Many approximation techniques for simulation of solutions of stochastic differential equations, such as the Monte Carlo methods, suffer convergence problems that in many cases may render the simulation unreliable and less numerically stable. To overcome these problems exact algorithms, i.e. algorithms that simulate according to the exact probability law of the process, have been recently developed. A. Beskos and G. O. Roberts introduced an Exact Algorithm for one-dimensional diffusions in 2005. In this thesis we will analyze in depth the main features of this algoritm which involves no approximation and returns skeletons of exact paths for particular classes of processes. The ?nal aim is to widen the range of application of this algorithm to the case of time-inhomogeneous one-dimensional SDEs.

Exact Simulation of time-inhomogeneous SDEs

Mazzonetto, Sara
2013/2014

Abstract

Many approximation techniques for simulation of solutions of stochastic differential equations, such as the Monte Carlo methods, suffer convergence problems that in many cases may render the simulation unreliable and less numerically stable. To overcome these problems exact algorithms, i.e. algorithms that simulate according to the exact probability law of the process, have been recently developed. A. Beskos and G. O. Roberts introduced an Exact Algorithm for one-dimensional diffusions in 2005. In this thesis we will analyze in depth the main features of this algoritm which involves no approximation and returns skeletons of exact paths for particular classes of processes. The ?nal aim is to widen the range of application of this algorithm to the case of time-inhomogeneous one-dimensional SDEs.
2013-07-05
122
simulation, exact simulation, SDE, stochastic
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.12608/18432