Expected level of a mean-reverting square-root process
Question
A process starts at and satisfies
for a standard Brownian motion . Assume the parameters keep strictly positive, so the square root is always defined (no proof needed). Find in terms of and evaluate at , , , , . Writing the value as with integers , give .
Short answer
. Applying the product rule to cancels in the drift and leaves a mean-zero stochastic integral, so , and . The volatility plays no role in the mean.
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