Portfolio Selection with Transaction Costs

Abstract

This thesis considers an investor who can distribute wealth between two assets , one with deterministic rate of growth (eg. bank deposit account) , the other with growth governed by a Brownian motion with drift (eg. equity share) . Transfers between these holdings incur proportional transaction costs . The investor may consume continuously and costlessly from the bank , and requires a consumption and investment strategy which maximises total discounted utility of consumption over an infinite horizon .For a large class of utility functions , it is proved that maximum utility is achieved by a strategy-which confines the investor's portfolio to a certain wedge-shaped region in the portfolio plane, by minimal trading, and allows consumption at a rate depending at any time on the current state of the portfolio .Moreover it is shown that the optimal strategy does not lead to bankruptcy in finite time.The problem is treated rigorously as a reflected diffusion process, and the existence and uniqueness of the optimally-controlled wealth process are demonstrated.

Dynamic portfolio selection with nonlinear transaction costs

“…transaction costs than the S-NT interfaces. This is in agreement with Constantinides (1986), and Davis & Norman (1990).…”

“…The B-NT interfaces are more sensitive to changes in proportional transaction costs than the S-NT interfaces. This is in agreement with Constantinides (1986), and Davis & Norman (1990).…”

Dynamic portfolio selection with nonlinear transaction costs

“…transaction costs than the S-NT interfaces. This is in agreement with Constantinides (1986), and Davis & Norman (1990).…”

“…The B-NT interfaces are more sensitive to changes in proportional transaction costs than the S-NT interfaces. This is in agreement with Constantinides (1986), and Davis & Norman (1990).…”

Dynamic portfolio selection with fixed and/or proportional transaction costs using non-singular stochastic optimal control theory

“…The B-NT interfaces are more sensitive to changes in proportional transaction costs than the S-NT interfaces. This is in agreement with Constantinides (1986) and Davis and Norman (1990). In the presence of fixed transaction costs only, the buy and sell targets almost coincide with the Merton line, and the targets are independent of the magnitude of the fixed transaction costs.…”

Money Matters: Broad Divisia Money and the Recovery of the US Nominal GDP From the COVID‐19 Recession

“…A second major factor is that as stock loads fall, the increased substitutability of money and stocks implies that negative shocks to stock returns will induce larger flights to quality and surges in money demand. This is consistent not only with theoretical work (Davis and Norman 1990, Liu 2004, and Liu and Loewenstein 2002 showing that high asset transfer costs create either zones of portfolio inaction or sluggish portfolio adjustment that become less pronounced as transfer costs fall but also with evidence the lower loads have induced higher US stock ownership rates (see Duca and Walker 2022) and that demand for simple-sum M2 became more sensitive to stock price shocks after load fees decline (Anderson, Bordo, and Duca 2017). For this reason, money demand is more susceptible to asset market shocks in eras when stock loads are lower.…”

Dynamic portfolio selection with nonlinear transaction costs

“…transaction costs than the S-NT interfaces. This is in agreement with Constantinides (1986), and Davis & Norman (1990).…”

“…The B-NT interfaces are more sensitive to changes in proportional transaction costs than the S-NT interfaces. This is in agreement with Constantinides (1986), and Davis & Norman (1990).…”

Dynamic portfolio selection with fixed and/or proportional transaction costs using non-singular stochastic optimal control theory

“…The B-NT interfaces are more sensitive to changes in proportional transaction costs than the S-NT interfaces. This is in agreement with Constantinides (1986) and Davis and Norman (1990). In the presence of fixed transaction costs only, the buy and sell targets almost coincide with the Merton line, and the targets are independent of the magnitude of the fixed transaction costs.…”

Money Matters: Broad Divisia Money and the Recovery of the US Nominal GDP From the COVID‐19 Recession

“…A second major factor is that as stock loads fall, the increased substitutability of money and stocks implies that negative shocks to stock returns will induce larger flights to quality and surges in money demand. This is consistent not only with theoretical work (Davis and Norman 1990, Liu 2004, and Liu and Loewenstein 2002 showing that high asset transfer costs create either zones of portfolio inaction or sluggish portfolio adjustment that become less pronounced as transfer costs fall but also with evidence the lower loads have induced higher US stock ownership rates (see Duca and Walker 2022) and that demand for simple-sum M2 became more sensitive to stock price shocks after load fees decline (Anderson, Bordo, and Duca 2017). For this reason, money demand is more susceptible to asset market shocks in eras when stock loads are lower.…”

Dynamic portfolio selection with nonlinear transaction costs

“…transaction costs than the S-NT interfaces. This is in agreement with Constantinides (1986), and Davis & Norman (1990).…”

“…The B-NT interfaces are more sensitive to changes in proportional transaction costs than the S-NT interfaces. This is in agreement with Constantinides (1986), and Davis & Norman (1990).…”

Dynamic portfolio selection with fixed and/or proportional transaction costs using non-singular stochastic optimal control theory

“…The B-NT interfaces are more sensitive to changes in proportional transaction costs than the S-NT interfaces. This is in agreement with Constantinides (1986) and Davis and Norman (1990). In the presence of fixed transaction costs only, the buy and sell targets almost coincide with the Merton line, and the targets are independent of the magnitude of the fixed transaction costs.…”

Money Matters: Broad Divisia Money and the Recovery of the US Nominal GDP From the COVID‐19 Recession

“…A second major factor is that as stock loads fall, the increased substitutability of money and stocks implies that negative shocks to stock returns will induce larger flights to quality and surges in money demand. This is consistent not only with theoretical work (Davis and Norman 1990, Liu 2004, and Liu and Loewenstein 2002 showing that high asset transfer costs create either zones of portfolio inaction or sluggish portfolio adjustment that become less pronounced as transfer costs fall but also with evidence the lower loads have induced higher US stock ownership rates (see Duca and Walker 2022) and that demand for simple-sum M2 became more sensitive to stock price shocks after load fees decline (Anderson, Bordo, and Duca 2017). For this reason, money demand is more susceptible to asset market shocks in eras when stock loads are lower.…”