Davis and Norman (1990) introduced a consumption-investment problem for a CRRA agent with proportional transaction costs and obtained a closed-form solution for it. Another advantage of the model was allowing for discontinuous strategy. For this purpose, the original Merton framework had to be upgraded to semimartingale dynamics. Portfolio value in each of the assets is described by the following equations:
dXt = (rtXt — Ct) dt — (1 + A) dLt + (1 — p) dMt, X0 = x,
dY t = aYt dt + oYt dwt + dLt — dMt, Y0 = y,
where coefficients A, p define proportional transaction costs, Lt, Mt are cumulative amounts of bought and sold risky asset respectively. Results demonstrated the existence of three behavioral regions for portfolio managers, and are presented in Fig. 3.
Unlike Merton’s case, th...Read More