Bayesian KANs achieve near-minimax posterior contraction rates in anisotropic Besov spaces.
problem Statistical foundation for Bayesian Kolmogorov-Arnold networks in anisotropic Besov spaces.
method Sparse Bayesian KANs with spike-and-slab priors, hyperprior on model size, and approximation complexity bounds.
result Posterior contraction rates depend on intrinsic anisotropic smoothness and effective dimension of the compositional structure.
In this paper we discuss the issue of computation of the bilateral credit valuation adjustment (CVA) under rating triggers, and in presence of ratings-linked margin agreements. Specifically, we consider collateralized OTC contracts, that are subject to rating triggers, between two parties -- an investor and a counterpa…
The paper shows how contracting elements in groups lead to large quotients with specific growth rates.
problem Understanding the growth rates of group actions with contracting elements.
method Using extension lemma, rotating families theory, and quasi-tree construction.
result There exist sequences of quotient groups with growth rates approaching the original group's growth rate.
Bayesian neural networks achieve optimal posterior contraction rates in Besov spaces with intrinsic dimensionality.
problem High-dimensional structured estimation problems with unknown smoothness levels.
method Sparse Bayesian neural networks with either sparse or continuous shrinkage priors.
result Optimal posterior contraction rates are achieved, adapting to the unknown smoothness level of the true function.
Study confined subgroups in groups with contracting elements, showing their growth rate is strictly greater than half of the ambient growth rate.
problem Understanding the growth rate of confined subgroups in groups with contracting elements.
method Through boundary actions, analyzing the Hopf decomposition and quotient growth.
result Confined subgroups have a growth rate strictly greater than half of the ambient growth rate.
The paper explores perpetual contracts in a financial market without arbitrage.
problem Modeling perpetual contracts in a continuous-time financial market.
method Derive model-free and semi-robust expressions for perpetual contracts' funding and discount rates.
result Explicit replication strategies for perpetual contracts are derived, relating them to traditional financial instruments.
Bayesian PINNs learn elliptic PDEs with near-minimax posterior contraction rate.
problem Learning elliptic PDEs with noisy data and non-homogeneous boundary conditions.
method Bayesian approach with a Hölder space prior on neural network weights.
result Posterior contracts at near-minimax rate without prior knowledge of solution smoothness.
In this article, exponential contraction in Wasserstein distance for heat semigroups of diffusion processes on Riemannian manifolds is established under curvature conditions where Ricci curvature is not necessarily required to be non-negative. Compared to the results of Wang (2016), we focus on explicit estimates for t…
Develops a contraction framework for MCMC mixing rates.
problem Proving mixing-time bounds for MCMC algorithms.
method Global and local contraction coefficients under Eγ-divergence. result Explicit global contraction coefficients for Gaussian smoothing.
New mortgage contracts reduce underwater default by adjusting loan balances, but must balance prepayment incentives.
problem Underwater default incentives in mortgages.
method Analyzes automatic balance adjustment and prepayment penalties in mortgage contracts.
result Automatic balance adjustments are preferable to traditional contracts at certain spreads, reducing underwater default.
We prove exponential growth rate of contractible closed geodesics for an arbitrary bumpy metric on manifolds of the form X#Y, where the fundamental group of X has a subgroup of finite index at least 3 and Y is simply connected and not a homotopy sphere.
This paper examines the relationship between Inverse Perpetual Swap contracts, a Bitcoin derivative akin to futures and the margin funding interest rates levied on BitMEX. This paper proves the Heteroskedastic nature of funding rates and goes onto establish a causal relationship between the funding rates and the Bitcoi…
New bounds for SA with arbitrary norm contractions and Markovian noise.
problem Finite-time analysis of two-time-scale stochastic approximation with arbitrary norm contractions and Markovian noise.
method Use of generalized Moreau envelope for arbitrary norm contractions and solutions of Poisson equation for Markovian noise.
result Mean square error decays at rates of O(1/n2/3) and O(1/n) under different conditions. Agent optimizes perpetual contract liquidation with transaction costs and risk.
problem Optimizing perpetual contract liquidation with transaction costs and risk.
method Solving stochastic control problem for optimal trading strategy.
result Closed-form expression and approximations for optimal strategy.
This study examines Gaussian processes on Riemannian manifolds and proves contraction rates.
problem Comparing intrinsic vs. extrinsic Gaussian processes on Riemannian manifolds.
method Proves optimal contraction rates for intrinsic Matérn Gaussian processes on compact Riemannian manifolds.
result Intrinsic Gaussian processes on Riemannian manifolds achieve better performance than extrinsic ones.
Investigates optimal withdrawal strategies in VA contracts with tax and ratchet mechanisms.
problem Optimizing withdrawal strategies and behavior of policyholders in VA contracts with tax and ratchet mechanisms.
method Solving a backward dynamic programming problem to optimize cash flows from VA contracts, considering hybrid products and taxation effects.
result Tax-shielding effect of the cash fund enhances contract attractiveness, ratchet mechanism discourages early surrender, and cash fund discourages active withdrawals.
