An Entropy-Regularised AI Framework for Multi-Asset Volatility Spillover Forecasting and CVaR-Constrained Portfolio...

Forecasting multi-asset volatility spillovers and turning the forecasts into risk-aware portfolios requires methods that uncover directional information flow between assets, compress the state into a minimal sufficient representation, deliver calibrated uncertainty, and respect explicit tail-risk limits. We propose TDV (Transfer-entropy, Dynamic-graph-attention, Variational-information-bottleneck), an information-theoretic artificial intelligence framework that couples a time-varying transfer entropy network with a graph attention encoder regularised by a variational information bottleneck, and demonstrates the practical value of the calibrated predictive distribution through a downstream entropy-regulated, CVaR-constrained portfolio application. We establish three theoretical results: L2 consistency of the k-nearest-neighbour transfer entropy estimator on α-mixing returns with rate OP(n-2/(2+d)), a PAC-Bayes generalisation bound of order O((I(X;Z)+log(1/δ))/n) for the bottleneck-encoded forecaster, and asymptotic CVaR feasibility of the plug-in allocation. In simulations across sparse Granger networks, contagion DCC-GARCH ensembles, and regime-switching factor models, the framework cuts spillover forecasting errors by 24 to 42 percent against LSTM, vanilla GAT, and Transformer baselines, and it recovers 1.6 additional nats of mutual information with the realised connectedness matrix. On a 32-asset global panel covering 2014 to 2025, the model delivers an out-of-sample R2 of 0.331, an annualised Sharpe ratio of 1.46 against 0.83 for an equally weighted benchmark, a maximum drawdown of 7.8 percent, and 95 percent CVaR reductions of 28 to 36 percent across sub-periods relative to a shrinkage minimum-variance baseline.