Expected Value of the exponential of a stochastic integral

Question

What is the expected value of the following process: $$ e^{\int_0^t B_u\, du} $$

Thanks.

score 2 · Answer 1 · edited Apr 13 '17 at 12:19

2

See here for the fact that $\int_0^t B_u du$ follows the normal distribution with zero mean and variance $\dfrac{t^3}{3}$.

See here for moment generating function(MGF) of normal distribution

edited Apr 13 '17 at 12:19

Community

answered Jan 20 '15 at 15:22

Petite Etincelle

Can you explain the passages to compute it please? I know that the Brownian Motion follows a Gaussian distribution by definition, but I don't understand how I can arrive to the Moment Generating Function of the Gaussian Random Variable.. – dubidub Jan 20 '15 at 15:49
@dubidub Here is a link showing that – Petite Etincelle Jan 20 '15 at 15:53

1 Answers1