NEW ADAPTIVE MONTE CARLO ALGORITHM FOR PARALLEL SOLUTION OF LARGE LINEAR SYSTEMS WITH APPLICATIONS

作者：Farnoosh Rahman^*; Aalaei Mahboubeh

来源：Proceedings of the Romanian Academy - Series A: Mathematics, Physics, Technical Sciences, Information Science , 2015, 16(1): 11-19.

• adaptive Monte Carlo algorithm
• large linear systems
• parallel solution
• option pricing

In this paper, a new adaptive Monte Carlo algorithm is proposed for solving large linear systems. The proposed algorithm converges much faster than the conventional Monte Carlo and achieves exponential convergence. The corresponding properties of the algorithm are discussed. It has simple structure, low cost, desirable speed and accuracy. Theoretical results are established to justify the convergence of the algorithm. To confirm the accuracy and efficiency of the proposed algorithm, it is used to solve large linear systems. The adaptive Monte Carlo algorithms are implemented for parallel solution of large linear systems on parallel machine with Message Passing Interface as inter node communication. Furthermore, we provide applications of the algorithm for option pricing, where the Black Scholes formula is converted to linear systems using discretization.

• 出版日期2015-3