Risk Analysis

An Interval Type-2 Version of Bayes Theorem Derived from Interval Probability Range Estimates Provided by Subject Matter Experts ArXiv ID: 2509.08834 “View on arXiv” Authors: John T. Rickard, William A. Dembski, James Rickards Abstract Bayesian inference is widely used in many different fields to test hypotheses against observations. In most such applications, an assumption is made of precise input values to produce a precise output value. However, this is unrealistic for real-world applications. Often the best available information from subject matter experts (SMEs) in a given field is interval range estimates of the input probabilities involved in Bayes Theorem. This paper provides two key contributions to extend Bayes Theorem to an interval type-2 (IT2) version. First, we develop an IT2 version of Bayes Theorem that uses a novel and conservative method to avoid potential inconsistencies in the input IT2 MFs that otherwise might produce invalid output results. We then describe a novel and flexible algorithm for encoding SME-provided intervals into IT2 fuzzy membership functions (MFs), which we can use to specify the input probabilities in Bayes Theorem. Our algorithm generalizes and extends previous work on this problem that primarily addressed the encoding of intervals into word MFs for Computing with Words applications. ...

Monte-Carlo Option Pricing in Quantum Parallel ArXiv ID: 2505.09459 “View on arXiv” Authors: Robert Scriba, Yuying Li, Jingbo B Wang Abstract Financial derivative pricing is a significant challenge in finance, involving the valuation of instruments like options based on underlying assets. While some cases have simple solutions, many require complex classical computational methods like Monte Carlo simulations and numerical techniques. However, as derivative complexities increase, these methods face limitations in computational power. Cases involving Non-Vanilla Basket pricing, American Options, and derivative portfolio risk analysis need extensive computations in higher-dimensional spaces, posing challenges for classical computers. Quantum computing presents a promising avenue by harnessing quantum superposition and entanglement, allowing the handling of high-dimensional spaces effectively. In this paper, we introduce a self-contained and all-encompassing quantum algorithm that operates without reliance on oracles or presumptions. More specifically, we develop an effective stochastic method for simulating exponentially many potential asset paths in quantum parallel, leading to a highly accurate final distribution of stock prices. Furthermore, we demonstrate how this algorithm can be extended to price more complex options and analyze risk within derivative portfolios. ...

Enhancing Investment Analysis: Optimizing AI-Agent Collaboration in Financial Research ArXiv ID: 2411.04788 “View on arXiv” Authors: Unknown Abstract In recent years, the application of generative artificial intelligence (GenAI) in financial analysis and investment decision-making has gained significant attention. However, most existing approaches rely on single-agent systems, which fail to fully utilize the collaborative potential of multiple AI agents. In this paper, we propose a novel multi-agent collaboration system designed to enhance decision-making in financial investment research. The system incorporates agent groups with both configurable group sizes and collaboration structures to leverage the strengths of each agent group type. By utilizing a sub-optimal combination strategy, the system dynamically adapts to varying market conditions and investment scenarios, optimizing performance across different tasks. We focus on three sub-tasks: fundamentals, market sentiment, and risk analysis, by analyzing the 2023 SEC 10-K forms of 30 companies listed on the Dow Jones Index. Our findings reveal significant performance variations based on the configurations of AI agents for different tasks. The results demonstrate that our multi-agent collaboration system outperforms traditional single-agent models, offering improved accuracy, efficiency, and adaptability in complex financial environments. This study highlights the potential of multi-agent systems in transforming financial analysis and investment decision-making by integrating diverse analytical perspectives. ...

A new measure of risk using Fourier analysis ArXiv ID: 2408.10279 “View on arXiv” Authors: Unknown Abstract We use Fourier analysis to access risk in financial products. With it we analyze price changes of e.g. stocks. Via Fourier analysis we scrutinize quantitatively whether the frequency of change is higher than a change in (conserved) company value would allow. If it is the case, it would be a clear indicator of speculation and with it risk. The entire methods or better its application is fairly new. However, there were severe flaws in previous attempts; making the results (not the method) doubtful. We corrected all these mistakes by e.g. using Fourier transformation instead of discrete Fourier analysis. Our analysis is reliable in the entire frequency band, even for fre-quency of 1/1d or higher if the prices are noted accordingly. For the stocks scrutinized we found that the price of stocks changes disproportionally within one week which clearly indicates spec-ulation. It would be an interesting extension to apply the method to crypto currencies as these currencies have no conserved value which makes normal considerations of volatility difficult. ...

Generative Machine Learning for Multivariate Equity Returns ArXiv ID: 2311.14735 “View on arXiv” Authors: Unknown Abstract The use of machine learning to generate synthetic data has grown in popularity with the proliferation of text-to-image models and especially large language models. The core methodology these models use is to learn the distribution of the underlying data, similar to the classical methods common in finance of fitting statistical models to data. In this work, we explore the efficacy of using modern machine learning methods, specifically conditional importance weighted autoencoders (a variant of variational autoencoders) and conditional normalizing flows, for the task of modeling the returns of equities. The main problem we work to address is modeling the joint distribution of all the members of the S&P 500, or, in other words, learning a 500-dimensional joint distribution. We show that this generative model has a broad range of applications in finance, including generating realistic synthetic data, volatility and correlation estimation, risk analysis (e.g., value at risk, or VaR, of portfolios), and portfolio optimization. ...