The aim of this work is to extend the capital growth theory developed by Kelly, Breiman, Cover and others to asset market models with transaction costs. We define a natural generalization of the notion of a numeraire portfolio proposed by Long and show how such portfolios can be used for...

In this paper, first we study a stochastic volatility market model for which an explicit candidate solution to the problem of maximizing utility function of terminal wealth is obtained. Applying this result, we present a complete solution for the Heston model which is a particular case of the...

We consider a large insurance company whose surplus (reserve) is modeled by a Brownian motion. The company invests its surplus in stock market assets which may or may not contain an element of risk. To minimize the insurance risk there is a possibility to reinsure a part or the whole insurance...

We consider a Brownian storage system with stepwise holding cost and linear cost of disposal. There are no limits on the rate of disposal. We seek a policy which minimizes total discounted cost on an infinite interval. It is proved that the optimal policy is characterized by two points: one is a...

In the recent work of Dempster, Evstigneev and Taksar (2006) it has been shown that the von Neumann-Gale model of economic dynamics can serve as a convenient and natural framework for the analysis of questions of asset pricing and hedging under transaction costs. The present article focuses on a...