Abstract:
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Stochastic differential equations provide accessible mathematical models that combine deterministic and probabilistic components of dynamic behavior of physical, financial, and social structures. Unfortunately, in many cases analytic solutions are not available for these SDEs, so we are required to use numerical methods to approximate the solution. The rate of convergence of such numerical methods is of great importance as it is related to the computational efficiency and numerical accuracy of the method. In this context, a newly proposed theorem will be discussed to study the strong (and weak) order of convergence numerically when the analytical solution of the SDE is not known. In the same light, it is a challenge to numerically compute the multiple stochastic integrals while implementing the Milstein method for a better rate of convergence for multidimensional SDEs. The talk will explore two proposed numerical methods for computing these multiple stochastic integrals while comparing their efficiency and effectiveness with other existing methods. The proposed methodologies will be elaborated with applications in widely used finance models like the Black-Scholes and Heston models.
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