E.6.1 The agent wishes to liquidate It shares between t and T using MOs. The value function is H(t, S. q) = sup Et,s.q (Su - kon) vu du - Qr (ST -aQ'7) VEALT where k > 0 is the temporary market impact, v, is the speed of trading, a 2 0 is the liquidation penalty, and dS, = odw (a) Show that the value function H satisfies 0 = -(0.H-S)2 -4ko,H -2ko20SSH. (b) Make the ansatz H(t, S, q) = h2(t)q2 + h, (t)q+ ho(t)+ qs (6.39) and show that the optimal liquidation rate is (6.40) 151:c) Let a > 00 and Show that (6.40} converges to (6.12). Moreover, discuss the intuition of the strategy when a O.