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June 23, 2005:
New design and layout finished and uploaded to OSWD. Since it is my first contribution to this site, it has been given the title "andreas01".

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Current Research

Optimal Investment with Transaction Costs

Optimal Trading with Transaction Costs in Futures Markets and Risk Neutral Strategies

Abstract: 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. Finally, we compare our solution
to the optimal portfolio process without transaction costs in the context of a risk-neutral statistical
arbitrage strategy on S&P500 Futures Index, and we obtain promising experimental results.

Statistical Arbitrage

Flexible least squares for temporal data mining and statistical arbitrage

Abstract: A number of recent emerging applications call for studying data streams, potentially infinite
flows of information updated in real-time. When multiple co-evolving data streams are observed,
an important task is to determine how these streams depend on each other, accounting for dynamic
dependence patterns without imposing any restrictive probabilistic law governing this dependence.
In this paper we argue that flexible least squares (FLS), a penalized version of ordinary least squares
that accommodates for time-varying regression coefficients, can be deployed successfully in this context.
Our motivating application is statistical arbitrage, an investment strategy that exploits patterns detected
 in financial data streams. We demonstrate that FLS is algebraically equivalent to the well-known
Kalman filter equations, and take advantage of this equivalence to gain a better understanding of FLS
 and suggest a more efficient algorithm. Promising experimental results obtained from a FLS-based
algorithmic trading system for the S&P 500 Futures Index are reported.

On-Line Portfolio Optimization

Robust On-Line Mean-Variance Portfolio Optimization and L-Efficient

In this paper we present an on-line robust approach to portfolio optimization. We establish an association between
least squares algorithm and mean-variance portfolio optimization, by mapping the latter to a projection problem.
We extend the result to the total least squares set up. We continue to offer two novel robust on-line
algorithms, namely Robust-Exponentially Weighted Least Squares (R-EWRLS) and Filter Factors (FF),
to obtain robust portfolio weights. We evaluate the two approaches against known benchmark techniques for
portfolio optimization, using spot foreign exchange data, to obtain promising experimental results. Finally, we introduce
the notion of L-Efficient Frontier, a convenient and beneficial way to visualize mean-variance frontier in a three
dimensional set up by including a regularization term.

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