0
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0answers
33 views

partial derivative of stochastic variable inside an integral

Very simple question, is it correct to take a partial derivative of stochastic variable inside an integral. If not, why? is$ \frac {\partial}{\partial R} \int_q^Q R(v) dv = \int_q^Q dv$ ? where R is ...
1
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0answers
18 views

Differential of $ \int_{0}^{t} e^{\int_{s}^{t} \sigma(\tau)dW(\tau)+(r(\tau)-\frac{1}{2}\sigma(\tau)^{2})d\tau} c(s)ds $

I think -- using the chain rule -- it's $$ e^{\int_{t}^{t}\cdots d\tau} c(t)dt \cdot e^{\int_{s}^{t} \sigma(\tau)dW(\tau)+(r(\tau)-\frac{1}{2}\sigma(\tau)^{2})d\tau}\cdot ...
2
votes
0answers
68 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
179 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
202 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 ...