An Exact Solution to a Dynamic Portfolio Choice Problem under Transactions Costs

Abstract

The presence of any friction in financial markets qualitatively changes the nature of the optimization problem faced by an investor. It requires one to either act or do nothing, an issue which, of course, does not arise in frictionless situations. The investor considered here accumulates wealth without consuming until some terminal point in time when he consumes all. His objective is to maximize the expected utility derived from that terminal consumption. We postpone the terminal point far into the future to obtain a stationary portfolio rule. The portfolio policy is in the form of two control barriers between which portfolio proportions are allowed to fluctuate. We show how to calculate them.

The Incentives of Hedge Fund Fees and High-Water Marks

“…To recover an explicit solution, we focus on the case of a long planning horizon. This approach has already proved effective in portfolio choice with leverage constraints (Grossman and Vila, 1992), drawdown constraints (Grossman and Zhou, 1993), and transaction costs (Dumas and Luciano, 1991). Following these authors, for each portfolio π, define the certainty equivalent rate of the corresponding fee process F π as 4 :…”

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.…”

Option pricing with transaction costs using a Markov chain approximation

“…(32) and (34) are the well known "value matching" conditions satisÿed by the value function of (2). (See, for example, Dixit (1991), Dumas (1991Dumas ( , 1992, Dumas and Luciano (1991), or the exposition by Harrison (1985) of the theory of optimally regulated Brownian motion.) They hold throughout the BUY and SELL regions, and (of course) at the boundaries y b ; y s , regardless of whether these are chosen optimally or not.…”

“…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.…”

“…Hodges and Neuberger (1989) recognised that a valuation method which incorporates some element of optimality, in the form of the agent's utility maximisation objective, is perhaps the most promising path to follow in designing e ective option hedging policies. This point was also made by Dumas and Luciano (1991). By comparing the utility achieved with and without the obligations of an option contract, Hodges and Neuberger speciÿed reservation bid and asking prices for an option by requiring that the same utility is achieved whether an option trade has been entered into or not.…”