New risk measures incorporate economic states to assess crude oil derivatives.
problem Assessing risk in crude oil derivatives with varying economic conditions.
method Introduced regime switching entropic risk measures using Markov chains.
result Closed formulae for risk measures derived, showing term structure and mean-reverting convenience yield.
The study explains why signature methods work in commodity futures term structure classification.
problem Lack of interpretability in signature methods for term structure classification.
method Introducing signature perturbations to explain the success of signature-based classification.
result The volatility of the convenience yield is the major discriminant for commodity markets classification.
Paper examines floating exercise boundaries for American options in time-inhomogeneous models.
problem Floating exercise boundaries in time-inhomogeneous models with negative interest rates or yields.
method Semi-analytical approach for pricing American options.
result Specialized pricing methodologies are required for models with floating exercise boundaries.
A new multi-factor model improves commodity pricing accuracy.
problem Enhancing accuracy in commodity pricing by integrating multiple risk factors.
method A four-factor model using Kalman filter for simultaneous estimation and state variable filtering.
result The four-factor model outperforms existing models in capturing futures term structures and crude oil pricing.
In this paper, we implement a stochastic deflator with five economic and financial risk factors: interest rates, market price of risk, stock prices, default intensities, and convenience yields. We examine the deflator with different financial assets, such as stocks, zero-coupon bonds, vanilla options, and corporate cou…
Defines and extends Lie algebroid prolongations in convenient settings.
problem Adapting Lie algebroid prolongations to convenient settings.
method Defined and adapted Lie algebroid prolongations over fibred manifolds.
result Stability of prolongations under projective and direct limits.
This paper provides a general result on controlling local Rademacher complexities, which captures in an elegant form to relate the complexities with constraint on the expected norm to the corresponding ones with constraint on the empirical norm. This result is convenient to apply in real applications and could yield re…
We review the basic definitions and properties concerning smooth structures, convenient spaces, diffeological spaces and tangent structures. The relation betwen them is described. A tangent structure is constructed for each pre-convenient space. This one is proved to be convenient iff the space and the tangent fibres c…
We study a stochastic control approach to managed futures portfolios. Building on the Schwartz 97 stochastic convenience yield model for commodity prices, we formulate a utility maximization problem for dynamically trading a single-maturity futures or multiple futures contracts over a finite horizon. By analyzing the a…
Algorithm counts intersections of normal curves efficiently.
problem Efficiently solving word problems in mapping class groups of punctured surfaces.
method Fast algorithm for counting intersections of normal curves on triangulated surfaces.
result Efficient solution of the word problem for mapping class groups of punctured surfaces.
This paper introduces an information-based model for the pricing of storable commodities such as crude oil and natural gas. The model uses the concept of market information about future supply and demand as a basis for valuation. Physical ownership of a commodity is taken to provide a stream of convenience dividends eq…
Extends Dirac structures to infinite dimensions, focusing on convenient Lie algebroids and manifolds.
problem Extending classical geometrical results from finite to infinite dimensions.
method Introduces partial Dirac structures on convenient Lie algebroids and manifolds, explores their properties and limits.
result Classical geometrical results can be extended to infinite dimensional contexts.
Introduces partial Jacobi manifolds in convenient spaces.
problem No specific problem stated; focuses on new mathematical structure.
method Introduces partial Jacobi manifold in convenient c∞-complete framework. result Characterizes the characteristic distribution of partial Jacobi manifolds.
Discuss various definitions of vector fields on manifolds leading to Lie algebras.
problem Defining vector fields on convenient manifolds.
method Various definitions of vector fields and their equivalence.
result Equivalent definitions of vector fields on manifolds.
We study boundary value problems for first-order elliptic differential operators on manifolds with compact boundary. The adapted boundary operator need not be selfadjoint and the boundary condition need not be pseudo-local. We show the equivalence of various characterisations of elliptic boundary conditions and demonst…
In the analysis of machine learning models, it is often convenient to assume that the parameters are IID. This assumption is not satisfied when the parameters are updated through training processes such as SGD. A relaxation of the IID condition is a probabilistic symmetry known as exchangeability. We show the sense in …
A new model explains relative spreads between economies using dynamic Nelson-Siegel and functional regression.
problem Analyzing and predicting relative spreads between economies in fixed income markets.
method State-space functional regression model incorporating dynamic Nelson-Siegel model and kernel PCA.
result The new model outperforms the dynamic Nelson-Siegel model in explaining relative spreads.
