Portfolio Selection via Topological Data Analysis ArXiv ID: 2308.07944 “View on arXiv” Authors: Unknown Abstract Portfolio management is an essential part of investment decision-making. However, traditional methods often fail to deliver reasonable performance. This problem stems from the inability of these methods to account for the unique characteristics of multivariate time series data from stock markets. We present a two-stage method for constructing an investment portfolio of common stocks. The method involves the generation of time series representations followed by their subsequent clustering. Our approach utilizes features based on Topological Data Analysis (TDA) for the generation of representations, allowing us to elucidate the topological structure within the data. Experimental results show that our proposed system outperforms other methods. This superior performance is consistent over different time frames, suggesting the viability of TDA as a powerful tool for portfolio selection. ...

Reconstructing cryptocurrency processes via Markov chains ArXiv ID: 2308.07626 “View on arXiv” Authors: Unknown Abstract The growing attention on cryptocurrencies has led to increasing research on digital stock markets. Approaches and tools usually applied to characterize standard stocks have been applied to the digital ones. Among these tools is the identification of processes of market fluctuations. Being interesting stochastic processes, the usual statistical methods are appropriate tools for their reconstruction. There, besides chance, the description of a behavioural component shall be present whenever a deterministic pattern is ever found. Markov approaches are at the leading edge of this endeavour. In this paper, Markov chains of orders one to eight are considered as a way to forecast the dynamics of three major cryptocurrencies. It is accomplished using an empirical basis of intra-day returns. Besides forecasting, we investigate the existence of eventual long-memory components in each of those stochastic processes. Results show that predictions obtained from using the empirical probabilities are better than random choices. ...

The Geometry of Constant Function Market Makers ArXiv ID: 2308.08066 “View on arXiv” Authors: Unknown Abstract Constant function market makers (CFMMs) are the most popular type of decentralized trading venue for cryptocurrency tokens. In this paper, we give a very general geometric framework (or ‘axioms’) which encompass and generalize many of the known results for CFMMs in the literature, without requiring strong conditions such as differentiability or homogeneity. One particular consequence of this framework is that every CFMM has a (unique) canonical trading function that is nondecreasing, concave, and homogeneous, showing that many results known only for homogeneous trading functions are actually fully general. We also show that CFMMs satisfy a number of intuitive and geometric composition rules, and give a new proof, via conic duality, of the equivalence of the portfolio value function and the trading function. Many results are extended to the general setting where the CFMM is not assumed to be path-independent, but only one trade is allowed. Finally, we show that all ‘path-independent’ CFMMs have a simple geometric description that does not depend on any notion of a ’trading history’. ...

A discretization scheme for path-dependent FBSDEs and PDEs ArXiv ID: 2308.07029 “View on arXiv” Authors: Unknown Abstract This study develops a numerical scheme for path-dependent FBSDEs and PDEs. We introduce a Picard iteration method for solving path-dependent FBSDEs, prove its convergence to the true solution, and establish its rate of convergence. A key contribution of our approach is a novel estimator for the martingale integrand in the FBSDE, specifically designed to handle path-dependence more reliably than existing methods. We derive a concentration inequality that quantifies the statistical error of this estimator in a Monte Carlo framework. Based on these results, we investigate a supervised learning method with neural networks for solving path-dependent PDEs. The proposed algorithm is fully implementable and adaptable to a broad class of path-dependent problems. ...

BIRP: Bitcoin Information Retrieval Prediction Model Based on Multimodal Pattern Matching ArXiv ID: 2308.08558 “View on arXiv” Authors: Unknown Abstract Financial time series have historically been assumed to be a martingale process under the Random Walk hypothesis. Instead of making investment decisions using the raw prices alone, various multimodal pattern matching algorithms have been developed to help detect subtly hidden repeatable patterns within the financial market. Many of the chart-based pattern matching tools only retrieve similar past chart (PC) patterns given the current chart (CC) pattern, and leaves the entire interpretive and predictive analysis, thus ultimately the final investment decision, to the investors. In this paper, we propose an approach of ranking similar PC movements given the CC information and show that exploiting this as additional features improves the directional prediction capacity of our model. We apply our ranking and directional prediction modeling methodologies on Bitcoin due to its highly volatile prices that make it challenging to predict its future movements. ...

Insurance pricing on price comparison websites via reinforcement learning ArXiv ID: 2308.06935 “View on arXiv” Authors: Unknown Abstract The emergence of price comparison websites (PCWs) has presented insurers with unique challenges in formulating effective pricing strategies. Operating on PCWs requires insurers to strike a delicate balance between competitive premiums and profitability, amidst obstacles such as low historical conversion rates, limited visibility of competitors’ actions, and a dynamic market environment. In addition to this, the capital intensive nature of the business means pricing below the risk levels of customers can result in solvency issues for the insurer. To address these challenges, this paper introduces reinforcement learning (RL) framework that learns the optimal pricing policy by integrating model-based and model-free methods. The model-based component is used to train agents in an offline setting, avoiding cold-start issues, while model-free algorithms are then employed in a contextual bandit (CB) manner to dynamically update the pricing policy to maximise the expected revenue. This facilitates quick adaptation to evolving market dynamics and enhances algorithm efficiency and decision interpretability. The paper also highlights the importance of evaluating pricing policies using an offline dataset in a consistent fashion and demonstrates the superiority of the proposed methodology over existing off-the-shelf RL/CB approaches. We validate our methodology using synthetic data, generated to reflect private commercially available data within real-world insurers, and compare against 6 other benchmark approaches. Our hybrid agent outperforms these benchmarks in terms of sample efficiency and cumulative reward with the exception of an agent that has access to perfect market information which would not be available in a real-world set-up. ...

