arXiv subjects

Ajay Kumar Verma

Publications and source records attributed to Ajay Kumar Verma.

4 recordsLinked to original sources

arXiv2026

From Classical Optimization to Bayesian Integration: A Comprehensive Analysis of Systematic Portfolio Management

This paper compares a series of contemporary portfolio construction approaches by employing ten U.S. stocks (TSLA, WMT, BAC, GS, LLY, MRK, GOOG, META, AAPL and XOM) in a time frame from September 2023 to December 2025. The paper explores both basic mean-variance optimization, constrained optimization, Fama French five factor regression modeling, Monte Carlo simulation, and the Black-Litterman model to determine how constraints to a solution, risk factors to a strategy, simulated approximations, and specific market views may all impact the outcome of portfolio allocation, performance and stability. Overall, the results show that standard optimization may result in highly concentrated portfolios, while constrained optimization leads to changes in portfolio allocations by altering the efficient frontier, five factor regression models suggest that a basic investment style of defensive large value and profitability exposure, Monte Carlo approximation is a viable technique to arrive at mean-variance optimal portfolios provided the simulations are high enough especially under a box constraint, the Black Litterman portfolio approach produces more economically intuitive allocations and greater stability compared to standard mean-variance optimization as the approach balances equilibrium returns with investor views.

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arXiv2026

Regime-Based Portfolio Allocation Using Hidden Markov Models and Reinforcement Learning

This study develops a regime-aware portfolio allocation framework that integrates Markov switching models with Reinforcement Learning (RL) to dynamically allocate across equities (SPY), long-term Treasuries (TLT), and gold (GLD). Using daily ETF data from 2004-2025, we first characterize market behavior through a discrete Markov chain and then estimate a three-state Gaussian Hidden Markov Model (HMM) selected by the Bayesian Information Criterion (BIC). The estimated regimes-low-volatility, transitional, and high-volatility-exhibit strong persistence and state-dependent return dynamics consistent with recent findings on nonlinear market states (Ardia et al., 2024; Gupta & Pierdzioch, 2023). State-conditional analysis shows that SPY dominates in stable regimes, while TLT and GLD provide protection during stressed periods, motivating regime-conditioned allocation rules. We evaluate rule-based rotation and RL-driven strategies using a 30% out-of-sample test window with a one-day execution lag to avoid look-ahead bias. Both HMM-based allocations outperform a passive SPY benchmark, while the RL policy achieves the highest risk-adjusted performance, delivering the strongest Sharpe ratio and materially lower drawdowns, yet remains fully interpretable through discrete regime-dependent actions. Sensitivity analysis confirms the robustness of the three-state specification relative to two-state alternatives. Overall, the results demonstrate that RL can systematically enhance HMM-based regime detection, providing a transparent, adaptive, and empirically grounded framework for tactical asset allocation. The combined HMM-RL system provides a transparent, rules-based approach to tactical allocation that improves risk-adjusted performance relative to standard benchmark strategies.

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arXiv2026

Stochastic Volatility, Jumps, and Rates: A Unified Framework for Option Pricing and Term-Structure Simulation

This study develops an integrated stochastic modeling framework for pricing short and medium-maturity equity options and assessing interest-rate risk using the Heston (1993), Bates (1996), and CIR (1985) models. We calibrate the Heston model using both the Lewis (2001) Fourier inversion and the Carr-Madan (1999) FFT approach, finding near-identical parameter sets, which is consistent with the calibration stability reported in recent studies such as Agazzotti et al. (2025). Extending the model to Bates shows that jump intensities converge to values effectively equal to zero for 60-day maturities, echoing empirical findings that jumps contribute marginally to short-term smile fitting. We further compare our calibration approach with the joint volatility-surface and variance-term-structure framework proposed by Yoo (2025), confirming that standard Heston/Bates calibration remains robust for the maturities considered. Finally, we calibrate the CIR short-rate model to the Euribor term structure, generating positive and economically consistent forward-rate scenarios in line with recent stochastic-rate option-pricing research by Jeon and Kim (2025). Overall, our results show that continuous stochastic volatility dominates near-term pricing dynamics, while stochastic interest rates materially influence valuations beyond one year.

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arXiv2026

Deep Learning Forecasting of the U.S. Aggregate Bond Index

This study looks at the statistical properties and predictability using deep learning methods of the U.S. aggregate bond index in daily observations spanning 2018 to February 2026. We first establish that index levels are extremely persistent and consistent with unitroot behavior (Dickey and Fuller), while log returns are covariance-stationary with weak linear dependence and pronounced volatility clustering characteristic of ARCH-type processes (Engle; Bollerslev). Motivated by the trade-off between stationarity and information retention, we construct a "stationary but maximally persistent" representation via fractional differencing (Granger and Joyeux; Hosking) following the procedure of L\'opez de Prado, and evaluate shorthorizon forecast using two neural paradigms: (i) Multilayer Perceptrons (MLPs) trained on lagged vectors with joint lag-length and hyperparameter tuning (Hornik et al.; Rumelhart et al.); and (ii) Convolutional Neural Networks (CNNs) trained on Gramian Angular Field (GAF) image encodings (Wang and Oates). Empirically, MLPs match the strong naive persistence benchmark on levels, collapse toward near-zero forecasts on returns, and achieve the strongest incremental performance on the fractionally differenced series, where moderate dependence remains but unit-root drift is attenuated. In contrast, CNN-GAF models deliver consistently negative out-of-sample R 2 across all three representations. Overall, the results imply that, for short-horizon forecasting of broad bond indices, the primary determinant of predictive performance is the transformation of the series-its degree of stationarity and memory-rather than architectural complexity. Lag-based models remain competitive under persistence, while GAFbased CNNs are better suited to pattern-based tasks than to persistence-dominated next-step prediction.

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