Develops hyperfinite G-expectation theory for continuous-time processes.
problem Creating a discrete model for continuous-time G-expectation. method Introduces hyperfinite G-expectation and develops its theory, proving existence of liftings. result Establishes existence theorem for liftings of continuous-time G-expectation. Develops non-standard analysis for coherent risk estimation.
problem Estimating coherent risk measures in financial contexts.
method Non-standard analysis, hyperfinite representations, discrete Kusuoka formulae, plug-in asymptotics.
result Uniform almost sure consistency and asymptotic normality of spectral plug-in estimators.
Groups acting on CAT(0) cube complexes have hyperfinite boundary actions.
problem Hyperfiniteness of boundary actions for special groups.
method Proving hyperfiniteness for groups acting on CAT(0) cube complexes.
result Boundary actions of virtually special groups are hyperfinite.
Unified framework for generative modeling using hyperfinite analysis.
problem Score-based generative modeling challenges.
method Hyperfinite analysis of score-based diffusion models.
result Unified hyperfinite framework connects various generative modeling methods.
We set forth a definition of hyperfinite knots. Loosely speaking, these are limits of certain sequences of knots with increasing crossing number. These limits exist in appropriate closures of quotient spaces of knots. We give examples of hyperfinite knots. These examples stem from an application of the Thermodynamic Li…
Study proves hyperfiniteness of mapping class group actions on surface graphs.
problem Hyperfiniteness of mapping class group actions on surface graphs.
method Infinite unicorn paths and Gromov boundaries of arc and curve graphs.
result Proves hyperfiniteness of orbit equivalence relations induced by mapping class group actions.
Hyperfinite knots, or limits of equivalence classes of knots induced by a knot invariant taking values in a metric space, were introduced in a previous article by the author. In this article, we present new examples of hyperfinite knots stemming from sequences of torus knots.
The end compactification |Γ| of the locally finite graph Γis the union of the graph and its ends, endowed with a suitable topology. We show that π_1(|Γ|) embeds into a nonstandard free group with hyperfinitely many generators, i.e. an ultraproduct of finitely generated free groups, and that the embedding we construct f…
Constructs a representation of the string 2-group on a von Neumann algebra.
problem Establishing a categorified spinor representation of the string 2-group.
method Using the Morita bicategory of von Neumann algebras, specifically the hyperfinite type III_1 factor.
result Demonstrates a categorification of the spinor representation.
The paper shows deep connections between exotic smoothings of a small R^4 (the spacetime), the leaf space of codimension-1 foliations (related to noncommutative algebras) and quantization. At first we relate a small exotic R^4 to codimension-1 foliations of the 3-sphere unique up to foliated cobordisms and characterize…
We present a new formulation of some basic differential geometric notions on a smooth manifold M, in the setting of nonstandard analysis. In place of classical vector fields, for which one needs to construct the tangent bundle of M, we define a prevector field, which is an internal map from *M to itself, implementing t…
The paper shows deep connections between exotic smoothings of small R^4, noncommutative algebras of foliations and quantization. At first, based on the close relation of foliations and noncommutative C*-algebras we show that cyclic cohomology invariants characterize some small exotic R^4. Certain exotic smooth R^4's de…
A new invariant from smooth 4-manifolds using von Neumann algebras.
problem Constructing a von Neumann algebra from smooth 4-manifolds.
method Geometric construction of von Neumann algebra from smooth structure, preserving unitary equivalence under diffeomorphisms.
result A new invariant of smooth 4-manifolds, the cosmological constant, can be estimated topologically.
New cohomology functors refine classical invariants of homotopy types.
problem Classifying maps between specific spaces up to homotopy.
method Descriptive set theory applied to Čech cohomology.
result Definable cohomology functors are complete invariants of homotopy types.
Survey finds LLMs match human economic expectations closely.
problem Understanding human economic expectations and their deviations.
method Survey of LLM's expectations based on news articles.
result LLM's expectations closely match existing surveys and exhibit deviations.
This paper proves Expected Shortfall is concave, not convex.
problem Understanding the convexity/concavity of Expected Shortfall.
method Analytical proof of concavity with respect to probability distributions.
result Expected Shortfall is concave, not convex.
