Bayesian Methods

Observation-driven Dirichlet models for compositional time series commonly use the additive log-ratio (ALR) link and include a moving-average (MA) term based on ALR residuals. In the standard Bayesian Dirichlet Auto-Regressive Moving-Average (B-DARMA) recursion, this MA regressor has a nonzero condi

This paper develops a framework to predict toxic trades that a broker receives from her clients. Toxic trades are predicted with a novel online learning Bayesian method which we call the projection-based unification of last-layer and subspace estimation (PULSE). PULSE is a fast and statistically-eff

We study the construction and rebalancing of sparse index-tracking portfolios from an operational research perspective, with explicit emphasis on uncertainty quantification and implementability. The decision variables are portfolio weights constrained to sum to one; the aims are to track a reference

Financial time series often exhibit skewness and heavy tails, making it essential to use models that incorporate these characteristics to ensure greater reliability in the results. Furthermore, allowing temporal variation in the skewness parameter can bring significant gains in the analysis of this

We introduce a novel machine learning model for credit risk by combining tree-boosting with a latent spatio-temporal Gaussian process model accounting for frailty correlation. This allows for modeling non-linearities and interactions among predictor variables in a flexible data-driven manner and for

Large Language Models (LLMs) excel at understanding context and qualitative nuances but struggle with the rigorous and transparent reasoning required in high-stakes quantitative domains such as financial trading. We propose a model-first hybrid architecture for the options “wheel” strategy that comb

Crypto enthusiasts claim that buying and holding crypto assets yields high returns, often citing Bitcoin’s past performance to promote other tokens and fuel fear of missing out. However, understanding the real risk-return trade-off and what factors affect future crypto returns is crucial as crypto b

This paper investigates the impact of posterior drift on out-of-sample forecasting accuracy in overparametrized machine learning models. We document the loss in performance when the loadings of the data generating process change between the training and testing samples. This matters crucially in set

Constructing the Implied Volatility Surface (IVS) is a challenging task in quantitative finance due to the complexity of real markets and the sparsity of market data. Structural models like Stochastic Alpha Beta Rho (SABR) model offer interpretability and theoretical consistency but lack flexibility

This paper investigates whether structural econometric models can rival machine learning in forecasting energy–macro dynamics while retaining causal interpretability. Using monthly data from 1999 to 2025, we develop a unified framework that integrates Time-Varying Parameter Structural VARs (TVP-SVA

Compositional time series frequently exhibit structural breaks due to external shocks, policy changes, or market disruptions. Standard methods either ignore such breaks or handle them through fixed effects that cannot extrapolate beyond the sample, or step-function dummies that impose instantaneous

Algorithmic trading relies on machine learning models to make trading decisions. Despite strong in-sample performance, these models often degrade when confronted with evolving real-world market regimes, which can shift dramatically due to macroeconomic changes-e.g., monetary policy updates or unanti

A long memory and non-linear realized volatility model class is proposed for direct Value at Risk (VaR) forecasting. This model, referred to as RNN-HAR, extends the heterogeneous autoregressive (HAR) model, a framework known for efficiently capturing long memory in realized measures, by integrating

We propose a new approach to volatility modeling by combining deep learning (LSTM) and realized volatility measures. This LSTM-enhanced realized GARCH framework incorporates and distills modeling advances from financial econometrics, high frequency trading data and deep learning. Bayesian inference

We introduce an ensemble learning method based on Gaussian Process Regression (GPR) for predicting conditional expected stock returns given stock-level and macro-economic information. Our ensemble learning approach significantly reduces the computational complexity inherent in GPR inference and lend

We employ a Bayesian modelling technique for high dimensional cointegration estimation to construct low volatility portfolios from a large number of stocks. The proposed Bayesian framework effectively identifies sparse and important cointegration relationships amongst large baskets of stocks across

Credibility theory combines individual experience with portfolio information for insurance pricing, but classical formulations focus primarily on conditional means and expected premiums. We propose a Dirichlet mixed-membership model (DMMM) for multivariate distributional credibility. Policyholder ri

We revisit Merton’s continuous-time portfolio selection through a data-driven, distributionally robust lens. Our aim is to tap the benefits of frequent trading over short horizons while acknowledging that drift is hard to pin down, whereas volatility can be screened using realized or implied measure

We develop a mathematical model for intraday dispatch of co-located wind-battery energy assets. Focusing on the primary objective of firming grid-side actual production vis-a-vis the preset day-ahead hourly generation targets, we conduct a comprehensive study of the resulting stochastic control prob

