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We presented Bayesian portfolio selection strategy, via the $k$ factor asset pricing model. If the market is information efficient, the proposed strategy will mimic the market; otherwise, the strategy will outperform the market. The strategy depends on the selection of a portfolio via Bayesian multiple testing methodologies. We present the "discrete-mixture prior" model and the "hierarchical Bayes model with horsesho…
The probabilistic reading of the cumulative accuracy profile (CAP) has a long industry lineage. Falkenstein, Boral and Carty (2000) state, in discrete form, that the default rate at a score percentile equals the portfolio average rate times the local slope of the power curve; van der Burgt (2008, 2019) formalizes this as the continuous identity $p(D\mid x) = p_D\, dy/dx$ and imports the continuous form as a working f…
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 performance of DRL agents has high variability and it is very sensible to the value of their hyperparameters. Bayesian opti…
We build on the work in Fackler and King 1990, and propose a more general calibration model for implied risk neutral densities. Our model allows for the joint calibration of a set of densities at different maturities and dates through a Bayesian dynamic Beta Markov Random Field. Our approach allows for possible time dependence between densities with the same maturity, and for dependence across maturities at the same …
We consider the estimation of the multi-period optimal portfolio obtained by maximizing an exponential utility. Employing Jeffreys' non-informative prior and the conjugate informative prior, we derive stochastic representations for the optimal portfolio weights at each time point of portfolio reallocation. This provides a direct access not only to the posterior distribution of the portfolio weights but also to their …
Algorithmic trading now represents a market exceeding $20 billion, where even marginal gains in signal robustness can translate into economically significant returns. Existing evaluations of equity prediction models do not explicitly target regime robustness during hyperparameter selection. Five model classes are trained on daily observations from approximately 300 large-cap US equities over eleven years, with Bayesi…
We propose an information-geometric framework for credit risk monitoring in which a bank's knowledge of a borrower is represented by a posterior distribution over latent dimensions of creditworthiness and financial fragility. Under a linear-Gaussian specification, Bayesian updating maps observed behavioural scores into Gaussian posterior beliefs, which form a statistical manifold endowed with the Fisher information m…
This paper extends the approximate Bayesian estimation framework for Stochastic Volatility in Mean (SVM) models to accommodate heavy-tailed distributions from the Scale Mixture of Normals (SMN) family. To overcome the computational challenges arising from these models, we propose a numerically stable estimation procedure that exploits special functions to eliminate the need for direct numerical integration. Furthermo…
Deep reinforcement learning (DRL) frameworks for portfolio optimization have shown promise for their ability to learn allocation rules dynamically from market data. However, these models fail to account for fat-tailed returns, which characterize actual market behavior with more frequent extreme events. Furthermore, historical data is treated homogeneously, without accounting for temporal importance, leading models to…
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 represents reduced-form volatility leverage and feedback effects through use of realized volatility proxies in conditional DLM…
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 and deterministic) are trained using both real and synthetically augmented data. The synthetic data is generated using …
Multimodal time-to-event prediction often requires integrating sensitive data distributed across multiple parties, making centralized model training impractical due to privacy constraints. At the same time, most existing multimodal survival models produce single deterministic predictions without indicating how confident the model is in its estimates, which can limit their reliability in real-world decision making. To…
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 structural breaks. We propose a minimal Bayesian framework in which this misspecification generates persistent prediction err…
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 overstatement of expected utility and an understatement of portfolio risk. We develop Bayesian Parametric Portfolio Policies (BPPP…
Prediction markets are often described as mechanisms that ``aggregate information'' into prices, yet the mapping from dispersed private information to observed market histories is typically noisy, endogenous, and shaped by heterogeneous and strategic participation. This paper formulates prediction markets as Bayesian inverse problems in which the unknown event outcome \(Y\in\{0,1\}\) is inferred from an observed hist…
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 suffers from two limitations: binary classification ignores default timing, treating early defaulters (high loss) equivalently…
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 unanticipated fluctuations in participant behavior. We identify two challenges that perpetuate this mismatch: (1) insufficient…
A Bayesian analytics framework that precisely quantifies uncertainty offers a significant advance for financial risk management. We develop an integrated approach that consistently enhances the handling of risk in market volatility forecasting, fraud detection, and compliance monitoring. Our probabilistic, interpretable models deliver reliable results: We evaluate the performance of one-day-ahead 95% Value-at-Risk (V…
Bayesian inference updates a prior distribution over parameters with data via Bayes’ rule to get a posterior — beliefs as probabilities, not just a point estimate.
The Kalman filter is the recursive Bayesian update for a linear-Gaussian state-space model: predict the hidden state, then correct with the new observation.
Bayesian inference updates a prior distribution over parameters with data via Bayes’ rule to get a posterior — beliefs as probabilities, not just a point estimate.
The Kalman filter is the recursive Bayesian update for a linear-Gaussian state-space model: predict the hidden state, then correct with the new observation.