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Papers in this area

24 featured work(s)

preprint2026arXiv

Quantifying the Risk-Return Tradeoff in Forecasting

Average forecast accuracy is not the same as forecast reliability. I treat forecast loss differentials relative to a benchmark as a return series. I then evaluate these returns using risk-adjusted performance measures from finance, including the Sharpe ratio, Sortino ratio, Omega ratio, and drawdown-based metrics. I also introduce the Edge Ratio capturing a model's propensity to deliver uniquely informative predictions relative to the forecasting frontier. I apply this framework to U.S. macroeconomic forecasting, comparing econometric benchmarks, machine learning models, a foundation model (TabPFN), and the Survey of Professional Forecasters. While it is often feasible to beat professional forecasters in terms of average accuracy, it is much harder to beat them on a risk-adjusted basis. They rarely exhibit catastrophic failures and often achieve high Edge Ratios, plausibly reflecting the value of contextual judgment. Nonetheless, selected machine learning methods deliver attractive risk profiles for specific targets. The framework naturally extends to meta-analyses across targets, horizons, and samples, illustrated with a density forecast evaluation and the M4 competition.

preprint2026arXiv

Beyond ESG Scores: Learning Dynamic Constraints for Sequential Portfolio Optimization

ESG-aware portfolio optimization is increasingly important for sustainable capital allocation, yet most learning-based methods still operationalize ESG by appending static scores to the policy observation or reward. This creates a mismatch for sequential control: ESG scores are noisy, provider-dependent, low-frequency, and temporally misaligned with sequential portfolio decisions, while financial evidence suggests that ESG is better treated as a portfolio preference, risk-exposure, or hedge dimension than as a robust alpha factor. We propose to impose ESG constraints without modifying the financial policy's observation or reward, using a Multimodal Action-Conditioned Constraint Field (MACF) that learns mechanism-specific ESG costs from point-in-time multimodal evidence and contemplated portfolio transitions. We then introduce MACF-X, a family of optimizer-specific adapters that converts MACF costs and uncertainties into native constrained-optimization interfaces through a shared slack- and uncertainty-aware pressure layer. Across multiple constraint-integration interfaces, MACF-X reduces tail ESG budget pressure while maintaining competitive financial performance. Ablations show that this improvement depends on dynamic evidence inputs and three-head decomposition, while static ESG-score proxies are nearly indistinguishable from score-shuffled noise baselines.

preprint2026arXiv

Sampler-Robust Optimization under Generative Models

Modern stochastic optimization pipelines increasingly rely on learned generative models to represent uncertainty, while downstream decisions are evaluated almost entirely through Monte Carlo scenarios. This shifts the operational object of uncertainty from an explicit probability law to the sampler induced by the learned generator. Reliability therefore depends on two errors: sampler misspecification and finite-simulation error. We propose Sampler-Robust Optimization (SRO), which optimizes decisions against the worst-case sampler induced by perturbing the learned generator. This sampler-first formulation aligns with simulation-based decision pipelines and admits a sharpness-aware interpretation: it favors decisions whose performance is stable under generator perturbations, rather than merely under the nominal sampler. Under a coverage assumption, we show that the empirical worst-case objective provides a high-probability upper certificate for the true population objective, with finite-simulation error partially absorbed by the robustification used to guard against sampler misspecification. The framework accommodates generative models with or without explicit densities and admits efficient minimax procedures. Portfolio-optimization experiments show that SRO produces more stable decisions and improves out-of-sample performance under distribution shift.

preprint2026arXiv

Learning to Spend: Model Predictive Control for Budgeting under Non-Stationary Returns

We study finite-horizon budget allocation as a closed-loop economic control problem and evaluate receding-horizon Model Predictive Control (MPC) relative to reactive budgeting policies. Budgets are allocated periodically under execution noise and operational constraints, while return efficiency may evolve over time. Using a controlled simulation framework motivated by digital marketing, we compare reactive pacing to MPC across environments with increasing degrees of non-stationarity. Our results show that non-stationarity alone does not justify predictive control. When return dynamics are stationary or evolve through unpredictable stochastic drift, MPC offers no systematic advantage over reactive baselines. By contrast, when return efficiency exhibits predictable structure over the planning horizon, that is captured through an underlying model, MPC consistently outperforms reactive budgeting by exploiting intertemporal trade-offs.

