2008/01/22 by Theodoros Tsagaris, Tsagaris, Theodoros
Economics, Econometrics and Finance · Mathematics · #Economic theories and models #Financial Markets and Investment Strategies #Stochastic processes and financial applications #math.OC #math.PR #msc:60G44 #msc:90C46 #msc:91B28 #msc:91B70 #q-fin.TR
paper · pdf · doi:10.48550/arxiv.0801.3348
28 pages, submitted to journal
arxiv created 2008/01/22 · arxiv updated 2009/12/01
We consider the Brownian market model and the problem of expected utility maximization of terminal wealth. We, specifically, examine the problem of maximizing the utility of terminal wealth under the presence of transaction costs of a fund/agent investing in futures markets. We offer some preliminary remarks about statistical arbitrage strategies and we set the framework for futures markets, and introduce concepts such as margin, gearing and slippage. The setting is of discrete time, and the price evolution of the futures prices is modelled as discrete random sequence involving Ito's sums. We assume the drift and the Brownian motion driving the return process are non-observable and the transaction costs are represented by the bid-ask spread. We provide explicit solution to the optimal portfolio process, and we offer an example using logarithmic utility.