A Discrete Itô Calculus Approach to He's Framework for Multi-Factor Discrete Markets

Details A Discrete Itô Calculus Approach to He's Framework for Multi-Factor Discrete Markets A Discrete Itô Calculus Approach to He's Framework for Multi-Factor Discrete Markets

2006-06-13

arxiv.org/abs/math/0606292v1

Mathematics

Probability

15pages

Scientific paper

In the present paper, a discrete version of It\^o's formula for a class of multi-dimensional random walk is introduced and applied to the study of a discrete-time complete market model which we call He's framework. The formula unifies continuous-time and discrete-time settings and by regarding the latter as the finite difference scheme of the former, the order of convergence is obtained. The result shows that He's framework cannot be of order 1 scheme except for the one dimensional case.

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