A Unified Approach to Portfolio Optimization with Linear Transaction Costs

In this paper we study the continuous time optimal portfolio selection problem for an investor with a finite horizon who maximizes expected utility of terminal wealth and faces transaction costs in the capital market. It is well known that, depending on a particular structure of transaction costs, such a problem is formulated and solved within either stochastic singular control or stochastic impulse control framework. In this paper we propose a unified framework, which generalizes the contemporary approaches and is capable to deal with any problem where transaction costs are a linear/piecewise-linear function of the volume of trade. We also discuss some methods for solving numerically the problem within our unified framework.portfolio choice, transaction costs, stochastic singular control, stochastic impulse control, computational methods

European Option Pricing and Hedging with both Fixed and Proportional Transaction Costs

In this paper we extend the utility based option pricing and hedging approach, pioneered by Hodges and Neuberger (1989) and further developed by Davis, Panas and Zariphopoulou (1993), for the market where each transaction has a fixed cost component. We present a model, where investors have a CARA utility, and derive some properties of reservation option prices. We suggest and implement discretization schemes for computing the reservation option prices. The numerical results of option pricing and hedging are presented for the case of European call options and the investors with different levels of ARA. We also try to reconcile our findings with such empirical pricing bias as the volatility smile.option pricing, transaction costs, stochastic control, Markov chain approximation

Optimal portfolio selection with both fixed and proportional transaction costs for a CRRA investor with finite horizon

In this paper we study the optimal portfolio selection problem for a constant relative risk averse investor who faces fixed and proportional transaction costs and maximizes expected utility of end-of-period wealth. We use a continuous time model and apply the method of the Markov chain approximation to solve numerically for the optimal trading policy. The numerical solution indicates that the portfolio space is divided into three disjoint regions (Buy, Sell, and No-Transaction), and four boundaries describe the optimal policy. If a portfolio lies in the Buy region, the optimal strategy is to buy the risky asset until the portfolio reaches the lower (Buy) target boundary. Similarly, if a portfolio lies in the Sell region, the optimal strategy is to sell the risky asset until the portfolio reaches the upper (Sell) target boundary. All these boundaries are functions of the investor's horizon and the composition of the investor's wealth. Some important properties of the optimal policy are as follows: As the terminal date approaches, the NT region widens. And the NT region widens as wealth declines. As the investor's wealth increases the target boundaries converge quickly to the NT boundaries in the corresponding model with proportional transaction costs only. As wealth becomes small, the target boundaries move closer to the Merton line. The closer the terminal date, the earlier this movement begins. The effects on the optimal policy from varying volatility, drift, CRRA, and the level of transaction costs are also examined