arXiv subjects

Abdulrahman Alswaidan

Publications and source records attributed to Abdulrahman Alswaidan.

3 recordsLinked to original sources

arXiv2026

Variance-Corrected Multi-Asset Equity Simulation with Hybrid Hidden Markov Marginals

Synthetic multi-asset equity data must reproduce each asset's return distribution and its relationship with the market. Reusing a generator fitted to full asset returns creates a problem: adding its draws to a market factor counts market variance twice. We derived a correction that centers and rescales each draw over a fixed horizon before adding the market factor, allowing reuse without fitting a second generator to regression residuals. We tested the correction on 423 non-market assets in a 424-asset United States equity and exchange-traded-fund universe, using hidden Markov generators with heavy-tailed emissions. The corrected paths retained heavy tails and recovered the calibrated market loadings with low error. On 416 complete asset histories held out from 2025, the correction improved the mean Kolmogorov-Smirnov pass rate over naive composition and brought the median ratio of synthetic to observed variance close to one. Its one-day left-tail 99% Value-at-Risk exceedance rate, using thresholds pooled across separate simulated paths, was 1.12%, compared with 1.16% for the residual-fit hidden Markov comparator and a nominal rate of 1%. We also tested a jump-duration mechanism that extended visits to extreme-return states and improved volatility clustering for the broad-market exchange-traded fund with ticker SPY. The multi-asset correction remained effective with jumps enabled, but transferring the SPY jump settings improved temporal fit in training and worsened it in the 2025 holdout. The method provides a way to reuse fitted asset generators for daily-fit comparisons. Its zero-sum residual constraint removes terminal residual uncertainty, and unmodeled dependence among asset-specific residuals can lead to overstated rebalancing returns. Code, cached inputs, result summaries, and instructions for fitting the per-asset models accompany the paper.

q-fin.ST↗

arXiv2026

Continuous Hidden Markov Models for Equity Returns: Heavy-Tail Emission Families and Regime-Conditional Value-at-Risk

Synthetic generators of daily equity returns let practitioners stress test, backtest, and design scenarios that a single realized market history cannot supply, but only if the generator reproduces the stylized facts of real returns: heavy tails, negligible linear autocorrelation, and slow decay of the absolute-return autocorrelation. Hidden Markov models with few Gaussian states were long thought unable to reproduce that slow decay, and the standard fix was to abandon them for more complex hidden semi-Markov models. We revisit this issue with a continuous hidden Markov model whose regime chain governs the autocorrelation while per-regime densities govern the marginal, separating the temporal and distributional sides of the original failure. A unified expectation-maximization framework fits Gaussian, Student-t, Laplace, and generalized-error emissions under shared forward-backward recursions and quantile-based initialization, and a spectral identity bounds the number of decay modes by the rank of the centred transition matrix. Across SPY walk-forward folds, a sector-balanced 30-ticker panel, a CRSP cross-decade transfer, and a six-asset basket, that bound was not binding once a few states were used: heavy-tailed marginals, not additional decay modes, closed most of the fit gap, recovering volatility clustering above the i.i.d. baseline and narrowing the kurtosis gap without a tuning hyperparameter. The original failure is therefore distributional, not temporal. On daily US equities, a simple, interpretable Markov model suffices, and unlike a bootstrap or semi-Markov fit that wins only on a single-window fit, the fitted model also yields a regime-conditional Value-at-Risk that passes a joint conditional-coverage test and a copula that reproduces cross-asset correlations: one interpretable generator serving both path simulation and downstream risk and portfolio tasks.

q-fin.ST↗

arXiv2026

Stochastic Attention via Langevin Dynamics on the Modern Hopfield Energy

Attention heads retrieve: given a query, they return a weighted average of stored values. We showed that this computation is one step of gradient descent on the modern Hopfield energy, and that Langevin sampling from the corresponding Boltzmann distribution yielded stochastic attention, a training-free sampler controlled by a single temperature parameter. Lowering the temperature gave exact retrieval; raising it gave open-ended generation. Because the energy gradient equals the attention map, no score network, training loop, or learned model was required, making the approach particularly suited to the low-data regime where learned generative models are starved of training signal. We derived an entropy inflection condition that identified the retrieval-to-generation transition temperature for any memory geometry and validated the sampler on five domains spanning two orders of magnitude in dimension. A single Boolean mask on the attention softmax, identical to the causal mask used in transformers but applied along the memory axis rather than the sequence axis, turned the sampler into a zero-shot class-conditional generator on Olivetti faces with no retraining and no learned classifier. On MNIST digit images, stochastic attention produced samples that were markedly more novel and more diverse than the best learned baseline while matching a Metropolis-corrected gold standard. On protein sequences from a small Pfam family, the generation regime preserved amino acid composition far more faithfully than a variational autoencoder at matched novelty, indicating that the training-free score function retained family-level fidelity that learned models lost. A denoising diffusion baseline failed across all memory sizes tested, producing samples indistinguishable from isotropic noise. The approach required no architectural changes to the underlying attention mechanism.

cs.LG↗