calculus, the aim of this work consisted computing the conditional expectation, related to the solution of the pricing problem of the American option, for the uni and bi-dimensional model, as a suitable ratio of ordinal expectations. The estimation of this ratio became possible by using the Monte Carlo simulations.

The International E-Conference on Pure and applied mathematical sciences (ICPAMS-2021) have been created to exchange knowledge and build durable collaborative framework projects. The first edition ICPAMS-2021 focuses on all areas of pure and applied mathematics and provides a rich program with high-level conferences by renown-invited speakers.The main topics of this conference are Algebra, Probability, Statistics, Partial Differential Equation, Optimization, Differential Calculus, Fractional Calculus, Modeling, and Numerical Analysis...