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There is probably an error in your formula for $\sum_0^s v_i$. You can use a trick to directly compute $E_0 e^{(1-\gamma)v_i}$ using \begin{align} E_0 e^{(1-\gamma)v_i}& = \Pi_0^s E_0e^{(1-\gamma)v_i}. \end{align} Notice $e^{(1-\gamma)v_i}$ is a random variable equal to 1 with probability $1-p$ and $(1-b)^{1-\gamma}$ with probability $p$. Therefore, \...


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