Conditional expectation of correlated processes
$begingroup$
Consider the known $C^1$ functions $f^1, f^2$ and the continuous semimartingales $X^1,X^2,S^1,S^2$ (solutions of a non-linear SDE). Suppose that $X^i$ is correlated to $S^1$ and $S^2$ with correlation $rho^{i,1}$ and $rho^{i,2}$ respectively ($i=1, 2$).
I want to compute the conditional expectations:
$E[X^i_t | S_t^1, S_t^2], i=1,2$.
$E[int_{0}^{t}f^i(s)dX^i_s | S_t^1, S_t^2], i=1,2$.- $E[(int_{0}^{t}f^1(s)dX^1_s)(int_{0}^{t}f^2(s)dX^2_s) | S_t^1, S_t^2]$
Does anyone have any idea how may I compute the above cond.expectations? Or any example that could help?
Thanks.
probability probability-theory stochastic-processes stochastic-calculus stochastic-integrals
asked Dec 10 '18 at 12:15
noob-mathematiciannoob-mathematician
748
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add a comment |
$begingroup$
Consider the known $C^1$ functions $f^1, f^2$ and the continuous semimartingales $X^1,X^2,S^1,S^2$ (solutions of a non-linear SDE). Suppose that $X^i$ is correlated to $S^1$ and $S^2$ with correlation $rho^{i,1}$ and $rho^{i,2}$ respectively ($i=1, 2$).
I want to compute the conditional expectations:
$E[X^i_t | S_t^1, S_t^2], i=1,2$.
$E[int_{0}^{t}f^i(s)dX^i_s | S_t^1, S_t^2], i=1,2$.- $E[(int_{0}^{t}f^1(s)dX^1_s)(int_{0}^{t}f^2(s)dX^2_s) | S_t^1, S_t^2]$
Does anyone have any idea how may I compute the above cond.expectations? Or any example that could help?
Thanks.
probability probability-theory stochastic-processes stochastic-calculus stochastic-integrals
asked Dec 10 '18 at 12:15
noob-mathematiciannoob-mathematician
748
$endgroup$
add a comment |
$begingroup$
Consider the known $C^1$ functions $f^1, f^2$ and the continuous semimartingales $X^1,X^2,S^1,S^2$ (solutions of a non-linear SDE). Suppose that $X^i$ is correlated to $S^1$ and $S^2$ with correlation $rho^{i,1}$ and $rho^{i,2}$ respectively ($i=1, 2$).
I want to compute the conditional expectations:
$E[X^i_t | S_t^1, S_t^2], i=1,2$.
$E[int_{0}^{t}f^i(s)dX^i_s | S_t^1, S_t^2], i=1,2$.- $E[(int_{0}^{t}f^1(s)dX^1_s)(int_{0}^{t}f^2(s)dX^2_s) | S_t^1, S_t^2]$
Does anyone have any idea how may I compute the above cond.expectations? Or any example that could help?
Thanks.
probability probability-theory stochastic-processes stochastic-calculus stochastic-integrals
asked Dec 10 '18 at 12:15
noob-mathematiciannoob-mathematician
748
$endgroup$
Consider the known $C^1$ functions $f^1, f^2$ and the continuous semimartingales $X^1,X^2,S^1,S^2$ (solutions of a non-linear SDE). Suppose that $X^i$ is correlated to $S^1$ and $S^2$ with correlation $rho^{i,1}$ and $rho^{i,2}$ respectively ($i=1, 2$).
I want to compute the conditional expectations:
$E[X^i_t | S_t^1, S_t^2], i=1,2$.
$E[int_{0}^{t}f^i(s)dX^i_s | S_t^1, S_t^2], i=1,2$.- $E[(int_{0}^{t}f^1(s)dX^1_s)(int_{0}^{t}f^2(s)dX^2_s) | S_t^1, S_t^2]$
Does anyone have any idea how may I compute the above cond.expectations? Or any example that could help?
Thanks.
probability probability-theory stochastic-processes stochastic-calculus stochastic-integrals
probability probability-theory stochastic-processes stochastic-calculus stochastic-integrals
asked Dec 10 '18 at 12:15
noob-mathematiciannoob-mathematician
748
asked Dec 10 '18 at 12:15
noob-mathematiciannoob-mathematician
748
edited Dec 10 '18 at 12:29
noob-mathematician
asked Dec 10 '18 at 12:15
noob-mathematiciannoob-mathematician
748
asked Dec 10 '18 at 12:15
noob-mathematiciannoob-mathematician
748
asked Dec 10 '18 at 12:15
noob-mathematiciannoob-mathematician
748
748
add a comment |
add a comment |
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