Networks & Graph Methods

Sustainable investing refers to the integration of environmental and social aspects in investors’ decisions. We propose a novel methodology based on the Triangulated Maximally Filtered Graph and node2vec algorithms to construct an hedging portfolio for climate risk, represented by various risk facto

Option pricing, a fundamental problem in finance, often requires solving non-linear partial differential equations (PDEs). When dealing with multi-asset options, such as rainbow options, these PDEs become high-dimensional, leading to challenges posed by the curse of dimensionality. While deep learni

Drawing inspiration from the significant impact of the ongoing Russia-Ukraine conflict and the recent COVID-19 pandemic on global financial markets, this study conducts a thorough analysis of three key crude oil futures markets: WTI, Brent, and Shanghai (SC). Employing the visibility graph (VG) meth

Correlation-diversified portfolios can be constructed by finding the maximum independent sets (MISs) in market graphs with edges corresponding to correlations between two stocks. The computational complexity to find the MIS increases exponentially as the size of the market graph increases, making th

We extend recurrent neural networks to include several flexible timescales for each dimension of their output, which mechanically improves their abilities to account for processes with long memory or with highly disparate time scales. We compare the ability of vanilla and extended long short term me

We present a novel methodology for modeling and forecasting multivariate realized volatilities using customized graph neural networks to incorporate spillover effects across stocks. The proposed model offers the benefits of incorporating spillover effects from multi-hop neighbors, capturing nonlinea

In this paper, we present a randomized extension of the deep splitting algorithm introduced in [Beck, Becker, Cheridito, Jentzen, and Neufeld (2021)] using random neural networks suitable to approximately solve both high-dimensional nonlinear parabolic PDEs and PIDEs with jumps having (possibly) inf

This paper develops a unified framework that links firm-level predictive signals, cross-asset spillovers, and the stochastic discount factor (SDF). Signals and spillovers are jointly estimated by maximizing the Sharpe ratio, yielding an interpretable SDF that both ranks characteristic relevance and

This paper evaluates the causal impact of Generative Artificial Intelligence (GenAI) adoption on productivity and systemic risk in the U.S. banking sector. Using a novel dataset linking SEC 10-Q filings to Federal Reserve regulatory data for 809 financial institutions over 2018–2025, we employ two

We propose DeePM (Deep Portfolio Manager), a structured deep-learning macro portfolio manager trained end-to-end to maximize a robust, risk-adjusted utility. DeePM addresses three fundamental challenges in financial learning: (1) it resolves the asynchronous “ragged filtration” problem via a Directe

This study models the monopoly pricing of weather index insurance as a Bowley-type sequential game involving a profit-maximizing insurer (leader) and a farmer (follower). The farmer chooses an insurance payoff to minimize a convex distortion risk measure, while the insurer anticipates this best resp

This paper introduces a hybrid framework for portfolio optimization that fuses Long Short-Term Memory (LSTM) forecasting with a Proximal Policy Optimization (PPO) reinforcement learning strategy. The proposed system leverages the predictive power of deep recurrent networks to capture temporal depend

Recent crises like the COVID-19 pandemic and geopolitical tensions have exposed vulnerabilities and caused disruptions of supply chains, leading to product shortages, increased costs, and economic instability. This has prompted increasing efforts to assess systemic risk, namely the effects of firm d

Since its advent in 2009, Bitcoin (BTC) has garnered increasing attention from both academia and industry. However, due to the massive transaction volume, no systematic study has quantitatively measured the asset decentralization degree specifically from a network perspective. In this paper, by cond

Defining and finalizing Mergers and Acquisitions (M&A) requires complex human skills, which makes it very hard to automatically find the best partner or predict which firms will make a deal. In this work, we propose the MASS algorithm, a specifically designed measure of similarity between companies