Study values and optimizes forestry leases under risk and uncertainty.
problem Valuing and optimizing forestry leases in the presence of catastrophe risk and parameter uncertainty.
method Stochastic bio-economic models, Kalman filter, maximum likelihood estimation, RBSDEs, Monte Carlo simulations.
result Conservative strategy is recommended due to parameter uncertainty.
The paper extends Nambu-Poisson structures to infinite dimensions.
problem Extending Nambu-Poisson structures to infinite dimensional settings.
method Adapting finite dimensional Nambu-Poisson structures to a convenient manifold setting.
result Classical results in finite dimensions can be extended to infinite dimensions for partial Nambu structures.
New topological complexity measures for neural networks.
problem Measuring complexity of neural network functions.
method Generalized piecewise-linear Morse theory applied to ReLU networks.
result Local complexity can be arbitrarily high.
Lie algebras of quotient groups defined under specific conditions.
problem Conditions for Lie differentiation of quotient groups.
method Diffeological group theory, tangent structure, Lie functor instantiation.
result Lie algebra structure on quotient groups derived from Lie algebras of parent groups.
A new modeling framework CSN simplifies and interprets machine learning models.
problem Complexity and interpretability issues in machine learning models.
method Combines spline transformation and cross-network to create CSN.
result CSN is as performant and interpretable as XGBoost and FCNN.
This paper is devoted to the framework of direct limit of anchored Banach bundles over a convenient manifold which is a direct limit of Banach manifold. In particular we give a criterion of integrability for distributions on such convenient manifolds which are locally direct limits of particular sequences of Banach anc…
Following the unified approach of A. Kriegl and P.W. Michor (1997) for a treatment of global analysis on a class of locally convex spaces known as convenient, we give a generalization of Rashevsky-Chow's theorem for control systems in regular connected manifolds modelled on convenient (infinite-dimensional) locally con…
The coefficient of the logarithmic term in the entropy on even spheres is re-computed by the local technique of integrating the finite temperature energy density up to the horizon on static d--dimensional de Sitter space and thence finding the entropy by thermodynamics. Numeric evaluation yields the known answer i.e. (…
Study shows how Poisson brackets factor on infinite dimensional manifolds.
problem Understanding Poisson brackets on infinite dimensional manifolds.
method Analyzes Poisson brackets on smoothly paracompact manifolds with specific properties.
result Dual map of a Poisson bracket factors as a smooth section of a vector bundle.
Variational inference has experienced a recent surge in popularity owing to stochastic approaches, which have yielded practical tools for a wide range of model classes. A key benefit is that stochastic variational inference obviates the tedious process of deriving analytical expressions for closed-form variable updates…
WEINCE improves contrastive learning by correcting softmax biases.
problem Softmax in InfoNCE can lead to misaligned statistical assumptions in contrastive learning.
method WEINCE uses anchor-wise online batch statistics to blend softmax logits with an endpoint shortfall correction.
result WEINCE yields consistent improvements in frozen-feature evaluation across five vision benchmarks.
Uniform proof for ultradifferentiability in various classes and dimensions.
problem Generalizing ultradifferentiability conditions to multidimensional cases and infinite dimensional spaces.
method Uniform proof approach that works in all cases and dimensions, including infinite dimensional Banach spaces and convenient vector spaces.
result Characterization of ultradifferentiability for general analytic germs and functions.
Survey on Nambu-Poisson structures in infinite dimensions.
problem Generalization of Poisson and Nambu-Poisson structures in infinite dimensions.
method Study properties of associated characteristic distribution and projective/direct limits.
result Properties and limits of Nambu-Poisson structures in convenient setting.
Extends Dirac structures to infinite dimensions for mechanical systems.
problem Adapting finite-dimensional Dirac structures to infinite-dimensional settings.
method Introduces partial Dirac structures and applies variational techniques to constraint Lagrangians on subbundles and singular distributions.
result Characterizes normal geodesics for conical Finsler metrics on Banach manifolds.