A new modular approximate Bayesian inferential framework is proposed that enables fast calculation of probabilistic predictions of future option prices. We exploit multiple information sources, including daily spot returns, high-frequency spot data and option prices. A benefit of this modular Bayesi

Can contagion be inferred from aggregated default data? We study this as a problem of identifiability, asking whether contagion generates components in default count distributions that remain distinct from those induced by macroeconomic fluctuations. We compare three dependence structures: cumulativ

While asset-pricing models increasingly recognize that factor risk premia are subject to structural change, existing literature typically assumes that investors correctly account for such instability. This paper studies how investors instead learn under a misspecified model that underestimates struc

Parametric portfolio policies may experience estimation risk. I develop a generalized Bayesian framework that updates priors, delivering a posterior distribution over characteristic tilts and out-of-sample returns that is the unique belief-updating rule consistent with the investor’s utility functio

This paper develops a Bayesian Generalised Pareto Regression (GPR) model to forecast extreme losses in Indian equity markets, with a focus on the Nifty 50 index. Extreme negative returns, though rare, can cause significant financial disruption, and accurate modelling of such events is essential for

Existing black-box portfolio management systems are prevalent in the financial industry due to commercial and safety constraints, though their performance can fluctuate dramatically with changing market regimes. Evaluating these non-transparent systems is computationally expensive, as fixed budgets

This study introduces a dynamic investment framework to enhance portfolio management in volatile markets, offering clear advantages over traditional static strategies. Evaluates four conventional approaches : equal weighted, minimum variance, maximum diversification, and equal risk contribution unde

We investigate the impact of several critical events associated with the Russo Ukrainian war, started officially on 24 February 2022 with the Russian invasion of Ukraine, on ten European electricity markets, two natural gas markets (the European reference trading hub TTF and N.Y. NGNMX market) and h

In this paper we consider the modeling of measurement error for fund returns data. In particular, given access to a time-series of discretely observed log-returns and the associated maximum over the observation period, we develop a stochastic model which models the true log-returns and maximum via a

There are several approaches to modeling and forecasting time series as applied to prices of commodities and financial assets. One of the approaches is to model the price as a non-stationary time series process with heteroscedastic volatility (variance of price). The goal of the research is to gener

In recent years, the dynamic factor model has emerged as a dominant tool in economics and finance, particularly for investment strategies. This model offers improved handling of complex, nonlinear, and noisy market conditions compared to traditional static factor models. The advancement of machine l

A semi-parametric joint Value-at-Risk (VaR) and Expected Shortfall (ES) forecasting framework employing multiple realized measures is developed. The proposed framework extends the realized exponential GARCH model to be semi-parametrically estimated, via a joint loss function, whilst extending existi

The present article explores the application of randomized control techniques in empirical asset pricing and performance evaluation. It introduces geometric random walks, a class of Markov chain Monte Carlo methods, to construct flexible control groups in the form of random portfolios adhering to in

It is well-known that decision-making problems from stochastic control can be formulated by means of a forward-backward stochastic differential equation (FBSDE). Recently, the authors of Ji et al. 2022 proposed an efficient deep learning algorithm based on the stochastic maximum principle (SMP). In

In credit risk analysis, survival models with fixed and time-varying covariates are widely used to predict a borrower’s time-to-event. When the time-varying drivers are endogenous, modelling jointly the evolution of the survival time and the endogenous covariates is the most appropriate approach, al

This paper addresses the challenge of model uncertainty in quantitative finance, where decisions in portfolio allocation, derivative pricing, and risk management rely on estimating stochastic models from limited data. In practice, the unavailability of the true probability measure forces reliance on

Parametric Portfolio Policies (PPP) estimate optimal portfolio weights directly as functions of observable signals by maximizing expected utility, bypassing the need to model asset returns and covariances. However, PPP ignores policy risk. We show that this is consequential, leading to an overstatem

Understanding how the composition of guest origin markets evolves over time is critical for destination marketing organizations, hospitality businesses, and tourism planners. We develop and apply Bayesian Dirichlet autoregressive moving average (BDARMA) models to forecast the compositional dynamics

Credit risk models are a critical decision-support tool for financial institutions, yet tightening data-protection rules (e.g., GDPR, CCPA) increasingly prohibit cross-border sharing of borrower data, even as these models benefit from cross-institution learning. Traditional default prediction suffer

This paper proposes three types of Bayesian CART (or BCART) models for aggregate claim amount, namely, frequency-severity models, sequential models and joint models. We propose a general framework for the BCART models applicable to data with multivariate responses, which is particularly useful for t

