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 (S. - kow) vu du - Qr (Sr -abt). 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= -(2.H-S)2 -4ka,H -2ko2@SSH . (b) Make the ansatz H(t, S, q) = hz(t)q2+ h,(t) q + ho(t)+ qs (6.39) and show that the optimal liquidation rate is T-t+. (6.40) 151(e) Let a > 00 and Show that (6.40} converges to (6.12). Moreover, discuss the intuition of the strategy when a 0