medium · Quantitative Finance stochastic
Given f(t, W_t) = t W_t, apply It^o's lemma to find df. Why is there no (1)/(2) f_xx dt term in this specific case?
- Because the function is not dependent on t^2.
- Because the product rule for differentials d(UV) = U dV + V dU is always sufficient for stochastic variables.
- Because Brownian motion is a martingale, making the second-order term unnecessary.
- Because the second partial derivative of f with respect to W_t is zero.
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