A useful expansion is Use this to express the exponential in equation (13.20) in linear terms of

Question:

A useful expansion is

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Use this to express the exponential in equation (13.20) in linear terms of powers of $\Delta t$ up to first order. Note that this differs from the expression in (13.19), so conclude that the standard form and the multiplicative (or lognormal) form of simulation are different even to first order. Show, however, that the expected values of the two expressions are identical to first order, and hence, over the long run the two methods should produce similar results.

Equations

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