We investigate an application of network centrality measures to portfolio optimization, by generalizing the method in [“Pozzi, Di Matteo and Aste, \emph{“Spread of risks across financial markets: better to invest in the peripheries”}, Scientific Reports 3:1665, 2013”], that however had significant l

Robust utility optimization enables an investor to deal with market uncertainty in a structured way, with the goal of maximizing the worst-case outcome. In this work, we propose a generative adversarial network (GAN) approach to (approximately) solve robust utility optimization problems in general a

In this paper, we present an artificial neural network framework for portfolio compression of a large portfolio of European options with varying maturities (target portfolio) by a significantly smaller portfolio of European options with shorter or same maturity (compressed portfolio), which also rep

Money launderers exploit the weaknesses in detection systems by purposefully placing their ill-gotten money into multiple accounts, at different banks. That money is then layered and moved around among mule accounts to obscure the origin and the flow of transactions. Consequently, the money is integ

We study the effect of stochastic feeding costs on animal-based commodities with particular focus on aquaculture. More specifically, we use soybean futures to infer on the stochastic behaviour of salmon feed, which we assume to follow a Schwartz-2-factor model. We compare the decision of harvesting

Decentralized finance (DeFi) can broaden access while leaving activity, network position, and infrastructure concentrated. We develop a four-dimensional framework for participation, activity distribution, structural position, and infrastructure dependence, integrating network theory, theorem-consist

We introduce a deep kernel hedging framework that combines the flexibility of deep learning with the structural inductive bias of kernel methods. The hedging functional is restricted to a reproducing kernel Hilbert space whose kernel is parameterized through a neural network embedding of the input f

This paper studies forward-looking stock-stock correlation forecasting for S&P 500 constituents and evaluates whether learned correlation forecasts can improve graph-based clustering used in basket trading strategies. We cast 10-day ahead correlation prediction in Fisher-z space and train a Temporal

Topological Data Analysis (TDA), an emerging field in investment sciences, harnesses mathematical methods to extract data features based on shape, offering a promising alternative to classical portfolio selection methodologies. We utilize persistence landscapes, a type of summary statistics for pers

This paper develops a unified framework for analyzing technology adoption in financial networks that incorporates spatial spillovers, network externalities, and their interaction. The framework characterizes adoption dynamics through a master equation whose solution admits a Feynman-Kac representati

Pricing multi-asset options via the Black-Scholes PDE is limited by the curse of dimensionality: classical full-grid solvers scale exponentially in the number of underlyings and are effectively restricted to three assets. Practitioners typically rely on Monte Carlo methods for computing complex inst

We present a novel numerical method for solving McKean-Vlasov forward-backward stochastic differential equations (MV-FBSDEs) with common noise, combining Picard iterations, elicitability and deep learning. The key innovation involves elicitability to derive a path-wise loss function, enabling effici

This study applies Empirical Mode Decomposition (EMD) to the MSCI World index and converts the resulting intrinsic mode functions (IMFs) into graph representations to enable modeling with graph neural networks (GNNs). Using CEEMDAN, we extract nine IMFs spanning high-frequency fluctuations to long-t

In the last five years, expected shortfall (ES) and stressed ES (SES) have become key required regulatory measures of market risk in the banking sector, especially following events such as the global financial crisis. Thus, finding ways to optimize their estimation is of great importance. We extend

Bitcoin operates as a macroeconomic paradox: it combines a strictly predetermined, inelastic monetary issuance schedule with a stochastic, highly elastic demand for scarce block space. This paper empirically validates the Endogenous Constraint Hypothesis, positing that protocol-level throughput limi

This paper investigates an optimal integration of deep learning with financial models for robust asset price forecasting. Specifically, we developed a hybrid framework combining a Long Short-Term Memory (LSTM) network with the Merton-Lévy jump-diffusion model. To optimise this framework, we employed

We present a fast and robust calibration method for stochastic volatility models that admit Fourier-analytic transform-based pricing via characteristic functions. The design is structure-preserving: we keep the original pricing transform and (i) split the pricing formula into data-independent inte-

