Tagged Questions
2
votes
0answers
59 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 ...
0
votes
0answers
15 views
Comparing optimum of two stochastic maximization problems
I want to show that
$$\arg\max_{x}\left(\int^b_a f(x,p) dp\right)>\arg\max_{x}\left(\int^b_a g(p)h(f(x,p)) dp\right)$$
where the parameters have the following properties $x,p,a,b>0$,
and the ...
3
votes
1answer
146 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
183 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 ...
