Fair Estimation of Capital Risk Allocation

Speaker:

Igor Cialenco, Associate Professor, Department of Applied Mathematics, Illinois Institute of Technology

 

Description:

We propose a novel methodology for estimation of risk capital allocation, rooted in the theory of dynamic risk measures. We work within a general, but tractable class of law-invariant coherent risk measures, with a particular focus on expected shortfall. We introduce the concept of fair capital allocations and provide explicit formulae for fair capital allocations in case when the constituents of the risky portfolio are jointly normally distributed. The main focus of the paper is on the problem of approximating fair portfolio allocations in the case of not fully known laws of the portfolio constituents. We define and study the concepts of fair allocation estimators and asymptotically fair allocation estimators. We derive several estimators, and prove their fairness and/or asymptotic fairness under normality as well as in a nonparametric setup. Last, but not least, we propose two backtesting methodologies that are oriented at assessing the performance of the allocation estimation procedure. All concepts will be illustrated via a numerical study. 

This is joint work with Tomasz R. Bielecki (Illinois Tech), Marcin Pitera (Jagiellonian University) and Thorsten Schmidt (University of Freiburg)

 

Topic:

Mathematical Finance, Stochastic Analysis, and Machine Learning