In briefLaplace transform of ruin time in the Cramér–Lundberg model with Erlang E₂(μ) claims: spectrum, exact moments, matrix reduction
SummaryThis paper studies the Laplace transform of the time of ruin in the classical Cramér–Lundberg model when claims follow an Erlang distribution with shape parameter 2. The authors derive an integro-differential equation with two boundary conditions and show that, for every positive discount rate, its characteristic polynomial has one negative and two distinct positive roots. They also construct a finite-dimensional matrix reduction of the convolution chain and obtain exact expressions for the ruin probability, mean time of ruin and higher moments, and prove analyticity in the discount rate.
In briefAI trading agents, market makers, and stress in automated markets
SummaryThe paper models trader types as AI agents defined by their reward functions and analyzes the feedback they create on a constant-product automated market maker (AMM). It shows that herd-dominated and arbitrage-dominated markets of equal size have identical return distributions and turnover, yet their stress episodes can differ in length by a factor that grows with the feedback-to-noise ratio. The authors find that profit-seeking agents tend to ride herds rather than lean against them, and that spread-earning market makers restore stability but make liquidity fragile, with maker-taker pricing being more effective than a uniform fee.
In briefRiskReason: A Benchmark for Checking Financial Risk Reasoning
SummaryThis paper introduces RiskReason, a benchmark for testing whether models can reason verifiably about financial risk across several risk-management mechanisms. It includes standard tasks for individual mechanisms and long-horizon tasks that combine multiple mechanisms, with reference outcomes, formal specifications, and reasoning annotations. Eleven model configurations were evaluated, with the strongest reaching 80.0 to 90.2 percent overall accuracy. The authors find that models can make incorrect risk decisions despite correct intermediate calculations, and conclude that aggregate accuracy alone is insufficient to measure reliability.
Nazanin Yousefi, Mohammadreza Ghafouri, Seyedreza Tavakoli et al.
In briefBoom-bust market model: how investor-market reflexivity amplifies non-equilibrium
SummaryThis paper introduces a multi-asset market model in which a single collective investor's demand moves prices and also depends on market performance, forming a reflexive loop in the spirit of Soros's theory. The market settles into a non-equilibrium steady state with broken detailed balance, where a probability current circulates among mispricing, demand and volatility. Calibrated to the S&P 500 from 1996 to 2024, the model reproduces stylised return facts and cross-sectional metrics, and its boom-bust cycle frequency falls within one-sigma ranges of the S&P 500.
