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June 26th, 2016, 04:50 AM   #1
amm
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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 04:59 AM.
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June 26th, 2016, 04:52 AM   #2
amm
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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 04:57 AM.
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