Group for Research in Decision Analysis

Multiobjective and Robust Optimization in Finance and Risk Management

Oleksandr Romanko Department of Computing and Software, McMaster University, Canada

Financial optimization models become a necessary tool of financial analysts due to recent developments in algorithms and software. The common feature of financial and risk management optimization problems is presence of multiple performance indicators (profit, return on investment, trading costs) and risk measures (volatility of investment returns, portfolio expected shortfall, Value-at-Risk, etc.). Due to that most of financial optimization models are multiobjective problems.

The solution of a multiobjective optimization problem is the set of Pareto efficient points, known as Pareto efficient frontier. We present a parametric optimization based methodology that allows computing Pareto front efficiently. Parametric optimization allows not only computing Pareto efficient frontiers for certain classes of optimization problems, but also helps to identify frontier structure, e.g., a piece-wise quadratic surface. Identified frontier structure is used to find better solutions and improve decision-making.

The main challenge of practical financial models is minimizing risk in the presence of uncertainty. Tackling uncertainty in financial optimization is discussed. We briefly describe a number of techniques to solve models involving uncertainty such as stochastic optimization and robust optimization. Robustness can be either incorporated in the optimization problem structure or can be considered as an additional objective in the multiobjective optimization problem. We discuss advantages and disadvantages of both approaches and illustrate those on practical examples.

Most of the illustrative examples are based on portfolio selection and risk management models that were developed at Algorithmics Incorporated, an IBM Company and are aimed for practical implementation and use by risk managers at different financial institutions and industrial enterprises. A number of optimization software packages are used for modeling and computations.

This seminar is organized jointly with the Montreal section of CORS.