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I assume $\alpha>0$. Let $V^\lambda$ be the solution of : \begin{equation*} \begin{cases} \frac{\partial V^\lambda}{\partial t} + \Bigl [ \alpha \Bigl(\mu - \frac{\lambda}{\alpha} - \log (S) \Bigr) S \Bigr ] \frac{\partial V^\lambda}{\partial S} + \frac{1}{2} \sigma^2 S^2 \frac{\partial^2 V^\lambda}{\partial S^2} - rV^\lambda = 0, \\ V^\lambda(S,T) = (S -...



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