Covariance matrices estimated from short, noisy, and non-Gaussian financial time series are notoriously unstable. Empirical evidence suggests that such covariance structures often exhibit power-law scaling, reflecting complex, hierarchical interactions among assets. Motivated by this observation, we

Risk management is a prominent issue in peer-to-peer lending. An investor may naturally reduce his risk exposure by diversifying instead of putting all his money on one loan. In that case, an investor may want to minimize the Value-at-Risk (VaR) or Conditional Value-at-Risk (CVaR) of his loan portfo

We propose a new pseudo-Siamese Network for Asset Pricing (SNAP) model, based on deep learning approaches, for conditional asset pricing. Our model allows for the deep alpha, deep beta and deep factor risk premia conditional on high dimensional observable information of financial characteristics and

We propose a mathematically rigorous framework for identifying and completing Coincidence of Wants (CoW) cycles in decentralized exchange (DEX) aggregators. Unlike existing auction based systems such as CoWSwap, our approach introduces an asset matrix formulation that not only verifies feasibility u

Efficient computation of Greeks for multi-asset options remains a key challenge in quantitative finance. While Monte Carlo (MC) simulation is widely used, it suffers from the large sample complexity for high accuracy. We propose a framework to compute Greeks in a single evaluation of a tensor train

Option pricing theory, such as the Black and Scholes (1973) model, provides an explicit solution to construct a strategy that perfectly hedges an option in a continuous-time setting. In practice, however, trading occurs in discrete time and often involves transaction costs, making the direct applica

Causal networks offer an intuitive framework to understand influence structures within time series systems. However, the presence of cycles can obscure dynamic relationships and hinder hierarchical analysis. These networks are typically identified through multivariate predictive modelling, but enfor

This paper investigates the dynamic interdependencies between the European insurance sector and key financial markets-equity, bond, and banking-by extending the Generalized Forecast Error Variance Decomposition framework to a broad set of performance and risk indicators. Our empirical analysis, base

We revisit the Bayesian Black-Litterman (BL) portfolio model and remove its reliance on subjective investor views. Classical BL requires an investor “view”: a forecast vector $q$ and its uncertainty matrix $Ω$ that describe how much a chosen portfolio should outperform the market. Our key idea is to

Fluctuations in stock prices are influenced by a complex interplay of factors that go beyond mere historical data. These factors, themselves influenced by external forces, encompass inter-stock dynamics, broader economic factors, various government policy decisions, outbreaks of wars, etc. Furthermo

This research proposes a cutting-edge ensemble deep learning framework for stock price prediction by combining three advanced neural network architectures: The particular areas of interest for the research include but are not limited to: Variational Autoencoder (VAE), Transformer, and Long Short-Ter

The failure of key financial institutions may accelerate risk contagion due to their interconnections within the system. In this paper, we propose a robust portfolio strategy to mitigate systemic risks during extreme events. We use the stock returns of key financial institutions as an indicator of t

Simulation methods have always been instrumental in finance, and data-driven methods with minimal model specification, commonly referred to as generative models, have attracted increasing attention, especially after the success of deep learning in a broad range of fields. However, the adoption of th

Weighted reciprocity between two agents can be defined as the minimum of sending and receiving value in their bilateral relationship. In financial networks, such reciprocity characterizes the importance of individual banks as both liquidity absorber and provider, a feature typically attributed to la

Temporal Graph Learning (TGL) is crucial for capturing the evolving nature of stock markets. Traditional methods often ignore the interplay between dynamic temporal changes and static relational structures between stocks. To address this issue, we propose the Dynamic Graph Representation with Contra

In this paper we develop a novel hidden Markov graphical model to investigate time-varying interconnectedness between different financial markets. To identify conditional correlation structures under varying market conditions and accommodate stylized facts embedded in financial time series, we rely

