Errata

    1. Page 33. Third displayed equation and text should be:
      x+u=\beta(v-\mu)+u
      As v and u are independent and normal, x+u is normal with mean 0
    2. Page 33. Fourth displayed equation, and sentence that follows should read:
      S=\mu+(x+u)\frac{\sigma}{2\sigma_u},

      so that the linear sensitivity parameter is \lambda=\sigma/(2\sigma_u).

    3. Page 36. First sentence in paragraph preceding 2.3.1 should read: In later chapters we show how trading algorithms are built to either take advantage of informational advantages or to adjust the depth at which LOs are posted to recover losses from trading with more informed traders.
    4. Page 37: the \Delta_a in F(\Delta_a) in the denominator should be \Delta_b. This is the right equation
      \Delta_b = \frac{1}{1+\frac{1-\alpha}{\alpha}\frac{(1-F(\Delta_b))/2}{1-p}}(\mu-V_L).
    5. Pages 110-111. The equations below (5.21) onwards should be

      •     \begin{equation*} \mathcal L^\pi_t = \left( r \,x + (\mu-r)\,\pi \right) \,\partial_x + \tfrac{1}{2}\sigma^2\,\pi^2\,\partial_{xx} + (\mu-r)\,S\,\partial_S +\tfrac{1}{2}\sigma^2\,S^2\,\partial_{SS}+\sigma^2\,\pi\,S\,\partial_{xS}\;.\\[1em] \end{equation*}

      •     \begin{equation*} \begin{split} 0= &\left( \partial_t + r\,x\,\partial_x +(\mu-r)\,S\,\partial_S+ \tfrac{1}{2}\,\sigma^2\,S^2\,\partial_{SS}\right) H \\ &+ \sup_\pi\left\{ \pi \,\left( (\mu-r)\,\partial_x +\sigma^2\,S\,\partial_{xS}\right) H + \tfrac{1}{2}\sigma^2\,\pi^2\,\partial_{xx}H\right\}\,,\\[1em] \end{split} \end{equation*}

      •     \begin{equation*}\begin{split} &\pi \,\left( (\mu-r)\,\partial_x +\sigma^2\,S\,\partial_{xS}\right) H + \tfrac{1}{2}\sigma^2\,\pi^2\,\partial_{xx}H\\ &\quad =\tfrac{1}{2}\,\sigma^2\,\partial_{xx}H \left(\left(\pi - \pi^*\right)^2 - (\pi^*)^2 \right)\;,\\[1em] \end{split} \end{equation*}

      •     \begin{equation*} \pi^* = -\frac{(\mu-r)\,\partial_xH +\sigma^2\,S\,\partial_{xS} H}{\sigma^2\,\partial_{xx}H}\\[1em] \end{equation*}

      •     \begin{equation*} 0=\left(\partial_t + r\,x\,\partial_x + (\mu-r)\,S\,\partial_S+\tfrac{1}{2}\,\sigma^2\,S^2\,\partial_{SS}\right)H - \frac{\left((\mu-r)\,\partial_xH +\sigma^2\,S\,\partial_{xS} H\right)^2}{2\,\sigma^2\,\partial_{xx}H}\;. \\[1em] \end{equation*}

    6. Page 111, the inequality in point (ii) should be \gamma<1 NOT \gamma>1. For \gamma>1, there is an upper bound on wealth, rather than a lower bound.
    7. In the exercises of Chapter 6 the liquidation penalty has the same typo in
      three places. The penalty is not ‘minus‘ Q_T^\nu(S_T-\alpha\,Q_T^\nu)^2 it should be ‘plus‘ Q_T^\nu(S_T-\alpha\,Q_T^\nu)
      The typos appear in first displayed equation in E.6.1, and equations (6.41) and (6.47)
    8. Page 175. There is a minus sign missing in equation (7.22) . The equation should be:
      h_1(t,\mu) = b\,\mathbb{E}_{t,\mu}\left[ \int^T_t \left( \frac{\zeta e^{\gamma (T-u)}- e^{-\gamma (T-u)} }{\zeta e^{\gamma (T-t)}-e^{-\gamma (T-t)} } \right) \,\mu_u\,du \right]\,.
    9. Equations (A.8), (A.11), (A.17), and (A.18) are all missing the term g_t\,\partial_y\ell(t,Y_t)\,dW_t. This change does NOT, however, alter the corresponding differential operators, as this term represents a martingale increment.
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