In this paper we consider the simulation-based Bayesian analysis of stochastic volatility in mean (SVM) models. Extending the highly efficient Markov chain Monte Carlo mixture sampler for the SV model proposed in Kim et al. (1998) and Omori et al. (2007), we develop an accurate approximation of the

We develop a framework for composite likelihood estimation of parametric continuous-time stationary Gaussian processes. We derive the asymptotic theory of the associated maximum composite likelihood estimator. We implement our approach on a pair of models that have been proposed to describe the rand

Skew-t copula models are attractive for the modeling of financial data because they allow for asymmetric and extreme tail dependence. We show that the copula implicit in the skew-t distribution of Azzalini and Capitanio (2003) allows for a higher level of pairwise asymmetric dependence than two popu

Predicting corporate default risk has long been a crucial topic in the finance field, as bankruptcies impose enormous costs on market participants as well as the economy as a whole. This paper aims to forecast frailty correlated default models with subjective judgements on a sample of U.S. public no

Portfolio optimization under cardinality constraints transforms the classical Markowitz mean-variance problem from a convex quadratic problem into an NP-hard combinatorial optimization problem. This paper introduces a novel approach using THRML (Thermodynamic HypergRaphical Model Library), a JAX-bas

DRL agents circumvent the issue of classic models in the sense that they do not make assumptions like the financial returns being normally distributed and are able to deal with any information like the ESG score if they are configured to gain a reward that makes an objective better. However, the per

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

Accurate prediction of financial market volatility is critical for risk management, derivatives pricing, and investment strategy. In this study, we propose a multitude of regime-switching methods to improve the prediction of S&P 500 volatility by capturing structural changes in the market across tim

We propose a two-level, learning-based portfolio method (RL-BHRP) that spreads risk across sectors and stocks, and adjusts exposures as market conditions change. Using U.S. Equities from 2012 to mid-2025, we design the model using 2012 to 2019 data, and evaluate it out-of-sample from 2020 to 2025 ag

Commodity Trading Advisors (CTAs) have historically relied on trend-following rules that operate on vastly different horizons from long-term breakouts that capture major directional moves to short-term momentum signals that thrive in fast-moving markets. Despite a large body of work on trend followi

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

For quantitative trading risk management purposes, we present a novel idea: the realized local volatility surface. Concisely, it stands for the conditional expected volatility when sudden market behaviors of the underlying occur. One is able to explore risk management usages by following the orthoti

We build a state-of-the-art dynamic model of private asset allocation that considers five key features of private asset markets: (1) the illiquid nature of private assets, (2) timing lags between capital commitments, capital calls, and eventual distributions, (3) time-varying business cycle conditio

This paper expands on stochastic volatility models by proposing a data-driven method to select the macroeconomic events most likely to impact volatility. The paper identifies and quantifies the effects of macroeconomic events across multiple countries on exchange rate volatility using high-frequency

We propose MoE-F - a formalized mechanism for combining $N$ pre-trained Large Language Models (LLMs) for online time-series prediction by adaptively forecasting the best weighting of LLM predictions at every time step. Our mechanism leverages the conditional information in each expert’s running perf

Modeling the trading volume curves of financial instruments throughout the day is of key interest in financial trading applications. Predictions of these so-called volume profiles guide trade execution strategies, for example, a common strategy is to trade a desired quantity across many orders in li

This research paper introduces innovative approaches for multivariate time series forecasting based on different variations of the combined regression strategy. We use specific data preprocessing techniques which makes a radical change in the behaviour of prediction. We compare the performance of th

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

Identifying the structural dependence between the cryptocurrencies and predicting market trend are fundamental for effective portfolio management in cryptocurrency trading. In this paper, we present a unified Bayesian framework based on potential field theory and Gaussian Process to characterize the

Financial order flow exhibits a remarkable level of persistence, wherein buy (sell) trades are often followed by subsequent buy (sell) trades over extended periods. This persistence can be attributed to the division and gradual execution of large orders. Consequently, distinct order flow regimes mig

Following the idea of Bayesian learning via Gaussian mixture model, we organically combine the backward-looking information contained in the historical data and the forward-looking information implied by the market portfolio, which is affected by heterogeneous expectations and noisy trading behavior

We develop a Quantile Bayesian Vector Autoregression (QBVAR) to forecast real oil prices across different quantiles of the conditional distribution. The model allows predictor effects to vary across quantiles, capturing asymmetries that standard mean-focused approaches miss. Using monthly data from