Limit order book (LOB) is a dynamic, event-driven system that records real-time market demand and supply for a financial asset in a stream flow. Event stream prediction in LOB refers to forecasting both the timing and the type of events. The challenge lies in modeling the time-event distribution to

The Lightning Network (LN) has emerged as a second-layer solution to Bitcoin’s scalability challenges. The rise of Payment Channel Networks (PCNs) and their specific mechanisms incentivize individuals to join the network for profit-making opportunities. According to the latest statistics, the total

This paper studies pricing of weather-derivative (WD) contracts on temperature and precipitation. For temperature-linked strangles in Toronto and Chicago, we benchmark a harmonic-regression/ARMA model against a feed-forward neural network (NN), finding that the NN reduces out-of-sample mean-squared

Calibrating the time-dependent Implied Volatility Surface (IVS) using sparse market data is an essential challenge in computational finance, particularly for real-time applications. This task requires not only fitting market data but also satisfying a specified partial differential equation (PDE) an

Hedging exotic options in presence of market frictions is an important risk management task. Deep hedging can solve such hedging problems by training neural network policies in realistic simulated markets. Training these neural networks may be delicate and suffer from slow convergence, particularly

The diffusion of financial news into market prices is a complex process, making it challenging to evaluate the connections between news events and market movements. This paper introduces FININ (Financial Interconnected News Influence Network), a novel market prediction model that captures not only t

In Reinforcement Learning (RL), multi-armed Bandit (MAB) problems have found applications across diverse domains such as recommender systems, healthcare, and finance. Traditional MAB algorithms typically assume stationary reward distributions, which limits their effectiveness in real-world scenarios

Inspired by the recently proposed Kolmogorov-Arnold Networks (KANs), we introduce the KAN-based Option Pricing (KANOP) model to value American-style options, building on the conventional Least Square Monte Carlo (LSMC) algorithm. KANs, which are based on Kolmogorov-Arnold representation theorem, off

Volatility, which indicates the dispersion of returns, is a crucial measure of risk and is hence used extensively for pricing and discriminating between different financial investments. As a result, accurate volatility prediction receives extensive attention. The Generalized Autoregressive Condition

Stock markets play an important role in the global economy, where accurate stock price predictions can lead to significant financial returns. While existing transformer-based models have outperformed long short-term memory networks and convolutional neural networks in financial time series predictio

We present a new deep primal-dual backward stochastic differential equation framework based on stopping time iteration to solve optimal stopping problems. A novel loss function is proposed to learn the conditional expectation, which consists of subnetwork parameterization of a continuation value and

We study the loan contracts offered by decentralised loan protocols (DLPs) through the lens of financial derivatives. DLPs, which effectively are clearinghouses, facilitate transactions between option buyers (i.e. borrowers) and option sellers (i.e. lenders). The loan-to-value at which the contract

Granger causality can uncover the cause and effect relationships in financial networks. However, such networks can be convoluted and difficult to interpret, but the Helmholtz-Hodge-Kodaira decomposition can split them into a rotational and gradient component which reveals the hierarchy of Granger ca

Financial networks can be constructed using statistical dependencies found within the price series of speculative assets. Across the various methods used to infer these networks, there is a general reliance on predictive modelling to capture cross-correlation effects. These methods usually model the

The innovative GNN-CL model proposed in this paper marks a breakthrough in the field of financial fraud detection by synergistically combining the advantages of graph neural networks (gnn), convolutional neural networks (cnn) and long short-term memory (LSTM) networks. This convergence enables multi

The application of deep learning techniques for predicting stock market prices is a prominent and widely researched topic in the field of data science. To effectively predict market trends, it is essential to utilize a diversified dataset. In this paper, we give a graph neural network based convolut

We devise a novel method for nowcasting implied volatility based on neural operators. Better known as implied volatility smoothing in the financial industry, nowcasting of implied volatility means constructing a smooth surface that is consistent with the prices presently observed on a given option m

