Title: On Arbitrage, Optimal Portfolio, and Equilibrium under Incomplete Market and Transaction Costs

Author: Jussi Keppo

Status: Systems Analysis Laboratory Research Reports A70, February 1998.

 This thesis considers mathematical finance in an incomplete market with transaction costs. It consists of two practical and two theoretical essays. The practical papers can be seen as an application of optimal portfolio selection and the theoretical papers study the market equilibrium conditions in the presence of incompleteness. The results indicate that the optimal hedging strategy differs significantly from the corresponding strategy in a frictionless market even at one- or two-day trading intervals and that under stochastic real foreign exchange rates international equilibrium is curved. In addition, it is shown that the market conditions hold in an incomplete market under frictions if the conditions hold in the projected markets that exist inside the initial market.