preprint2026arXiv

Auditing Marketing Budget Allocation with Hindsight Regret

Organizations routinely make strategic budget allocations under operational constraints, but often lack a principled way to assess whether realized allocations were close to the best feasible choices in hindsight. We present a retrospective auditing framework based on hindsight regret, defined as the opportunity cost of the realized allocation relative to a constraint-faithful benchmark under the same budget and stability guardrails. The framework estimates regime-specific spend--response functions from historical logs, computes feasible hindsight allocations via constrained optimization, and propagates uncertainty through Monte Carlo evaluation to produce regret distributions, expected lift, and probability-of-improvement summaries. This separates allocation inefficiency from uncertainty in the estimated response surfaces. Experiments on real marketing allocation logs show that the framework yields interpretable post-hoc diagnostics and reveals a practical trade-off between allocation flexibility and detectability: moderate feasible reallocations often capture most measurable gain, while larger shifts move into weak-support regions with higher uncertainty. The result is a practical method for auditing historical budget decisions when online experimentation is costly or infeasible.

preprint2022arXiv

Some connections between higher moments portfolio optimization methods

In this paper, different approaches to portfolio optimization having higher moments such as skewness and kurtosis are classified so that the reader can observe different paradigms and approaches in this field of research which is essential for practitioners in Hedge Funds in particular. Several methods based on different paradigms such as utility approach and multi-objective optimization are reviewed and the advantage and disadvantageous of these ideas are explained. Keywords: multi-objective optimization, portfolio optimization, scalarization, utility

preprint2026arXiv

Deep Reinforcement Learning Framework for Diversified Portfolio Management Across Global Equity Markets

This study develops and evaluates a deep reinforcement learning framework for dynamic portfolio allocation across global equity markets. The Soft Actor-Critic algorithm is used to learn continuous portfolio weights within a Markov Decision Process, incorporating transaction costs, turnover penalties, and diversification constraints into the reward function. Five model configurations are compared, varying in reward formulation, policy structure (flat versus hierarchical Dirichlet), portfolio constraints, and temporal encoder (LSTM versus Transformer), and evaluated via walk-forward optimization across sixteen out-of-sample folds spanning 2003-2026 on the Nasdaq-100, Nikkei 225, and Euro Stoxx 50. Results show that RL strategies achieve competitive risk-adjusted performance primarily in the Euro Stoxx 50, where statistically significant abnormal returns are observed, but the central hypothesis is only partially confirmed: no strategy achieves statistically significant excess returns relative to Buy and Hold under HAC-robust inference across all markets. Regime analysis reveals that RL adds the most value during periods of elevated uncertainty, while ensemble aggregation across markets improves risk-adjusted performance and confirms the benefits of geographic diversification.

preprint2024arXiv

Constrained Max Drawdown: a Fast and Robust Portfolio Optimization Approach

We propose an alternative linearization to the classical Markowitz quadratic portfolio optimization model, based on maximum drawdown. This model, which minimizes maximum portfolio drawdown, is particularly appealing during times of financial distress, like during the COVID-19 pandemic. In addition, we will present a Mixed-Integer Linear Programming variation of our new model that, based on our out-of-sample results and sensitivity analysis, delivers a more profitable and robust solution with a 200 times faster solving time compared to the standard Markowitz quadratic formulation.

preprint2023arXiv

Optimization of portfolios with cryptocurrencies: Markowitz and GARCH-Copula model approach

The growing interest in cryptocurrencies has drawn the attention of the financial world to this innovative medium of exchange. This study aims to explore the impact of cryptocurrencies on portfolio performance. We conduct our analysis retrospectively, assessing the performance achieved within a specific time frame by three distinct portfolios: one consisting solely of equities, bonds, and commodities; another composed exclusively of cryptocurrencies; and a third, which combines both 'traditional' assets and the best-performing cryptocurrency from the second portfolio.To achieve this, we employ the classic variance-covariance approach, utilizing the GARCH-Copula and GARCH-Vine Copula methods to calculate the risk structure. The optimal asset weights within the optimized portfolios are determined through the Markowitz optimization problem. Our analysis predominantly reveals that the portfolio comprising both cryptocurrency and traditional assets exhibits a higher Sharpe ratio from a retrospective viewpoint and demonstrates more stable performances from a prospective perspective. We also provide an explanation for our choice of portfolio optimization based on the Markowitz approach rather than CVaR and ES.