Quantifying Outlierness of Funds from their Categories using Supervised Similarity ArXiv ID: 2308.06882 “View on arXiv” Authors: Unknown Abstract Mutual fund categorization has become a standard tool for the investment management industry and is extensively used by allocators for portfolio construction and manager selection, as well as by fund managers for peer analysis and competitive positioning. As a result, a (unintended) miscategorization or lack of precision can significantly impact allocation decisions and investment fund managers. Here, we aim to quantify the effect of miscategorization of funds utilizing a machine learning based approach. We formulate the problem of miscategorization of funds as a distance-based outlier detection problem, where the outliers are the data-points that are far from the rest of the data-points in the given feature space. We implement and employ a Random Forest (RF) based method of distance metric learning, and compute the so-called class-wise outlier measures for each data-point to identify outliers in the data. We test our implementation on various publicly available data sets, and then apply it to mutual fund data. We show that there is a strong relationship between the outlier measures of the funds and their future returns and discuss the implications of our findings. ...

AI-Assisted Investigation of On-Chain Parameters: Risky Cryptocurrencies and Price Factors ArXiv ID: 2308.08554 “View on arXiv” Authors: Unknown Abstract Cryptocurrencies have become a popular and widely researched topic of interest in recent years for investors and scholars. In order to make informed investment decisions, it is essential to comprehend the factors that impact cryptocurrency prices and to identify risky cryptocurrencies. This paper focuses on analyzing historical data and using artificial intelligence algorithms on on-chain parameters to identify the factors affecting a cryptocurrency’s price and to find risky cryptocurrencies. We conducted an analysis of historical cryptocurrencies’ on-chain data and measured the correlation between the price and other parameters. In addition, we used clustering and classification in order to get a better understanding of a cryptocurrency and classify it as risky or not. The analysis revealed that a significant proportion of cryptocurrencies (39%) disappeared from the market, while only a small fraction (10%) survived for more than 1000 days. Our analysis revealed a significant negative correlation between cryptocurrency price and maximum and total supply, as well as a weak positive correlation between price and 24-hour trading volume. Moreover, we clustered cryptocurrencies into five distinct groups using their on-chain parameters, which provides investors with a more comprehensive understanding of a cryptocurrency when compared to those clustered with it. Finally, by implementing multiple classifiers to predict whether a cryptocurrency is risky or not, we obtained the best f1-score of 76% using K-Nearest Neighbor. ...

ChatGPT-based Investment Portfolio Selection ArXiv ID: 2308.06260 “View on arXiv” Authors: Unknown Abstract In this paper, we explore potential uses of generative AI models, such as ChatGPT, for investment portfolio selection. Trusting investment advice from Generative Pre-Trained Transformer (GPT) models is a challenge due to model “hallucinations”, necessitating careful verification and validation of the output. Therefore, we take an alternative approach. We use ChatGPT to obtain a universe of stocks from S&P500 market index that are potentially attractive for investing. Subsequently, we compared various portfolio optimization strategies that utilized this AI-generated trading universe, evaluating those against quantitative portfolio optimization models as well as comparing to some of the popular investment funds. Our findings indicate that ChatGPT is effective in stock selection but may not perform as well in assigning optimal weights to stocks within the portfolio. But when stocks selection by ChatGPT is combined with established portfolio optimization models, we achieve even better results. By blending strengths of AI-generated stock selection with advanced quantitative optimization techniques, we observed the potential for more robust and favorable investment outcomes, suggesting a hybrid approach for more effective and reliable investment decision-making in the future. ...

UAMM: Price-oracle based Automated Market Maker ArXiv ID: 2308.06375 “View on arXiv” Authors: Unknown Abstract Automated market makers (AMMs) are pricing mechanisms utilized by decentralized exchanges (DEX). Traditional AMM approaches are constrained by pricing solely based on their own liquidity pool, without consideration of external markets or risk management for liquidity providers. In this paper, we propose a new approach known as UBET AMM (UAMM), which calculates prices by considering external market prices and the impermanent loss of the liquidity pool. Despite relying on external market prices, our method maintains the desired properties of a constant product curve when computing slippages. The key element of UAMM is determining the appropriate slippage amount based on the desired target balance, which encourages the liquidity pool to minimize impermanent loss. We demonstrate that our approach eliminates arbitrage opportunities when external market prices are efficient. ...