Title:

The effect of transaction costs on portfolio optimisation in discrete time

There are different theoretical approaches to the construction of a portfolio which offer maximum expected returns for a given level of risk tolerance and where the goal is to find the optimal investment rule. Each investor has a certain utility for money which is reflected by the choice of a utility function. In this work, two different types of risk averse utility functions (the power utility function and an exponential one) are studied in discrete time without making any assumptions about the underlying probability distribution of the returns of the asset prices. Each investor chooses, at the beginning of an investment period, the feasible portfolio allocation which maximises the expected value of the utility function for terminal wealth. Effects of both large and small proportional transaction costs on the choice of an optimal portfolio are taken into account. The transaction regions are approximated by using asymptotic methods, when the proportional transaction costs are small, and by using expansions about critical points for large transaction costs. At first the onerisky asset case is looked at then a multiasset case is studied. A method for computing the distribution of the total wealth of the portfolio is then developed using a chosen distribution for the returns: the lognormal and then a distribution derived from the maximum entropy. The Value at Risk is then defined and used to constrain the portfolio optimisation problem with a different utility: the utility of consumption.