preprint2023arXiv

Enhancing CVaR portfolio optimisation performance with GAM factor models

We propose a discrete-time econometric model that combines autoregressive filters with factor regressions to predict stock returns for portfolio optimisation purposes. In particular, we test both robust linear regressions and general additive models on two different investment universes composed of the Dow Jones Industrial Average and the Standard & Poor's 500 indexes, and we compare the out-of-sample performances of mean-CVaR optimal portfolios over a horizon of six years. The results show a substantial improvement in portfolio performances when the factor model is estimated with general additive models.

preprint2022arXiv

Statistical Arbitrage for Multiple Co-Integrated Stocks

In this article, we analyse optimal statistical arbitrage strategies from stochastic control and optimisation problems for multiple co-integrated stocks with eigenportfolios being factors. Optimal portfolio weights are found by solving a Hamilton-Jacobi-Bellman (HJB) partial differential equation, which we solve for both an unconstrained portfolio and a portfolio constrained to be market neutral. Our analyses demonstrate sufficient conditions on the model parameters to ensure long-term stability of the HJB solutions and stable growth rates for the optimal portfolios. To gauge how these optimal portfolios behave in practice, we perform backtests on historical stock prices of the S&P 500 constituents from year 2000 through year 2021. These backtests suggest three key conclusions: that the proposed co-integrated model with eigenportfolios being factors can generate a large number of co-integrated stocks over a long time horizon, that the optimal portfolios are sensitive to parameter estimation, and that the statistical arbitrage strategies are more profitable in periods when overall market volatilities are high.

preprint2023arXiv

Sector Rotation by Factor Model and Fundamental Analysis

This study presents an analytical approach to sector rotation, leveraging both factor models and fundamental metrics. We initiate with a systematic classification of sectors, followed by an empirical investigation into their returns. Through factor analysis, the paper underscores the significance of momentum and short-term reversion in dictating sectoral shifts. A subsequent in-depth fundamental analysis evaluates metrics such as PE, PB, EV-to-EBITDA, Dividend Yield, among others. Our primary contribution lies in developing a predictive framework based on these fundamental indicators. The constructed models, post rigorous training, exhibit noteworthy predictive capabilities. The findings furnish a nuanced understanding of sector rotation strategies, with implications for asset management and portfolio construction in the financial domain.

preprint2023arXiv

Correlation-diversified portfolio construction by finding maximum independent set in large-scale market graph

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 the MIS selection in a large-scale market graph difficult. Here we construct a diversified portfolio by solving the MIS problem for a large-scale market graph with a combinatorial optimization solver (an Ising machine) based on a quantum-inspired algorithm called simulated bifurcation (SB) and investigate the investment performance of the constructed portfolio using long-term historical market data. Comparisons using stock universes of various sizes [TOPIX 100, Nikkei 225, TOPIX 1000, and TOPIX (including approximately 2,000 constituents)] show that the SB-based solver outperforms conventional MIS solvers in terms of computation-time and solution-accuracy. By using the SB-based solver, we optimized the parameters of a MIS portfolio strategy through iteration of the backcast simulation that calculates the performance of the MIS portfolio strategy based on a large-scale universe covering more than 1,700 Japanese stocks for a long period of 10 years. It has been found that the best MIS portfolio strategy (Sharpe ratio = 1.16, annualized return/risk = 16.3%/14.0%) outperforms the major indices such as TOPIX (0.66, 10.0%/15.2%) and MSCI Japan Minimum Volatility Index (0.64, 7.7%/12.1%) for the period from 2013 to 2023.

preprint2023arXiv

Sectoral portfolio optimization by judicious selection of financial ratios via PCA

