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Let $B=(B_t^1,B_t^2,B_t^3)$ a $\mathbb R^3$-valued Brownian motion. Let $r_t$ (risk free rate) be bounded and deterministic. Let consider the DISCOUNTED market $$d\overline X_t^1=\frac52dt+2dB_t^1-dB_t^2-dB_t^3$$ $$d\overline X_t^2=7dt+2dB_t^1+2dB_t^2-10dB_t^3$$ $$d\overline X_t^3=\frac72dt+4dB_t^1-3dB_t^2+dB_t^3$$ I have already found that the market is arbitrage free.

I would like to find the risk-neutral price of the following claim:$$H=e^{X_T^1+ X_T^3}$$ (note: here the $X_T^1,X_T^3$ are not discounted) but i'm stack. Any help please?

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  • $\begingroup$ Are there 3 different $X_t$ processes? In your notation it seems the same process. $\endgroup$ – Daneel Olivaw Jan 26 at 0:30
  • $\begingroup$ Also what are the $B$s at the end of each equation? $\endgroup$ – Daneel Olivaw Jan 26 at 0:32
  • $\begingroup$ @DaneelOlivaw yes sorry, now I edit it $\endgroup$ – Buddy_ Jan 26 at 8:02
  • $\begingroup$ @DaneelOlivaw don't you have any suggestion? $\endgroup$ – Buddy_ Jan 26 at 15:57
  • $\begingroup$ why not to use montecarlo to compute the price?? $\endgroup$ – Valometrics.com Jan 26 at 20:43

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