Dr. Pavel Gapeev

The problems of risk sensitive portfolio optimisation under transaction costs have taken a considerable attention in the recent literature on mathematical finance. We study the associated problems of risk sensitive utility indifference pricing for perpetual American options with fixed transaction costs in the classical model of financial market with two tradable assets. Assume that the investors trading in the market must pay transaction costs equal to a fixed fraction of the entire portfolio wealth each time they trade. The objective is to maximise the asymptotic (risk null and risk adjusted) exponential growth rates based on the expected logarithmic or power utility of the difference between the terminal portfolio wealth and a certain amount of the option payoffs. It is shown that the optimal trading policy keeps the number of shares held in the assets unchanged between the transactions. In order to determine the optimal trading times and