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

Robust optimization provides a principled framework for decision-making under uncertainty, with broad applications in finance, engineering, and operations research. In portfolio optimization, uncertainty in expected returns and covariances demands methods that mitigate estimation error, parameter in

Mean-variance analysis is widely used in portfolio management to identify the best portfolio that makes an optimal trade-off between expected return and volatility. Yet, this method has its limitations, notably its vulnerability to estimation errors and its reliance on historical data. While shrinka

The analysis of market correlations is crucial for optimal portfolio selection of correlated assets, but their memory effects have often been neglected. In this work, we analyse the mean market correlation of the S&P500 which corresponds to the main market mode in principle component analysis. We fi

Estimating time-varying correlation matrices is challenging because existing methods may adapt slowly to structural changes, impose insufficient regularization, or produce diffuse posterior uncertainty. In moderate dimensions, an additional difficulty is summarizing the estimated evolving dependence

Networks underpin systems that range from finance to biology, yet their structure is often only partially observed. Current reconstruction methods typically fit the parameters of a model anew to each snapshot, thus offering no guidance to predict future configurations. Here, we develop a Bayesian ap

Recent work has emphasized the diversification benefits of combining trend signals across multiple horizons, with the medium-term window-typically six months to one year-long viewed as the “sweet spot” of trend-following. This paper revisits this conventional view by reallocating exposure dynamicall

Optimal portfolio allocation is often formulated as a constrained risk problem, where one aims to minimize a risk measure subject to some performance constraints. This paper presents new Bayesian Optimization algorithms for such constrained minimization problems, seeking to minimize the conditional

We present a novel Bayesian framework for quantifying uncertainty in portfolio temperature alignment models, leveraging the X-Degree Compatibility (XDC) approach with the scientifically validated Finite Amplitude Impulse Response (FaIR) climate model. This framework significantly advances the widely

Vector Error Correction Model (VECM) is a classic method to analyse cointegration relationships amongst multivariate non-stationary time series. In this paper, we focus on high dimensional setting and seek for sample-size-efficient methodology to determine the level of cointegration. Our investigati

We apply empirical Bayes (EB) to mine data on 136,000 long-short strategies constructed from accounting ratios, past returns, and ticker symbols. This ``high-throughput asset pricing’’ matches the out-of-sample performance of top journals while eliminating look-ahead bias. Naively mining for the lar

We develop a posteriori primal-dual bounds for numerical approximations of European option prices in the Uncertain Volatility Model. Given a smooth candidate approximation of the value function, a feedback control induced by its Hessian yields a primal lower bound. On the dual side, we derive a repr

We introduce a dynamic spatiotemporal volatility model that extends traditional approaches by incorporating spatial, temporal, and spatiotemporal spillover effects, along with volatility-specific observed and latent factors. The model offers a more general network interpretation, making it applicabl

We develop a liquidity-sensitive multivariate volatility framework to improve the estimation of time-varying covariance structures under market frictions. We introduce two novel portfolio-level liquidity measures, liquidity jump and liquidity diffusion, which capture magnitude and volatility of liqu

We explore the abilities of two machine learning approaches for no-arbitrage interpolation of European vanilla option prices, which jointly yield the corresponding local volatility surface: a finite dimensional Gaussian process (GP) regression approach under no-arbitrage constraints based on prices,

This paper proposes a machine learning assisted portfolio optimization framework designed for low data environments and regime uncertainty. We construct a teacher student learning pipeline in which a Conditional Value at Risk (CVaR) optimizer generates supervisory labels, and neural models (Bayesian

A fast simulation framework for stochastic Volterra processes based on Random Fourier Features (RFF) approximation of the kernel is developed. After recalling the main properties of Volterra processes and reviewing existing numerical simulation methods, an accelerated scheme is introduced that relie

In this paper we develop Maximum likelihood (ML) based algorithms to calibrate the model parameters in credit rating transition models. Since the credit rating transition models are not Gaussian linear models, the celebrated Kalman filter is not suitable to compute the likelihood of observed migrati

This research incorporates realized volatility and overnight information into risk models, wherein the overnight return often contributes significantly to the total return volatility. Extending a semi-parametric regression model based on asymmetric Laplace distribution, we propose a family of RES-CA

We propose a novel framework for risk-sensitive reinforcement learning (RSRL) that incorporates robustness against transition uncertainty. We define two distinct yet coupled risk measures: an inner risk measure addressing state and cost randomness and an outer risk measure capturing transition dynam

