Daily Papers

We revisit Tirole's classic paper "Asset Bubbles and Overlapping Generations" (1985, Econometrica) in the case of a dividend-paying asset. Recently, Pham and Toda (2026) constructed a counterexample to Proposition 1(c), showing that Tirole's equilibrium classification is incorrect as stated and that long-run outcomes can depend on initial capital. This paper characterizes the entire set of equilibrium initial asset prices under capital over-accumulation. Exactly one of three regimes occurs: (i) a unique bubbleless equilibrium with capital converging to zero (capital collapse), (ii) a unique asymptotically bubbly equilibrium converging to a positive steady state (bubble necessity), or (iii) a continuum of equilibria with different long-run bubble behavior (indeterminacy). We further derive a threshold for initial capital under the bubble necessity condition, establish preference-free sufficient conditions for capital collapse, and show that the continuum in the pure bubble model survives sufficiently small dividend perturbations. Closed-form examples illustrate the possible long-run outcomes.

When forecasting hourly returns for 1,000 US equities, we observe an unexpected phenomenon: predictions become nearly flat and show poor stock ranking, as measured by cross-sectional correlation. We call this forecast collapse. Surprisingly, the phenomenon largely disappears when forecasting trading volume under the same setting. We investigate forecast collapse across time-series foundation models (TSFMs), twelve deep-learning forecasting models, and 97 public benchmark configurations, and find that it is closely tied to target predictability. We identify two distinct reasons behind it: low predictability limits the amplitude of calibrated point forecasts, while per-series objectives leave cross-series structure unidentified. These findings reveal a calibration-ranking tradeoff: optimizing squared error leads to flat predictions, whereas directly optimizing cross-sectional correlation improves ranking but can inflate forecast amplitude by more than an order of magnitude. To address this tradeoff, we introduce CalibRank, a simple objective that balances calibration and ranking. On Finance1K, CalibRank nearly triples cross-sectional correlation while keeping amplitude close to the target, and improves correlation on all tested models. Our results reveal a blind spot in conventional time-series evaluation: per-series metrics can hide failures in cross-series structure needed by downstream decisions.

Despite significant progress in model editing methods, their application in real-world scenarios remains challenging as they often cause large language models (LLMs) to collapse. Among them, ROME is particularly concerning, as it could disrupt LLMs with only a single edit. In this paper, we study the root causes of such collapse. Through extensive analysis, we identify two primary factors that contribute to the collapse: i) inconsistent handling of prefixed and unprefixed keys in the parameter update equation may result in very small denominators, causing excessively large parameter updates; ii) the subject of collapse cases is usually the first token, whose unprefixed key distribution significantly differs from the prefixed key distribution in autoregressive transformers, causing the aforementioned issue to materialize. To validate our findings, we propose a simple yet effective approach: uniformly using prefixed keys during editing phase and adding prefixes during testing phase to ensure the consistency between training and testing. The experimental results show that the proposed solution can prevent model collapse while maintaining the effectiveness of the edits.

Variational Autoencoders (VAEs) frequently suffer from posterior collapse, a failure mode in which the approximate posterior converges to the prior, rendering the latent code uninformative. Despite extensive research, a unified account of why collapse occurs has remained an open question. We identify and formalize two logically independent but coupled causes. Gradient imbalance occurs when the decoder's reconstruction signal vanishes faster than the KL regularization pressure as the posterior widens. Information gap occurs when the stochastic sampling step discards a substantial fraction of the encoder's computed representation, attenuating decoder sensitivity and making collapse inexpensive. Both causes share the same collapse trajectory, and we show that the information gap is algebraically equivalent to mismatch between the aggregate posterior and the prior, unifying two pathologies. Subsequently, we introduce λ-VAE, which resolves both causes through a single modification to the reparameterization step: the sampling noise is scaled by per-dimension exponent, while the KL penalty retains the original posterior variance. This asymmetry shifts the stable training attractor away from the degenerate collapsed state, driving all latent dimensions toward the same equilibrium -- a mechanism we term variance equalization. A closed-form optimal exponent per dimension follows from a net information gain objective, with a single hyperparameter controlling the reconstruction-generation tradeoff. We validate on standard benchmarks (Binary MNIST, Binary Omniglot, CIFAR-10, CelebA-64), showing consistent reductions in collapsed dimensions, information capacity gains of up to 2.8times nats, and reconstruction quality improvements of up to +0.33 BPD.

In the era of proliferation of large language and image generation models, the phenomenon of "model collapse" refers to the situation whereby as a model is trained recursively on data generated from previous generations of itself over time, its performance degrades until the model eventually becomes completely useless, i.e the model collapses. In this work, we study this phenomenon in the setting of high-dimensional regression and obtain analytic formulae which quantitatively outline this phenomenon in a broad range of regimes. In the special case of polynomial decaying spectral and source conditions, we obtain modified scaling laws which exhibit new crossover phenomena from fast to slow rates. We also propose a simple strategy based on adaptive regularization to mitigate model collapse. Our theoretical results are validated with experiments.

This paper proposes a formal framework for reverse stress testing geopolitical risk in corporate credit portfolios. A joint macro-financial scenario vector, augmented with an explicit geopolitical risk factor, is mapped into stressed probabilities of default and losses given default. These stresses are then propagated to portfolio tail losses through a latent factor structure and translated into a stressed CET1 ratio, jointly accounting for capital depletion and risk-weighted asset dynamics. Reverse stress testing is formulated as a constrained maximum likelihood problem over the scenario space. This yields a geopolitical point reverse stress test, or design point, defined as the most probable scenario that breaches a prescribed capital adequacy constraint under a reference distribution. The framework further characterises neighbourhoods and near optimal sets of reverse stress scenarios, allowing for sensitivity analysis and governance oriented interpretation. The approach is compatible with internal rating based models and supports implementation at the exposure or sector level.

Systemic financial risk refers to the simultaneous failure or destabilization of multiple financial institutions, often triggered by contagion mechanisms or common exposures to shocks. In this paper, we present a dynamical model of bank leverage (the ratio of asset holdings to equity) a quantity that both reflects and drives risk dynamics. We model how banks, constrained by Value-at-Risk (VaR) regulations, adjust their leverage in response to changes in the price of a single asset, assumed to be held in fixed proportion across banks. This leverage-targeting behavior introduces a procyclical feedback loop between asset prices and leverage. In the dynamics, this can manifest as logistic-like behavior with a rich bifurcation structure across model parameters. By analyzing these coupled dynamics in both isolated and interconnected bank models, we outline a framework for understanding how systemic risk can emerge from seemingly rational micro-level behavior.