I woud like to calculate the Value at Risk of an Ito Integral in the following form in the limit! $$\lim_{\Delta t\to 0}\frac{1}{\Delta t}VaR_{q,t}\left[\int_t^{t+\Delta t}b(s,y(s))\pi_y^c(s,y(s))d \,W_s\right]$$ where $$b(s,y(s))\pi_y^c(s,y(s))$$
is stochastic. (As if they were nonrandom, the whole distribution of Ito integral was normal and then calculation of a quantile like VaR was pretty easy!)
I guess although we don't know the distribution of Ito integral when the integrand is stochastic, but in the limit it can be normal. Don't know how?!