Embedding value investment in portfolio optimization models has always been a challenge. In this paper, we attempt to incorporate it by employing principal component analysis to filter out dominant financial ratios from each sector and thereafter, use the portfolio optimization model incorporating second-order stochastic dominance criteria to derive an optimal investment. We consider a total of $11$ financial ratios corresponding to each sector representing four categories of ratios, namely liquidity, solvency, profitability, and valuation. PCA is then applied over a period of 10 years to extract dominant ratios from each sector in two ways, one from the component solution and the other from each category on the basis of their communalities. The two-step Sectoral Portfolio Optimization (SPO) model is then utilized to build an optimal portfolio. The strategy formed using the formerly extracted ratios is termed PCA-SPO(A) and the latter PCA-SPO(B). The results obtained from the proposed strategies are compared with those from mean-variance, minimum variance, SPO, and nominal SSD models, with and without financial ratios. The empirical performance of proposed strategies is analyzed in two ways, viz., using a rolling window scheme and using market trend scenarios for S\&P BSE 500 (India) and S\&P 500 (U.S.) markets. We observe that the proposed strategy PCA-SPO(B) outperforms all other models in terms of downside deviation, CVaR, VaR, Sortino, Rachev, and STARR ratios over almost all out-of-sample periods. This highlights the importance of value investment where ratios are carefully selected and embedded quantitatively in portfolio selection process.

preprint2022arXiv

Asset Allocation: From Markowitz to Deep Reinforcement Learning

Asset allocation is an investment strategy that aims to balance risk and reward by constantly redistributing the portfolio's assets according to certain goals, risk tolerance, and investment horizon. Unfortunately, there is no simple formula that can find the right allocation for every individual. As a result, investors may use different asset allocations' strategy to try to fulfil their financial objectives. In this work, we conduct an extensive benchmark study to determine the efficacy and reliability of a number of optimization techniques. In particular, we focus on traditional approaches based on Modern Portfolio Theory, and on machine-learning approaches based on deep reinforcement learning. We assess the model's performance under different market tendency, i.e., both bullish and bearish markets. For reproducibility, we provide the code implementation code in this repository.

preprint2023arXiv

Dynamic Spatial Autoregressive Models with Autoregressive and Heteroskedastic Disturbances

We propose a new class of models specifically tailored for spatio-temporal data analysis. To this end, we generalize the spatial autoregressive model with autoregressive and heteroskedastic disturbances, i.e. SARAR(1,1), by exploiting the recent advancements in Score Driven (SD) models typically used in time series econometrics. In particular, we allow for time-varying spatial autoregressive coefficients as well as time-varying regressor coefficients and cross-sectional standard deviations. We report an extensive Monte Carlo simulation study in order to investigate the finite sample properties of the Maximum Likelihood estimator for the new class of models as well as its flexibility in explaining several dynamic spatial dependence processes. The new proposed class of models are found to be economically preferred by rational investors through an application in portfolio optimization.

preprint2022arXiv

Hierarchical Risk Parity and Minimum Variance Portfolio Design on NIFTY 50 Stocks

Portfolio design and optimization have been always an area of research that has attracted a lot of attention from researchers from the finance domain. Designing an optimum portfolio is a complex task since it involves accurate forecasting of future stock returns and risks and making a suitable tradeoff between them. This paper proposes a systematic approach to designing portfolios using two algorithms, the critical line algorithm, and the hierarchical risk parity algorithm on eight sectors of the Indian stock market. While the portfolios are designed using the stock price data from Jan 1, 2016, to Dec 31, 2020, they are tested on the data from Jan 1, 2021, to Aug 26, 2021. The backtesting results of the portfolios indicate while the performance of the CLA algorithm is superior on the training data, the HRP algorithm has outperformed the CLA algorithm on the test data.

