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.

Liquidity shocks and equilibrium liquidity premia

“…Because of the law of large numbers, agents exit at a rate of l per unit of time, leaving the economy with a constant mass of agents. 6 See, for example, [12,[14][15][16]19,27,31,32]. 7 Without loss of generality, our set of agents is the unit interval.…”

Optimal lifetime consumption and investment under a drawdown constraint

“…He and Pagès [10] and El Karoui and Jeanblanc [8] extended the Merton model to allow for the presence of labor income. Constantinides and Magill [3], Davis and Norman [7], and Shreve and Soner [21] considered the case where the risky asset is subject to proportional transaction costs. Ben Tahar, Soner and Touzi [2] considered the case where the sales of the risky asset are subject to taxes on the capital gains.…”

Option pricing with transaction costs using a Markov chain approximation

“…This feature is (notoriously) common to models with transaction costs. Constantinides (1986), Davis and Norman (1990), Dumas and Luciano (1991) and Shreve and Soner (1994) do ÿnd, in the inÿnite-horizon (and hence, time independent) case, for HARA utility functions, an analytic form for the value function. However, the boundaries of the NT region must still be located numerically.…”