Defines g-expectation of distributions and its applications.
problem Defining g-expectation of distributions. method Two special cases of nonlinear g and law-invariant g-expectation. result Explicit derivation of g-expectation of distributions. Introduces a new conditional expectation under distorted probabilities, addressing time-inconsistency.
problem Time-inconsistency in nonlinear expectations under probability distortion.
method Localizes probability distortion and constructs a time-consistent conditional expectation.
result Constructs a conditional expectation that is time-consistent and corresponds to a parabolic differential equation.
Choquet and minimax expectations are equivalent in European option pricing.
problem Pricing European options in incomplete markets.
method Comparing Choquet and minimax expectations in the context of European options.
result Choquet and minimax expectations are equal for European options.
Active inference minimizes expected free energy for optimal behavior.
problem Understanding and optimizing behavior in complex systems.
method Combines Bayesian decision theory, optimal Bayesian design, and the free energy principle.
result Active inference emerges as a unified framework for information-seeking, utility maximization, and goal-directed behavior.
Extends sublinear expectations to random sets, identifying extremal and constructing methods.
problem Extending sublinear expectations to random sets.
method Identifying extremal expectations and presenting general construction methods.
result Identification of extremal sublinear and superlinear expectations.
Study on expectile and expected shortfall for tail risk assessment.
problem Comparing expectile and expected shortfall for tail risk assessment.
method Duality results and optimized certainty equivalent.
result Derived bounds and asymptotic behavior of expectile with respect to expected shortfall.
We provide a general construction of time-consistent sublinear expectations on the space of continuous paths. It yields the existence of the conditional G-expectation of a Borel-measurable (rather than quasi-continuous) random variable, a generalization of the random G-expectation, and an optional sampling theorem that…
Paper introduces EEMs for pricing contingent claim returns.
problem Computing expected future prices of contingent claims.
method Dynamic change of measure approach to construct EEMs.
result EEMs provide physical and pricing expectations of contingent claim prices.
New method for predicting portfolio dynamics using non-Euclidean geometry.
problem Predicting efficient portfolios with geometric structure.
method Non-Euclidean conditional expectation and filtering equations.
result Accurate numerical forecasts of portfolio dynamics.
Study on expected critical points of real Lefschetz pencils.
problem Counting critical points in real Lefschetz pencils.
method Asymptotic probabilistic real Riemann-Hurwitz formula.
result Asymptotic expected number and distribution of critical points.
Paper proposes using expectation models for planning in stochastic environments.
problem Intractability of learning distribution and sample models in large state and action spaces.
method Proposes using approximate expectation models for MBRL, analyzes linear and non-linear parametrizations, and presents a policy evaluation algorithm.
result Planning with an expectation model is equivalent to planning with a distribution model under certain conditions.
Dual representation and properties of expectile-based expected shortfall studied.
problem Studying the expectile-based expected shortfall as a risk measure.
method Provided dual representation in terms of Bochner integral, showed boundedness properties, and computed for selected distributions.
result Explicit dual representation and boundedness properties of expectile-based expected shortfall.
The paper proposes a new risk measure, Expected Downside Risk, to explain risk-preference.
problem Contradictory empirical findings between risk and reward.
method Introducing Expected Downside Risk (EDR) as a new risk measure.
result EDR better explains investors' utility perception and can model both positive and negative risk-reward relationships.
We refine Expected Shortfall by controlling different tail portions, offering tailored risk assessments.
problem Risk assessment in financial positions, especially in tail regions.
method Introducing adjusted Expected Shortfall measures that control different tail portions.
result Adjusted Expected Shortfall measures ensure risk does not exceed specified thresholds for various probability levels.
Derives backward differentiation for Bermudan product valuation.
problem Valuation of Bermudan products using conditional expectation.
method Three properties for backward differentiation of algorithms with conditional expectation.
result Clean and simple implementation of backward differentiation.
New unbiased gradient estimators for complex optimization problems.
problem Unbiased and variance-limited gradient estimation for conditional stochastic optimization.
method Developed multilevel Monte Carlo gradient estimators for conditional stochastic optimization problems.
result Unbiased and finite variance gradient estimators for conditional stochastic optimization problems.
New approach uses nonlinear expectations to estimate extreme risks.
problem Estimating tail quantities in heavy-tailed data.
method Data-robust expectation and regularization for Pareto distributions.
result Qualitative requirement for reliable estimation of extreme risks.
