Modern AI Tools and the Indian IT Sector: A Jump-Augmented Physics-Informed Framework for Narrative Shocks, Repricing and Sector Allocation in NIFTY IT

Abstract

Between February and September 2026 the NIFTY IT index gave up roughly a quarter of its value while the underlying industry kept growing, a divergence that market commentary attributed almost entirely to the arrival of increasingly capable coding and agentic AI tools. This paper asks what the right allocation response to such a repricing is, and answers it with physics rather than pattern fitting. We extend the physics-informed pipeline of Part I from a pure diffusion to a jump-augmented Merton problem in which capability announcements arrive as a Poisson stream of two-sided, negatively skewed narrative shocks. The resulting Hamilton-Jacobi-Bellman equation is a partial integro-differential equation whose optimal fraction has no closed form; we prove that the first-order condition has a unique admissible root, and give an a-posteriori bound that controls the value-function error by the physics residual. A from-scratch physics informed network, trained on the equation alone with no market data, recovers the semi-analytic value component to a relative L2 error of 2.1×10−4 for a constant announcement intensity and 2.9×10−3 for a ramped one, with the realised error inside the bound by a factor of four. Calibrating to the observed NIFTY IT state of 10 September 2026 and backtesting over 400 simulated five-year paths net of 25 basis points of Indian transaction costs, we find a sharply asymmetric result. Averaged over states, jump awareness barely moves the static weight, from 0.569 to 0.546. Conditioned on the state it moves it by almost an order of magnitude, from 0.93 in quiet periods to 0.11 inside an announcement cluster. An oracle that is told the state reaches a Sharpe ratio of 0.39 against 0.28 for buy-and-hold, while a tradable trailing-window detector falls to 0.19 after estimation error and 4.3 units of annual turnover. The governing equation therefore supplies the correct response to AI narrative risk; the binding constraint is detecting the narrative state, and that is where engineering effort belongs. The backtest uses a calibrated market simulator, not real exchange data.