The accurate prediction of stock movements is crucial for investment strategies. Stock prices are subject to the influence of various forms of information, including financial indicators, sentiment analysis, news documents, and relational structures. Predominant analytical approaches, however, tend

In this study, we model the Indian stock market as heterogenous scale free network, which is then embedded in a two dimensional hyperbolic space through a machine learning based technique called as coalescent embedding. This allows us to apply the hyperbolic kmeans algorithm on the Poincare disc and

This paper explores the utilization of Temporal Graph Networks (TGN) for financial anomaly detection, a pressing need in the era of fintech and digitized financial transactions. We present a comprehensive framework that leverages TGN, capable of capturing dynamic changes in edges within financial ne

Time-series with volatility clustering pose a unique challenge to uncertainty quantification (UQ) for returns forecasts. Methods for UQ such as Deep Evidential regression offer a simple way of quantifying return forecast uncertainty without the costs of a full Bayesian treatment. However, the Normal

Detecting anomalies is important for identifying inefficiencies, errors, or fraud in business processes. Traditional process mining approaches focus on analyzing ‘flattened’, sequential, event logs based on a single case notion. However, many real-world process executions exhibit a graph-like struct

We propose a novel approach to marked Hawkes kernel inference which we name the moment-based neural Hawkes estimation method. Hawkes processes are fully characterized by their first and second order statistics through a Fredholm integral equation of the second kind. Using recent advances in solving

In this research, we introduce a novel methodology for the index tracking problem with sparse portfolios by leveraging topological data analysis (TDA). Utilizing persistence homology to measure the riskiness of assets, we introduce a topological method for data-driven learning of the parameters for

We propose a time series forecasting method named Quantum Gramian Angular Field (QGAF). This approach merges the advantages of quantum computing technology with deep learning, aiming to enhance the precision of time series classification and forecasting. We successfully transformed stock return time

Developing a generative model of realistic order flow in financial markets is a challenging open problem, with numerous applications for market participants. Addressing this, we propose the first end-to-end autoregressive generative model that generates tokenized limit order book (LOB) messages. The

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

We consider the supervised learning problem of learning the price of an option or the implied volatility given appropriate input data (model parameters) and corresponding output data (option prices or implied volatilities). The majority of articles in this literature considers a (plain) feed forward

We propose a novel data-driven neural network (NN) optimization framework for solving an optimal stochastic control problem under stochastic constraints. Customized activation functions for the output layers of the NN are applied, which permits training via standard unconstrained optimization. The o

We propose two parametric approaches to evaluate swing contracts with firm constraints. Our objective is to define approximations for the optimal control, which represents the amounts of energy purchased throughout the contract. The first approach involves approximating the optimal control by means

We investigate the concept of network momentum, a novel trading signal derived from momentum spillover across assets. Initially observed within the confines of pairwise economic and fundamental ties, such as the stock-bond connection of the same company and stocks linked through supply-demand chains

In this paper we demonstrate both theoretically as well as numerically that neural networks can detect model-free static arbitrage opportunities whenever the market admits some. Due to the use of neural networks, our method can be applied to financial markets with a high number of traded securities

We develop a spouse-protected tontine in which a first death changes the household state but generates no pool transfer. The same account remains attached to the household contract until extinction and funds a spouse-only continuation phase if the retiree dies first. We derive contract-level actuari

Recursive differenced forecasting, the standard remedy for non-stationarity, predicts one-step changes and integrates them by cumulative summation. We show that this reconstruction is a discrete integrator with a pole on the unit circle, so the biased increment errors of a learned nonlinear model ar

This paper studies the problem of hedging and pricing a European call option under proportional transaction costs, from two complementary perspectives. We first derive the optimal hedging strategy under CARA utility, following the stochastic control framework of Davis et al. (1993), characterising t