The paper develops a valuation framework for GLWB-LTC contracts with Levy dynamics and stochastic interest rates.
problem Valuation of GLWB-LTC contracts with financial guarantees, longevity protection, and health-contingent LTC payments.
method Coupling a recombining Hull-White trinomial tree with an IMEX finite difference scheme, incorporating a seven-state health model.
result Hybrid tree-IMEX method delivers stable long-maturity prices consistent with simulation benchmarks.
The paper tackles robust control for insurance contracts under uncertain transition rates.
problem Maximizing utility in insurance contracts with uncertain transition rates.
method Novel robust utility maximization problem under bounded cumulative transition rate uncertainty, using worst-case scenario analysis.
result Existence and uniqueness of worst-case and best-case reserves for insurance contracts.
Bayesian posterior contraction rates improve with decreasing tails
problem Bayesian posterior contraction in nonparametric settings
method Using p-exponential tails for contraction rates result Improvement in contraction rates with decreasing tails
Abstract framework for cross-currency interest rate contracts.
problem Handling cross-currency markets with collateral and incompleteness.
method Developed a general HJM framework for abstract market indices.
result Enabled simultaneous description of multiple currency interest rate products.
Study loan contracts in DLPs using derivatives pricing and neural networks.
problem Optimizing and hedging risks in decentralized lending contracts.
method Derivatives pricing theory, deep neural networks, and statistical arbitrage.
result Developed a method to hedge risks in lending contracts and exploit arbitrage opportunities.
Optimizes capital structure for life insurance companies with surplus participation.
problem Determining the optimal participation rate in life insurance contracts.
method Adapted Leland's dynamic capital structure model to life insurance context.
result Optimal participation rate is highly sensitive to contract duration and tax rate.
Bayesian method with Gaussian process priors achieves optimal convergence rates for regression function and its derivatives.
problem Estimating the regression function and its derivatives in nonparametric regression.
method Bayesian approach with Gaussian process priors, focusing on convergence rates and plug-in property.
result Equivalence of convergence rates of posterior distributions and Bayes estimators for regression function and its derivatives.
We prove that the Ricci flow that contracts a hyperbolic cusp has curvature decay like one over time squared. In order to do this, we prove a new Li-Yau type differential Harnack inequality for Ricci flow on surfaces.
The paper explores local-correlation models for pricing complex financial contracts.
problem Calibrating synthetic quanto forward contracts and composite options.
method Design on-line calibration procedures for local and stochastic volatility models.
result Calibration performance of local-correlation models compared to simpler approximations.
Study examines risk premium convergence rates in risk sharing contracts.
problem Analyzing risk premium convergence rates in risk sharing contracts.
method Examines the limiting behavior of risk premium associated with Pareto optimal risk sharing contracts under general law-invariant risk measures.
result Risk premium convergence rate is typically n1/2, not n. The analysis of classical consensus algorithms relies on contraction properties of adjoints of Markov operators, with respect to Hilbert's projective metric or to a related family of seminorms (Hopf's oscillation or Hilbert's seminorm). We generalize these properties to abstract consensus operators over normal cones, w…
Gibbs sampler contracts entropy under strong log-concavity, improving mixing time.
problem Improving the mixing time of Gibbs sampler under strong log-concavity.
method Analyzing Gibbs sampler contraction under strong log-concavity, providing sharp contraction rate.
result Gibbs sampler contracts entropy linearly with condition number and independent of dimension under strong log-concavity.
The paper analyzes distributed Bayesian inference and its Frequentist guarantees.
problem Analyzing large decentralized datasets with distributed Bayesian inference.
method Establishes Frequentist properties for distributed (non-)Bayesian inference.
result Distributed Bayesian inference retains parametric efficiency and enhances robustness.
Bayesian nonparametric models get better posterior estimates via SPDE methods.
problem Estimating posterior distributions in nonparametric Bayesian models.
method Extending diffusion methods to SPDEs on Hilbert spaces for posterior contraction and Laplace approximation.
result Derivation of posterior contraction rates and finite-sample Bernstein von Mises results.
The paper analyzes contraction rates for GP regression approximations.
problem Computational infeasibility of exact GP posterior in large-scale applications.
method Lanczos and conjugate gradient approximations of the posterior mean.
result Minimax contraction rates for these approximations in large-scale applications.
Study on reinsurance decisions using mean-variance criterion with irreversible contracts.
problem Optimizing reinsurance premiums and contracts in a Stackelberg game with irreversible contracts.
method Unified singular control framework applied to both discrete and continuous time reinsurance contracts.
result A single once-for-all reinsurance contract is preferred over multiple contracts, and the signing time is crucial.
