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5

Ask minus bid has nothing to do with the mid price - it is the spread. Generally you see a collection of bid/offer orders resting on different price levels. In the simplest case, you just see one bid at price $p_b$ and one offer at price $p_a$. In this case the mid price is $$ p_m = \frac{p_a + p_b}{2} $$ That's all there is to it - you don't need to "...


2

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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