In this note, we study the ultimate ruin probabilities of a real-valued L{é}vy process X with light-tailed negative jumps. It is well-known that, for such L{é}vy processes, the probability of ruin decreases as an exponential function with a rate given by the root of the Laplace exponent, when the initial value goes to …
This paper presents generalized momentum mappings for covariant Hamiltonian field theories. The new momentum mappings arise from a generalization of symplectic geometry to LVY, the bundle of vertically adapted linear frames over the bundle of field configurations Y. Specifically, the generalized field momentum obs…
This article is devoted to the maximisation of HARA utilities of L{é}vy switching process on finite time interval via dual method. We give the description of all f-divergence minimal martingale measures in initially enlarged filtration, the expression of their Radon-Nikodym densities involving Hellinger and Kulback-Lei…
In this paper, we study the ruin problem with investment in a general framework where the business part X is a L{é}vy process and the return on investment R is a semimartingale. We obtain upper bounds on the finite and infinite time ruin probabilities that decrease as a power function when the initial capital increases…
Let M be a manifold, V be a vector field on M, and B be a Banach space. For any fixed function f:M→B and any fixed complex number λ, we study Hyers-Ulam stability of the global differential equation Vy=λy+f.
An asset network systemic risk (ANWSER) model is presented to investigate the impact of how shadow banks are intermingled in a financial system on the severity of financial contagion. Particularly, the focus of this study is the impact of the following three representative topologies of an interbank loan network betwee…
In this paper, we provide a representation theorem for dynamic capital allocation under It{ô}-L{é}vy model. We consider the representation of dynamic risk measures defined under Backward Stochastic Differential Equations (BSDE) with generators that grow quadratic-exponentially in the control variables. Dynamic capital …
We introduce a class of interest rate models, called the α-CIR model, which gives a natural extension of the standard CIR model by adopting the α-stable L{é}vy process and preserving the branching property. This model allows to describe in a unified and parsimonious way several recent observations on the sovereign …
The Wiener-Hopf factorization is obtained in closed form for a phase type approximation to the CGMY Lévy process. This allows, for the approximation, exact computation of first passage times to barrier levels via Laplace transform inversion. Calibration of the CGMY model to market option prices defines the risk neutral…
Method extends option valuation for 2D Lévy models.
problem Valuation of European options under 2-asset infinite-activity Lévy models.
method Developed numerical method extending Wang et al. (2007) for 1D to 2D, using Fourier transform for integral term and semi-Lagrangian theta-method for temporal discretization.
result Favourable second-order convergence for Normal Tempered Stable dynamics.
Paper reduces dimensionality for robust option pricing in 2-asset markets.
problem Robust option pricing in multi-asset markets with sub- or supermodular payoffs.
method Investigates the geometry of VMOT solutions, proving dimension reduction for 2 assets and developing a Sinkhorn algorithm.
result Dimension reduction to single-factor structure for 2-asset markets, significantly reducing computational time and improving accuracy.
Many recent papers address reading comprehension, where examples consist of (question, passage, answer) tuples. Presumably, a model must combine information from both questions and passages to predict corresponding answers. However, despite intense interest in the topic, with hundreds of published papers vying for lead…
Constructs supermartingale couplings with full marginals constraints.
problem Optimal transport for supermartingale couplings with multiple marginals.
method Markovian iteration of one-period optimal supermartingale couplings.
result Explicit construction of supermartingale processes solving optimal transport problem.
We prove that a compact stratied space satises the Riemannian curvature-dimension condition RCD(K, N) if and only if its Ricci tensor is bounded below by K ∈ R on the regular set, the cone angle along the stratum of codimension two is smaller than or equal to 2π and its dimension is at most equal to N. This gives…
The distribution of trade sizes and trading volumes are investigated based on the limit order book data of 22 liquid Chinese stocks listed on the Shenzhen Stock Exchange in the whole year 2003. We observe that the size distribution of trades for individual stocks exhibits jumps, which is caused by the number preference…
We provide an empirical investigation aimed at uncovering the statistical properties of intricate stock trading networks based on the order flow data of a highly liquid stock (Shenzhen Development Bank) listed on Shenzhen Stock Exchange during the whole year of 2003. By reconstructing the limit order book, we can extra…
Modeling financial markets with a novel order flow model.
problem Inconsistent parameter values from long-range memory estimators.
method Tsallis q-exponential distribution for limit order cancellation times.
result Improved accuracy in predicting financial market dynamics.
