Probabilistic Scenario Optimisation

Paolo Sironi

Creating a new theory is not like destroying an old barn and erecting a skyscraper in its place. It is rather like climbing a mountain, gaining new and wider views, discovering unexpected connections between our starting points and its rich environment. But the point from which we started out still exists and can be seen, although it appears smaller and forms a tiny part of our broad view gained by the mastery of the obstacles on our adventurous way up.

Albert Einstein (1879–1955)

PSO is an exhaustive enumeration technique for designing goal-based and long-term optimal investing. In this chapter we present a step-by-step process from potential to admissible portfolios, and discuss low-discrepancy sequences and lexicographical representations, risk-adequate portfolios and the goal-based objective function.

INTRODUCTION

Markowitz has shaped the landscape of portfolio optimisation since the introduction of the mean–variance approach in the 1950s, and subsequent academic advances have further refined his original ideas, particularly regarding the risk measure definition (eg, semi-variance and expected shortfall). The change in perspective introduced by Black and Litterman