My Math Forum Expected value of sde

 June 26th, 2016, 03:50 AM #1 Newbie   Joined: Jun 2016 From: italy Posts: 2 Thanks: 0 Expected value of sde I have those sdes: $$dS(t) = mS(t)dt + e^{Y_t}S(t)dB(t)$$ and $$dY(t) = a(v − Y(t))dt + ab(pdB(t) +(1-p)dW(t))$$ where B,W independent Brownian motions and a,v,p,ba,v,p,b and mm known constants. How can I calculate the expected value of S(t)? Last edited by amm; June 26th, 2016 at 03:59 AM.
 June 26th, 2016, 03:52 AM #2 Newbie   Joined: Jun 2016 From: italy Posts: 2 Thanks: 0 I have reached to that but i dont know how to calculate the expected value of the last two terms: $$S_t= S_0 \exp\left( mt-\frac12\int_{0}^{t}e^{2Y_s}ds+\int_{0}^{t}e^{Y_s}d B_s\right)\quad$$ Also , $$Y_t=Y_0e^{-a*t}+v(1-e^{-at})+abp\int_{0}^{t}e^{-a(t-s)}dB_s+ab(1-p)\int_{0}^{t}e^{-a(t-s)}dW_s\quad$$ Last edited by amm; June 26th, 2016 at 03:57 AM.

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