Is there a closed form solution to compute expectation of this time series / stochastic process?

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$
textrmSuppose you have a time series Y_t
textrm which moves via normal random variable boldsymboll_t\\
y_t+1
= left{beginmatrix
0, y_tleq 0
\
max[0, y_tcdot (1+r)+l_t], y_t> 0
endmatrixright.
\\
textrmWhere l_t
sim
textrmN(mu , sigma)
textrm. If we fix
y_0
textrm above 0 and parameters mu
textrm, r, sigma above 0,
\
textrmthen is there a closed form solution for computing the expectation of
Y_T textrm forall textrm T ?
$




stochastic-processes expectation markov-chains time-series




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    $
    textrmSuppose you have a time series Y_t
    textrm which moves via normal random variable boldsymboll_t\\
    y_t+1
    = left{beginmatrix
    0, y_tleq 0
    \
    max[0, y_tcdot (1+r)+l_t], y_t> 0
    endmatrixright.
    \\
    textrmWhere l_t
    sim
    textrmN(mu , sigma)
    textrm. If we fix
    y_0
    textrm above 0 and parameters mu
    textrm, r, sigma above 0,
    \
    textrmthen is there a closed form solution for computing the expectation of
    Y_T textrm forall textrm T ?
    $




    stochastic-processes expectation markov-chains time-series




    share|cite|improve this question





















      up vote
      0
      down vote

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      up vote
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      down vote

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      $
      textrmSuppose you have a time series Y_t
      textrm which moves via normal random variable boldsymboll_t\\
      y_t+1
      = left{beginmatrix
      0, y_tleq 0
      \
      max[0, y_tcdot (1+r)+l_t], y_t> 0
      endmatrixright.
      \\
      textrmWhere l_t
      sim
      textrmN(mu , sigma)
      textrm. If we fix
      y_0
      textrm above 0 and parameters mu
      textrm, r, sigma above 0,
      \
      textrmthen is there a closed form solution for computing the expectation of
      Y_T textrm forall textrm T ?
      $




      stochastic-processes expectation markov-chains time-series




      share|cite|improve this question











      $
      textrmSuppose you have a time series Y_t
      textrm which moves via normal random variable boldsymboll_t\\
      y_t+1
      = left{beginmatrix
      0, y_tleq 0
      \
      max[0, y_tcdot (1+r)+l_t], y_t> 0
      endmatrixright.
      \\
      textrmWhere l_t
      sim
      textrmN(mu , sigma)
      textrm. If we fix
      y_0
      textrm above 0 and parameters mu
      textrm, r, sigma above 0,
      \
      textrmthen is there a closed form solution for computing the expectation of
      Y_T textrm forall textrm T ?
      $





      stochastic-processes expectation markov-chains time-series





      share|cite|improve this question










      share|cite|improve this question




      share|cite|improve this question









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