Performing Bayesian Risk Aggregation using Discrete Approximation Algorithms with Graph Factorization

TL;DR

This paper introduces two algorithms for Bayesian risk aggregation that handle hybrid dependencies and high-dimensional Bayesian networks, improving inference in financial risk modeling.

Contribution

The paper presents novel algorithms for Bayesian risk aggregation, addressing hybrid dependencies and providing a universal inference method for complex Bayesian networks.

Findings

Effective handling of hybrid models with continuous and discrete variables.

Universal inference algorithm for complex Bayesian network models.

Enhanced accuracy in risk aggregation for high-dimensional data.

Abstract

Risk aggregation is a popular method used to estimate the sum of a collection of financial assets or events, where each asset or event is modelled as a random variable. Applications, in the financial services industry, include insurance, operational risk, stress testing, and sensitivity analysis, but the problem is widely encountered in many other application domains. This thesis has contributed two algorithms to perform Bayesian risk aggregation when model exhibit hybrid dependency and high dimensional inter-dependency. The first algorithm operates on a subset of the general problem, with an emphasis on convolution problems, in the presence of continuous and discrete variables (so called hybrid models) and the second algorithm offer a universal method for general purpose inference over much wider classes of Bayesian Network models.