Adaptive Monte Carlo Algorithms for Stopped Diffusion

• We present adaptive algorithms for weak approximation of stopped diffusion using the Monte Carlo Euler method. The goal is to compute an expected value of a given function g depending on the solution X of an Itô stochastic differential equation and on the first exit time τ from a given domain.The main steps in the extension to stopped diffusion processes are to use a conditional probability to estimate the first exit time error and introduce difference quotients to approximate the initial data of the dual solutions.

Ämnesord

NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

Nyckelord

adaptive mesh refinement algorithm

diffusion with boundary

barrier option

Monte Carlo method

weak approximation

MATHEMATICS

MATEMATIK

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