Anti-money laundering (AML) systems are important for protecting the global economy. However, conventional rule-based methods rely on domain knowledge, leading to suboptimal accuracy and a lack of scalability. Graph neural networks (GNNs) for digraphs (directed graphs) can be applied to transaction

Whether heterogeneous investor flows transmit private information across stocks or merely reflect coordinated responses to public signals remains an open question in market microstructure. We construct Transfer Entropy (TE) networks from investor-type flows – foreign, institutional, and individual

Credit risk scoring must support high-stakes lending decisions where data distributions change over time, probability estimates must be reliable, and group-level fairness is required. While modern machine learning models improve default prediction accuracy, they often produce poorly calibrated score

This paper introduces MarketGAN, a factor-based generative framework for high-dimensional asset return generation under severe data scarcity. We embed an explicit asset-pricing factor structure as an economic inductive bias and generate returns as a single joint vector, thereby preserving cross-sect

We use the discrete Ollivier-Ricci graph curvature with Ricci flow to examine the intrinsic geometry of financial markets through the empirical correlation graph of the NASDAQ 100 index. Our main result is the development of a technique to perform surgery on the neckpinch singularities that form dur

This study evaluates deep neural networks for forecasting probability distributions of financial returns. 1D convolutional neural networks (CNN) and Long Short-Term Memory (LSTM) architectures are used to forecast parameters of three probability distributions: Normal, Student’s t, and skewed Student

The rise of decentralized finance (DeFi) has created a growing demand for accurate yield and performance forecasting to guide liquidity allocation strategies. In this study, we benchmark six models, XGBoost, Random Forest, LSTM, Transformer, quantum neural networks (QNN), and quantum support vector

Financial markets are dynamic, interconnected systems where local shocks can trigger widespread instability, challenging portfolio managers and policymakers. Traditional correlation analysis often miss the directionality and temporal dynamics of information flow. To address this, we present a unifie

We examine strategically incorporating broad stock market leveraged exchange-traded funds (LETFs) into investment portfolios. We demonstrate that easily understandable and implementable strategies can enhance the risk-return profile of a portfolio containing LETFs. Our analysis shows that seemingly

The paper explores the use of Deep Reinforcement Learning (DRL) in stock market trading, focusing on two algorithms: Double Deep Q-Network (DDQN) and Proximal Policy Optimization (PPO) and compares them with Buy and Hold benchmark. It evaluates these algorithms across three currency pairs, the S&P 5

We compare traditional approach of computing logarithmic returns with the fractional differencing method and its tempered extension as methods of data preparation before their usage in advanced machine learning models. Differencing parameters are estimated using multiple techniques. The empirical in

Corporate fraud detection aims to automatically recognize companies that conduct wrongful activities such as fraudulent financial statements or illegal insider trading. Previous learning-based methods fail to effectively integrate rich interactions in the company network. To close this gap, we colle

This paper addresses the critical disconnect between prediction and decision quality in portfolio optimization by integrating Large Language Models (LLMs) with decision-focused learning. We demonstrate both theoretically and empirically that minimizing the prediction error alone leads to suboptimal

The complexity of stocks and industries presents challenges for stock prediction. Currently, stock prediction models can be divided into two categories. One category, represented by GRU and ALSTM, relies solely on stock factors for prediction, with limited effectiveness. The other category, represen

Equity market dynamics are conventionally investigated in name space where stocks are indexed by company names. In contrast, by indexing stocks based on their ranks in capitalization, we gain a different perspective of market dynamics in rank space. Here, we demonstrate the superior performance of s

Maintaining a balance between returns and volatility is a common strategy for portfolio diversification, whether investing in traditional equities or digital assets like cryptocurrencies. One approach for diversification is the application of community detection or clustering, using a network repres

Production networks constitute the backbone of every economic system. They are inherently fragile as several recent crises clearly highlighted. Estimating the system-wide consequences of local disruptions (systemic risk) requires detailed information on the supply chain networks (SCN) at the firm-le