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June 26th, 2016, 04:50 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 $$dY(t) = a(v − Y(t))dt + ab(pdB(t) +(1p)dW(t))$$ 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 04:59 AM. 
June 26th, 2016, 04:52 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 , $$Y_t=Y_0e^{a*t}+v(1e^{at})+abp\int_{0}^{t}e^{a(ts)}dB_s+ab(1p)\int_{0}^{t}e^{a(ts)}dW_s\quad$$ Last edited by amm; June 26th, 2016 at 04:57 AM. 

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