This paper shows a buy-and-hold strategy is asymptotically log-optimal for a market with a dominant asset.
problem Finding a safe and optimal investment strategy in a market with a dominant asset.
method Investment strategy based on the dominant asset and buy-and-hold approach.
result Buy-and-hold strategy on the dominant asset is asymptotically log-optimal with a sublinear rate of convergence.
This paper extends Kelly Criterion to include rebalancing frequency for optimal portfolio selection.
problem Optimizing a portfolio with multiple assets and varying rebalancing frequency.
method Using Kelly Criterion, the paper derives necessary and sufficient conditions for the frequency-based Kelly optimal portfolio.
result Proves the necessity and sufficiency of conditions for the frequency-based Kelly optimal portfolio.
The paper introduces BCART models for aggregate claim amount, improving frequency-severity and joint modeling.
problem Modeling aggregate claim amount with frequency-severity and joint dependencies.
method Developed three types of BCART models: frequency-severity, sequential, and joint models. Used various distributions for claim severity data.
result Weibull distribution outperforms gamma and lognormal for right-skewed, heavy-tailed claim severity data.
The paper uses model-based trees to create interpretable surrogate models for complex machine learning models.
problem Interpreting complex machine learning models.
method Using model-based trees to partition feature space and create interpretable models.
result Model-based trees generate optimal surrogate models that balance interpretability and performance.
Gauge Flow Models use a learnable Gauge Field in Generative Flow Models.
problem Improving generative model performance.
method Integrates a learnable Gauge Field into Flow ODEs.
result Gauge Flow Models outperform traditional Flow Models in Flow Matching experiments.
The study examines how model predictions hold up under model extensions.
problem Model predictions may not be robust under model extensions, limiting their applicability.
method The study uses causal ordering to assess robustness of qualitative model predictions and characterizes model extensions that preserve predictions.
result Conditions and techniques are provided to assess robustness of model predictions under model extensions.
MALC combines interpretable linear models with black-box models for better predictions and transparency.
problem Combining interpretability with black-box models for better predictions.
method Formulates MALC as a convex optimization problem and uses accelerated proximal gradient method for training.
result MALC provides an efficient frontier balancing prediction accuracy and transparency.
Revises Bayesian model averaging for foundation models.
problem Ensemble pre-trained and lightly-finetuned foundation models for improved classification performance.
method Introduces trainable linear classifiers and computationally cheaper model averaging scheme (OMA).
result Ensembled models can better predict on various datasets.
Paper introduces symmetric divergence link models for probability distributions.
problem Symmetric divergence measures for probability distributions.
method Two general classes of link models: one for survival functions and another for cumulative probability distribution functions.
result Advantages of symmetric divergence measures over asymmetric measures for model averaging and feature assessment.
New method to handle credit portfolio model uncertainties.
problem Model risk in credit portfolio models.
method Demonstrates comprehensive yet easy-to-implement approach to uncertainty in model parameters.
result Comprehensive method to deal with model uncertainties.
The paper tests stock return models and uses LSTM to predict stock returns.
problem Validating stock return models and predicting stock returns.
method Used Fama-French three-factor, four-factor, and five-factor models; also used LSTM model.
result Fama-French five-factor model shows better validity for stock returns.
Researchers review challenges in interpreting additive models, especially neural additive models.
problem Challenges in interpreting additive models, particularly neural additive models.
method Review of generalized additive models and discussion of nonidentifiability.
result Challenges in claiming interpretability or suitability for safety-critical applications of additive models.
Proposes a decision-theoretic approach for enhancing model interpretability in Bayesian frameworks.
problem Challenges the traditional approach of restricting model structure for interpretability in Bayesian frameworks.
method Introduces an interpretability utility function and a two-step method involving a reference model and a proxy model.
result Demonstrates that the proposed method generates more accurate models with the same level of interpretability.
Novel hybrid modeling combines ML and physics for real-time diagnosis.
problem Real-time diagnosis of complex systems.
method Combines machine learning and physics-based models to create reduced-order models.
result Generated models are two orders of magnitude simpler, improving efficiency.
