Questions / Quant research, Stochastic calculus & linear algebra
∫ W dW, evaluated
On a path where W₁ = 1.5, what is ∫₀¹ W dW?
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Answer: 0.625 value units (5/8)
- ∫₀ᵀ W dW = (W_T² − T)/2.
- (2.25 − 1)/2 = 0.625.
Interview shortcut. Itô: ∫W dW = (W_T² − T)/2 = (2.25 − 1)/2.
Takeaway. The Itô integral subtracts T/2 from the calculus answer.
In the app this has a follow-up where one thing about the setup changes. Try the follow-up.