Consider the reserve price from the algorithm: $$ r(s, t) = s - q\gamma \sigma^2(T-t) $$ where $s$ is the initial value of mid-price on the market, $q$ is a number of stocks that trader has, $\gamma$ is a risk aversion parameter, $T$ is time till trader holds his assets. Also consider reserve bid and ask prices, which equals to: $$ r^{ask} = s + \frac{\gamma \sigma^2 (T-t) + \frac{2}{\gamma}ln(1+\frac{\gamma}{k})}{2}\\ r^{bid} = s - \frac{\gamma \sigma^2 (T-t) + \frac{2}{\gamma}ln(1+\frac{\gamma}{k})}{2} $$

i found out, that reserve bid, ask prices could intersect the mid price, but i don't understand why it happens? Mid price moves up or down with probability $\pm\sigma\sqrt{dt}$ respectively starting from $s$ value, $dt$ is a step. Could anybody help to understand, why such situation happens?



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