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I would like to compute the expectation of the following expectation

$\mathbb{E}[\int_a^\infty e^{-rt}\min(x_t,c)\,dt]\,$

where a, r, c are constants, $dx_t = \mu x_t dt + \sigma x_t dW_t$ is a geometrical Brownian motion with $(\mu < r)$ and $\min(x_t,c)$ denotes the minimum of $x_t$ and c. Any help would be much appreciated!

  • 0
    What do you know? What did you try? Where are you stuck?2012-01-12
  • 0
    I know that $\lim_{c \to \infty}$ the expectation of the integral is $\frac{x_a}{r-\mu}$2012-01-12

1 Answers 1