We examine the intertemporal optimal portfolio selection and consumption rule of an investor with a constant relative risk aversion who faces proportional transaction costs when trading between a risk-free asset and N risky assets. The investor's objective is to maximize the total utility of...

A crucial assumption in the Black-Scholes theory of options pricing is the no transaction costs assumption. However, following such a strategy in the presence of transaction costs would lead to immediate ruin. This paper presents a stochastic control approach to the pricing and hedging of a...

Option pricing theory is considered when the underlying asset price satisfies a stochastic differential equation which is driven by random motions generated by stable distributions. The properties of the stable distributions are discussed and their connection with the theory of fractional...

The solution to the intertemporal optimal portfolio selection and consumption rule with small transaction costs is derived via the use of perturbation analysis for the two assets portfolio, one risky and one riskfree. This methodology allows us to apply a broader specification for the function...

Barrier options are considered for Asian options using a differential equation method. Solutions are obtained in the form of Fourier series for barriers which expand or contract as they approach maturity. Rigorous bounds are obtained. It is shown that by differentiating with respect to a...

The inclusion of transaction costs in the optimal portfolio selection and consumption rule problem is accomplished via the use of perturbation analyses. The portfolio under consideration consists of more than one risky asset, which makes numerical methods impractical. The objective is to...

In this paper we examine the Akian, Menaldi and Sulem (1996) model for the optimal management of a portfolio, when there are transaction costs which are equal to a fixed percentage of the amount transacted. We analyse this model in the realistic limit of small transaction costs. Although the...