CRS model improves ranking data modeling with theoretical guarantees.
problem Lack of rich, multimodal models for ranking data.
method Contextual Repeated Selection (CRS) model for multimodal ranking data.
result CRS model significantly outperforms existing methods in various ranking contexts.
Interpretable machine learning has become a strong competitor for traditional black-box models. However, the possible loss of the predictive performance for gaining interpretability is often inevitable, putting practitioners in a dilemma of choosing between high accuracy (black-box models) and interpretability (interpr…
Sigma models linked to Gross-Neveu models via quiver varieties.
problem Understanding the relationship between sigma models and Gross-Neveu models.
method Exploring the mathematical correspondence between sigma models and Gross-Neveu models, including their geometric and trigonometric/elliptic deformations.
result Sigma models are mathematically equivalent to Gross-Neveu models under certain conditions.
Simple models are preferred over complex models, but over-simplistic models could lead to erroneous interpretations. The classical approach is to start with a simple model, whose shortcomings are assessed in residual-based model diagnostics. Eventually, one increases the complexity of this initial overly simple model a…
Matryoshka hides secret models in a carrier model, achieving high capacity and robustness.
problem Stealing functionality of private ML data by hiding models in a carrier model.
method Parameter sharing approach exploiting the learning capacity of the carrier model.
result Hides a 26x larger secret model or 8 secret models in the carrier model.
Eigen-stratified models reduce model size and improve performance.
problem Large model size in Laplacian-regularized stratified models.
method Formulate eigen-stratified models with linear combinations of bottom eigenvectors of the graph Laplacian.
result Significant reduction in model size with eigen-stratified models.
Seq2Seq models speed up epidemic model predictions.
problem Complex epidemic models are computationally expensive.
method Used deep seq2seq models as surrogates for complex models.
result Surrogates predict scenarios up to several thousand times faster.
This work develops scalable model selection methods with fast update and selection.
problem Efficient model selection for large pools of candidate models.
method Isolated model embedding, which supports asymptotically fast update and selection.
result Standardized Embedder achieves competitive model selection performances.
Paper proposes BMPO to optimize policies using bidirectional models.
problem Model-based reinforcement learning's reliance on forward model accuracy.
method Develops BMPO using both forward and backward models for policy optimization.
result BMPO outperforms state-of-the-art methods in sample efficiency and asymptotic performance.
Copulas outperform marginal models in multivariate risk forecasting, reducing model risk by narrowing down the set of models.
problem Model risk in multivariate risk forecasting, especially during crises.
method Comprehensive empirical study comparing Copula-GARCH models with fixed marginals, copulas, or neither.
result Model risk is almost entirely due to copula choice, not marginal models.
This paper distills a complex travel mode choice model into simpler, interpretable models.
problem Lack of interpretability in complex machine learning models for travel behavior.
method Model distillation combined with market segmentation.
result Generated interpretable models that closely match the predictions of the original complex model.
BayesBlend blends multiple models' predictions for better insurance loss predictions.
problem Improving insurance loss predictions by combining multiple models.
method Pseudo-Bayesian model averaging, stacking, and hierarchical stacking.
result BayesBlend provides a user-friendly way to blend model predictions and estimate weights.
The paper identifies when larger models improve predictions and proposes a switcher model.
problem Understanding when larger models benefit from added complexity.
method Numerical studies on T5 architecture to analyze predictive uncertainty and model performance.
result Large models improve on examples where small models are uncertain, but not on certain examples.
Aggregates models from different datasets using shared latent structures.
problem Aggregating models from heterogeneous datasets with shared latent structures.
method Bayesian nonparametrics for identifying correspondences among local model parameterizations.
result Framework successfully aggregates various model types across different applications.
Improved diffusion model generation speed with speculative sampling.
problem Generating samples from computationally expensive diffusion models.
method Extending speculative sampling to diffusion models, using fast draft models for candidate token generation.
result Significant speedup in generation, halving the number of function evaluations.
DBNs improve accuracy of biological ODE models with missing data.
problem Uncertainty in biological ODE models with missing data.
method Converted ODE models to DBNs and used Particle Filtering for parameter estimation.
result DBNs can accurately infer model variables with missing data.
We propose a generalization of neural network sequence models. Instead of predicting one symbol at a time, our multi-scale model makes predictions over multiple, potentially overlapping multi-symbol tokens. A variation of the byte-pair encoding (BPE) compression algorithm is used to learn the dictionary of tokens that …