preprint2023arXiv

On Frequency-Based Optimal Portfolio with Transaction Costs

The aim of this paper is to investigate the impact of rebalancing frequency and transaction costs on the log-optimal portfolio, which is a portfolio that maximizes the expected logarithmic growth rate of an investor's wealth. We prove that the frequency-dependent log-optimal portfolio problem with costs is equivalent to a concave program and provide a version of the dominance theorem with costs to determine when an investor should invest all available funds in a particular asset. Then, we show that transaction costs may cause a bankruptcy issue for the frequency-dependent log-optimal portfolio. To address this issue, we approximate the problem to obtain a quadratic concave program and derive necessary and sufficient optimality conditions. Additionally, we prove a version of the two-fund theorem, which states that any convex combination of two optimal weights from the optimality conditions is still optimal. We test our proposed methods using both intraday and daily price data. Finally, we extend our empirical studies to an online trading scenario by implementing a sliding window approach. This approach enables us to solve a sequence of concave programs rather than a potentially computational complex stochastic dynamic programming problem.

preprint2023arXiv

Markov Decision Processes under Model Uncertainty

We introduce a general framework for Markov decision problems under model uncertainty in a discrete-time infinite horizon setting. By providing a dynamic programming principle we obtain a local-to-global paradigm, namely solving a local, i.e., a one time-step robust optimization problem leads to an optimizer of the global (i.e. infinite time-steps) robust stochastic optimal control problem, as well as to a corresponding worst-case measure. Moreover, we apply this framework to portfolio optimization involving data of the S&P 500. We present two different types of ambiguity sets; one is fully data-driven given by a Wasserstein-ball around the empirical measure, the second one is described by a parametric set of multivariate normal distributions, where the corresponding uncertainty sets of the parameters are estimated from the data. It turns out that in scenarios where the market is volatile or bearish, the optimal portfolio strategies from the corresponding robust optimization problem outperforms the ones without model uncertainty, showcasing the importance of taking model uncertainty into account.

preprint2022arXiv

Portfolio Optimization on NIFTY Thematic Sector Stocks Using an LSTM Model

Portfolio optimization has been a broad and intense area of interest for quantitative and statistical finance researchers and financial analysts. It is a challenging task to design a portfolio of stocks to arrive at the optimized values of the return and risk. This paper presents an algorithmic approach for designing optimum risk and eigen portfolios for five thematic sectors of the NSE of India. The prices of the stocks are extracted from the web from Jan 1, 2016, to Dec 31, 2020. Optimum risk and eigen portfolios for each sector are designed based on ten critical stocks from the sector. An LSTM model is designed for predicting future stock prices. Seven months after the portfolios were formed, on Aug 3, 2021, the actual returns of the portfolios are compared with the LSTM-predicted returns. The predicted and the actual returns indicate a very high-level accuracy of the LSTM model.

preprint2022arXiv

Deep differentiable reinforcement learning and optimal trading

In many reinforcement learning applications, the underlying environment reward and transition functions are explicitly known differentiable functions. This enables us to use recent research which applies machine learning tools to stochastic control to find optimal action functions. In this paper, we define differentiable reinforcement learning as a particular case of this research. We find that incorporating deep learning in this framework leads to more accurate and stable solutions than those obtained from more generic actor critic algorithms. We apply this deep differentiable reinforcement learning (DDRL) algorithm to the problem of one asset optimal trading strategies in various environments where the market dynamics are known. Thanks to the stability of this method, we are able to efficiently find optimal strategies for complex multi-scale market models. We also extend these methods to simultaneously find optimal action functions for a wide range of environment parameters. This makes it applicable to real life financial signals and portfolio optimization where the expected return has multiple time scales. In the case of a slow and a fast alpha signal, we find that the optimal trading strategy consists in using the fast signal to time the trades associated to the slow signal.

preprint2026arXiv

Do Better Volatility Forecasts Lead to Better Portfolios? Evidence from Graph Neural Networks

This paper tests whether graph neural networks improve realized volatility forecasts and whether those forecasts improve portfolio performance. Using weekly realized volatility for 465 S\&P 500 equities from 2015--2025, Heterogeneous Autoregressive and Long Short-Term Memory baselines are compared against GraphSAGE models built on rolling correlation, sector, and Granger-causal graphs, with and without macro regime features. The empirical finding is that the model with the lowest forecast MSE, the model with the highest cross-sectional ranking accuracy, and the model with the highest portfolio Sharpe ratio are three different models. Forecast accuracy, ranking quality, and portfolio performance are related but not interchangeable objectives. Graph volatility models add value only when the portfolio rule can exploit the cross-sectional structure they encode.

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