In this paper, we modify the Bayes risk for the expectile, the so-called variantile risk measure, to better capture extreme risks. The modified risk measure is called the adjusted standard-deviatile. First, we derive the asymptotic expansions of the adjusted standard-deviatile. Next, based on the fi

Accurate industry classification is critical for many areas of portfolio management, yet the traditional single-industry framework of the Global Industry Classification Standard (GICS) struggles to comprehensively represent risk for highly diversified multi-sector conglomerates like Amazon. Previous

The Geometric Brownian Motion (GBM) is a standard model in quantitative finance, but the potential function of its stochastic differential equation (SDE) cannot include stable nonzero prices. This article generalises the GBM to an SDE with polynomial drift of order q and shows via model selection th

We study how a central bank should dynamically set short-term nominal interest rates to stabilize inflation and unemployment when macroeconomic relationships are uncertain and time-varying. We model monetary policy as a sequential decision-making problem where the central bank observes macroeconomic

We present a new class of Bayesian dynamic models for bivariate price-realized volatility time series in financial forecasting. A novel dynamic gamma process model adopted for realized volatility is integrated with traditional Bayesian dynamic linear models (DLMs) for asset price series. This repres

In this paper, we propose a novel frequency-severity joint trip-level risk index that combines the frequency of abnormal driving patterns with a severity component reflecting how extreme such behavior is relative to a portfolio-level baseline. Severity is quantified through an inverse-probability pe

Mobilising private capital is a critical bottleneck of the energy transition, yet recent crisis-driven windfall profits for fossil power firms suggest that market signals may still favour carbon-intensive assets. Here we analyse a panel of 900 European power firms (2001-2023) to resolve whether thes

Modern high-frequency trading (HFT) environments are characterized by sudden price spikes that present both risk and opportunity, but conventional financial models often fail to capture the required fine temporal structure. Spiking Neural Networks (SNNs) offer a biologically inspired framework well-

We explore a link between stochastic volatility (SV) and path-dependent volatility (PDV) models. Using assumed density filtering, we map a given SV model into a corresponding PDV representation. The resulting specification is lightweight, improves in-sample fit, and delivers robust out-of-sample for

This paper develops a coupled model for day-ahead electricity prices and average daily temperature which allows to model quanto weather and energy derivatives. These products have gained on popularity as they enable to hedge against both volumetric and price risks. Electricity day-ahead prices and a

This paper addresses the challenges faced in large-volume trading, where executing substantial orders can result in significant market impact and slippage. To mitigate these effects, this study proposes a volatility-volume-based order slicing strategy that leverages Exponential Weighted Moving Avera

\begin{“abstract”} In this paper, we integrated the statistical arbitrage strategy, pairs trading, into the Black-Litterman model and constructed efficient mean-variance portfolios. Typically, pairs trading underperforms under volatile or distressed market condition because the selected asset pairs

The European carbon market plays a pivotal role in the European Union’s ambitious target of achieving carbon neutrality by 2050. Understanding the intricacies of factors influencing European Union Emission Trading System (EU ETS) market prices is paramount for effective policy making and strategy im

Due to major shifts in European energy supply, a structural change can be observed in Austrian electricity spot price data starting from the second quarter of the year 2021 onward. In this work we study the performance of two different factor models for the electricity spot price in three different

Credit risk in the China’s bond market has become increasingly evident, creating a progressively escalating risk of default for credit bond investors. Given the current incomplete and inaccurate bond information disclosure, timely tracking and forecasting the individual credit bond default risks hav

Prediction-market price moves are widely treated as informationally equivalent: a price jump is read the same way regardless of whether it reflects durable Bayesian updating, transient liquidity pressure, strategic position adjustment, or genuine disagreement. This paper formalizes the Signal Credib

This study introduces a dynamic Bayesian network (DBN) framework for forecasting value at risk (VaR) and stressed VaR (SVaR) and compares its performance to several commonly applied models. Using daily S&P 500 index returns from 1991 to 2020, we produce 10-day 99% VaR and SVaR forecasts using a roll

We propose a general CoVaR framework that extends the traditional CoVaR by incorporating diverse expert views and information, such as asset moment characteristics, quantile insights, and perspectives on the relative loss distribution between two assets. To integrate these expert views effectively w

Short-term sentiment forecasting in financial markets (e.g., stocks, indices) is challenging due to volatility, non-linearity, and noise in OHLC (Open, High, Low, Close) data. This paper introduces a novel CMG (Chaos-Markov-Gaussian) framework that integrates chaos theory, Markov property, and Gauss