This is an overview article. After an introduction to convenient calculus in infinite dimensions, the foundational material for manifolds of mappings is presented. The central character is the smooth convenient manifold C∞(M,N) of all smooth mappings from a finite dimensional Whitney manifold germ M into a …
Study on diffeologies on locally convex spaces and smooth multiplication of distributions.
problem Geometric characterization and smoothness of distribution multiplication.
method Investigation of canonical and c∞-diffeologies on locally convex spaces, proving geometric characterizations, and comparing diffeologies. result Established a framework for nonlinear distribution theory beyond manifolds, realizing microlocally multipliable distributions as a diffeological colimit.
Study derives CEV volatility for SABR model, reducing approximation error.
problem Approximating SABR model volatility accurately.
method New analytic approximations of CEV volatility derived from SABR model.
result CEV volatility approximation yields finite value at zero strike.
Spot option prices, forwards and options on forwards relevant for the commodity markets are computed when the underlying process S is modelled as an exponential of a process ξ with memory as e.g. a Lévy semi-stationary process. Moreover a risk premium \r{ho} representing storage costs, illiquidity, convenience yield or…
COMP-AMS optimizes distributed training with compressed gradients, achieving similar accuracy with less communication.
problem Efficiently training large-scale models in distributed environments with reduced communication costs.
method Distributed optimization framework using gradient averaging and adaptive AMSGrad, with gradient compression and error feedback.
result COMP-AMS achieves the same convergence rate and linear speedup as standard AMSGrad with less communication.
Improves meta-learning efficiency with mixed-mode differentiation.
problem Efficiently calculating complex derivatives in meta-learning.
method Mixed-Flow Meta-Gradients (MixFlow-MG) for scalable differentiation.
result Significant memory and time improvements in meta-learning tasks.
We extend Dupire's formula for stochastic interest rates and local volatility.
problem Deriving formulas for stochastic interest rates and local volatility.
method Generalizations of Dupire's formula for stochastic drift and local volatility.
result Validated the limits of the generalized Dupire formulae for specific cases.
We prove that direct limits of finite dimensional Lie algebroids and their prolongations can be endowed with structures of convenient spaces.
Web browser autofill predicts form field labels for convenience.
problem Predicting form field labels for autofill in web browsers.
method Machine learning solution implemented as a web service using Azure ML Studio.
result Improved form field label prediction for autofill.
In this new version, we correct some typos. For the readers' convenience, we also added some footnotes and more details for certain lemmas and theorems.
With a view towards applications in the theory of infinite-dimensional representations of finite-dimensional Lie supergroups, we introduce a new category of supermanifolds. In this category, supermanifolds of `maps' and `fields' (fibre bundle sections) exist. In particular, loop supergroups can be realised globally in …
New method detects essential tori in mixed singularity links.
problem Detecting essential tori in mixed singularity link complements.
method Analyzing properties of defining mixed polynomials.
result Explicit criteria for essential tori existence.
We proved that the solutions of C2 class of certain ODEs or PDEs belong to a class of harmonic maps between two convenient generalized Lagrange spaces.
We study diffeologies on locally convex spaces and their application to smooth multiplication of distributions.
problem Constructing smooth multiplication of distributions on locally convex spaces.
method Using diffeological colimits and wavefront-set criterion.
result Proving smooth multiplication of microlocally multipliable distributions.
Proposes logistic-beta process for modeling dependent probabilities with beta marginals.
problem Limited work on flexible and computationally convenient stochastic process extensions for dependent random probabilities.
method Introduces logistic-beta process with logistic transformation and beta marginals, capable of modeling dependence in discrete and continuous domains.
result Logistic-beta processes enable effective posterior inference and design of computationally tractable dependent Bayesian nonparametric models.
Squared families are a new model class derived from linear transformations, offering convenient properties and universal approximation.
problem Developing a new class of probability models that are easier to handle and have useful properties.
method Introducing squared families as families of probability densities obtained by squaring a linear transformation of a statistic, and showing their properties and applications.
result Squared families have convenient properties and can approximate target densities well.
We provide an intergral lift of the combinatorial definition of Heegaard Floer homology for nice diagrams, and show that the proof of independence using convenient diagrams adapts to this setting.