标题： 统计套利与期货市场中的交易成本最优交易 显示英文标题

标题： Statistical Arbitrage and Optimal Trading with Transaction Costs in Futures Markets

摘要： 我们考虑布朗市场模型和终端财富预期效用最大化的問題。 我们具体研究在存在交易成本的情况下，一个投资于期货市场的基金/代理人的终端财富效用最大化问题。 我们对统计套利策略提出一些初步的评论，并设定期货市场的框架，介绍保证金、杠杆和滑点等概念。 该设置为离散时间，期货价格的演变被建模为涉及伊藤求和的离散随机序列。 我们假设驱动收益过程的漂移和布朗运动是不可观测的，交易成本由买卖价差表示。 我们提供了最优投资组合过程的显式解，并使用对数效用提供了一个例子。 显示英文摘要

摘要： 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.