Large language models have shown great potential as forecasting tools in finance and economics, but backtesting performance is subject to look-ahead bias if the period overlaps with an LLM’s training window. Prompt-based attempts to avoid look-ahead bias require that LLMs understand chronology. We test LLMs’ ability to understand and enforce chronological order in three types of tasks: sorting randomly shuffled historical events; conditional sorting of events defined by some conditions; and anachronism detection based on intersections of multiple timelines. Our experiments use events that we first confirm are known to the LLM; this ensures that we test chronological understanding on an LLM’s pretrained internal knowledge. Across three LLM families— GPT-4.1 (standard), GPT-5 (hybrid-reasoning), and Claude 3.7 Sonnet (large-reasoning, with and without Extended Thinking), we find that performance degrades rapidly with problem complexity but improves greatly for reasoning models with test-time extended reasoning. These patterns are important for the real-time application of LLMs in finance.

This paper develops methods for computationally efficient calculation of value-at-risk (VAR) in the presence of heavy-tailed risk factors. The methods model market risk factors through a multivariate t-distribution, which has both heavy tails and empirical support. Our key mathematical result is a transform analysis of a quadratic form in multivariate t random variables. Using this result, we develop two computational methods. The first uses Fourier transform inversion to develop a heavy-tailed delta-gamma approximation; this method is extremely fast, but like any delta-gamma method is only as accurate as the quadratic approximation. For greater accuracy, we therefore develop an efficient Monte Carlo method; this method uses our heavy-tailed delta-gamma approximation as a basis for variance reduction. Specifically, we use the numerical approximation to design a combination of importance sampling and stratified sampling of market scenarios that can produce enormous speed-ups compared with standard Monte Carlo.

Intimtesirnal perturbation analysis is a technique for estimating derivatives of performance indices from simulation or observation of discrete event systems.Such derivative estimates are useful in performing optimization and sensitivity analysis through simulation.A general formulation of finite-horizon perturbation analysls derivative estimates is given, and then sufficient conditions for their use is presented with a variety of queuing systems.