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 Advanced Statistics Advanced Probability and Statistics Math Forum

 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. Tags expected, ito, sde Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post jbergin Probability and Statistics 1 December 23rd, 2014 08:14 AM luccin Advanced Statistics 1 July 21st, 2014 05:32 AM maevious pacha Advanced Statistics 0 February 26th, 2014 09:40 AM mathbeauty Advanced Statistics 0 August 10th, 2010 01:12 PM kahalla Advanced Statistics 0 March 9th, 2010 12:53 AM

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