A variable annuity contract with Guaranteed Minimum Withdrawal Benefit (GMWB) promises to return the entire initial investment through cash withdrawals during the contract plus the remaining account balance at maturity, regardless of the portfolio performance. Under the optimal(dynamic) withdrawal strategy of a policyh…
In recent years, a market for mortality derivatives began developing as a way to handle systematic mortality risk, which is inherent in life insurance and annuity contracts. Systematic mortality risk is due to the uncertain development of future mortality intensities, or {\it hazard rates}. In this paper, we develop a …
Study of participating policies with guaranteed minimum interest rate and surrender option.
problem Analyzing the value and optimal surrender strategy of participating policies with minimum interest rate guarantee and surrender option.
method Probabilistic analysis using optimal stopping and free boundary theory.
result Identification of an optimal surrender strategy involving stop-loss and too-good-to-persist boundaries.
The paper proves scalar curvature decay for uniformly contractible manifolds with finite asymptotic dimension.
problem Proving decay of scalar curvature for uniformly contractible manifolds with finite asymptotic dimension.
method Using index pairing between Dirac operators and compactly supported vector bundles with Lipschitz control, and Lipschitz control for topological K-theory of finite dimensional simplicial complexes.
result The scalar curvature decays to zero at a rate depending only on the contractibility radius and the diameter control of the asymptotic dimension.
In this paper we investigate the local risk-minimization approach for a combined financial-insurance model where there are restrictions on the information available to the insurance company. In particular we assume that, at any time, the insurance company may observe the number of deaths from a specific portfolio of in…
The paper addresses pricing interest rate derivatives in markets with volatility uncertainty.
problem Pricing interest rate derivatives under uncertainty about volatility.
method Modeling volatility uncertainty with G-Brownian motion and defining forward sublinear expectation.
result Developed robust pricing formulas for interest rate derivatives.
This work studies the contraction coefficients of Schrödinger bridge problems in linear systems.
problem Optimally controlling the evolution of a system's state density over time.
method Analyzes and improves the convergence rates of dynamic Schrödinger systems via geometric and control-theoretic interpretations.
result New insights into improving computation of worst-case contraction coefficients by preconditioning.
Based on a new coupling approach, we prove that the transition step of the Hamiltonian Monte Carlo algorithm is contractive w.r.t. a carefully designed Kantorovich (L1 Wasserstein) distance. The lower bound for the contraction rate is explicit. Global convexity of the potential is not required, and thus multimodal targ…
Bayesian framework for sphere regression using Gaussian fields.
problem Nonparametric regression on the sphere with Gaussian priors.
method Isotropic Gaussian field priors, harmonic structure, exact posterior distributions, optimal spectral truncation, posterior contraction rates.
result Sharp posterior contraction rates for Gaussian priors with polynomially decaying angular power spectra.
This paper optimizes perpetual contract liquidity by accounting for funding rates.
problem Optimal liquidity provision for perpetual contracts with stochastic funding rates.
method Formulated a control problem, solved with a HJB scheme, and calibrated on real data.
result Funding-aware market making improves performance and reduces inventory risk.
Voluntary insurance contracts constitute a puzzle because they increase the expectation value of one party's wealth, whereas both parties must sign for such contracts to exist. Classically, the puzzle is resolved by introducing non-linear utility functions, which encode asymmetric risk preferences; or by assuming the p…
In this paper we study iterative procedures for stationary equilibria in games with large number of players. Most of learning algorithms for games with continuous action spaces are limited to strict contraction best reply maps in which the Banach-Picard iteration converges with geometrical convergence rate. When the be…
New stability theory for Sinkhorn semigroups with explicit decay rates.
problem Stability and convergence of Sinkhorn iterations for various divergences.
method Operator-theoretic framework based on Lyapunov techniques.
result Explicit exponential decay rates for Sinkhorn iterates.
The paper analyzes convergence rates for stochastic approximation and reinforcement learning.
problem Establishing almost sure convergence rates for stochastic approximation and reinforcement learning under Markovian noise.
method A novel Lyapunov drift construction that applies a Poisson-equation based correction for Markovian noise to the Moreau-envelope smoothing for contractive mappings.
result Almost sure convergence rates for specific learning rates are derived, with rates arbitrarily close to o(n1−2η) and o(n−1). Paper analyzes Hit-and-Run's convergence rates and applies similar methods to randomized Kaczmarz.
problem Quantifying advantages of Hit-and-Run's coordinate-free property.
method Sharp estimates via coupling methods and mixing time bounds.
result Ballistic and superdiffusive convergence rates in certain settings.
We prove the local convergence to minima and estimates on the rate of convergence for the stochastic gradient descent method in the case of not necessarily globally convex nor contracting objective functions. In particular, the results are applicable to simple objective functions arising in machine learning.