This paper optimizes speech recognition WER via sampling.
problem Improving word error rate (WER) in speech recognition.
method Optimizing expected WER by sampling paths from lattices used in sMBR training.
result Optimizing WER during acoustic model training gives a 5% relative improvement in WER.
Expected signatures map data streams to lower dimensions, improving ML performance.
problem Leveraging model-free embeddings for domain-agnostic machine learning.
method Expected signatures map data streams to lower dimensions, with convergence results bridging empirical and theoretical estimators.
result A modified expected signature estimator with lower mean squared error for martingale processes.
We offer a simplified proof for Expected Shortfall's dual representation.
problem The dual representation of Expected Shortfall.
method Basic properties of quantile functions.
result New proof of Expected Shortfall's subadditivity.
We study the dynamic indifference pricing with ambiguity preferences. For this, we introduce the dynamic expected utility with ambiguity via the nonlinear expectation--G-expectation, introduced by Peng (2007). We also study the risk aversion and certainty equivalent for the agents with ambiguity. We obtain the dynamic …
The paper revisits expected signatures in semimartingale models, providing new formulae and simplifying complexity.
problem Computing expected signatures in semimartingale models.
method Revisits and provides new formulae for computing expected signatures in a general semimartingale setting.
result Log-transform of expected signatures simplifies complexity, leading to signature cumulants.
This paper solves a coinsurance problem using fuzzy numbers and expected utility operators.
problem Formulating a coinsurance problem in the possibilistic setting of expected utility operators.
method Developed a framework using expected utility operators to model risk aversion and solve the coinsurance problem.
result Various formulas for the optimal T-coinsurance rate are derived for specific utility functions and fuzzy numbers. Research shows that information asymmetry affects how quickly companies adjust their capital structure and expected returns.
problem The relationship between capital structure adjustment speed and expected returns is influenced by information asymmetry.
method A hybrid data regression model was used to test the hypotheses based on data from 120 companies in the Tehran Stock Exchange.
result Information asymmetry positively affects the relationship between capital structure adjustment speed and expected returns.
Expected Shortfall (ES) in several variants has been proposed as remedy for the defi-ciencies of Value-at-Risk (VaR) which in general is not a coherent risk measure. In fact, most definitions of ES lead to the same results when applied to continuous loss distributions. Differences may appear when the underlying loss di…
This paper distills Bayesian posterior expectations for deep neural networks.
problem Improving deep neural network performance and uncertainty quantification.
method Develops a framework for distilling expectations from Bayesian posterior distributions using Monte Carlo samples.
result The framework successfully distills posterior predictive distribution and expected entropy.
Unified theory of θ-expectations derived from chaotic dynamics.
problem Non-convex stochastic control problems outside G-expectations.
method Spectral theory of transfer operators for uniformly hyperbolic flows, viscosity solutions to HJB equations.
result Affine Hessian, non-convex gradient structure of θ-expectation. Proposes data-driven methods for estimating conditional expectations.
problem Estimating conditional expectations when underlying density is unknown.
method Data-driven techniques to directly estimate conditional expectations from training data.
result Extends data-driven method to solve nonlinear equations in stochastic optimization.
News on inflation and monetary policy impacts US household inflation expectations.
problem Understanding how news affects inflation expectations.
method Monthly disaggregated US data from 1978 to 2016, controlling for various factors.
result News on rising inflation and easier monetary policy has a stronger impact on inflation expectations.
In this paper we will discuss the optimal risk transfer problems when risk measures are generated by G-expectations, and we present the relationship between inf-convolution of G-expectations and the inf-convolution of drivers G.
Paper tackles conditional expectation estimation using compactification operators.
problem Estimating conditional expectations from product of two random variables.
method Operator theoretic approach using kernel integral operators in reproducing kernel Hilbert space.
result Solutions allow numerical approximation and convergence of data-driven implementations.
Paper solves optimization problems with convex expectation constraints using a new algorithm.
problem Minimizing convex expectation functions with inequality convex expectation constraints.
method Stochastic Augmented Lagrangian-Type Algorithm (Stochastic Linearized Proximal Method of Multipliers).
result Algorithm achieves O(K−1/2) convergence rates for objective reduction and constraint violation.