2
votes
0answers
67 views

How to calculate the following expectation

I have a problem to find the expectation of the following expression, $$E\left[W_T e^{\int_0^T(W_s)ds}\right].$$ Here, $W_T$ is a Brownian motion. Any suggestions as to how to proceed with it? Many ...
3
votes
1answer
175 views

Integral paradox: Deterministic integral interpreted as limiting case of stochastic integral

The value of a stochastic integral, in this case integrating a Wiener process with respect to itself $$\int_0^T W(t)\;dW(t)$$ is dependent on the chosen position of the endpoint of the subintervals. ...
1
vote
1answer
199 views

Integration Order Reversal

I have a question regarding integration order reversal in a stochastic integral. This is a homework problem of the form "Show this is true". My problem is 1) my results are not exactly the same as the ...