Learning implicit risk preferences in portfolio optimisation

This project aims to identify agent’s preferences in risky environments like the financial market. Identifying and modeling of agent’s risk preferences is central to finance and economics applications. For example, expected utility theory (EUT) postulates that every risk-averse agent maximizes the expected value of the future uncertain payoff for some non-decreasing concave utility function. “Popular” utility functions include quadratic, power and negative exponential utilities. However, a general methodology for robustly identifying an exact form of the utility function for a given agent remains an open issue. The issue here is that most of investors do not know the exact numerical representation of their utility function, and the idea is to “learn” or “extract” hidden/implicit risk preferences of investors based on the actions they made in the past. Identified preferences can then be used to recommend best future investment strategies in changing market on an individual basis. This will allow investors to get higher-profit and lower-risk investment portfolios.

In the deterministic setting, the classical approach of Afriat (1967) finds a utility function that rationalises given (available) consumer’s demand data. This project will address similar problem in a risky environment, based on the idea of inverse portfolio optimization, developed by Grechuk and Zabarankin (2014, 2016). However, a rationalising utility function is typically either non-unique or may not exist at all. Non-uniqueness will be resolved by identifying optimal/robust candidates based on specified criteria, whereas non-existence will be addressed by identifying approximate solutions for given data sets and by analysing their appropriateness for representing agent’s risk preferences. If approximate solutions are found to be unsatisfactory, an alternative theory for identifying agent’s risk preferences will be suggested by the Ph.D. student and supervisor. For example, the theory of coherent risk measures may be appropriate. Other theories will be tested as well.