On-device research index

arXiv research

A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.

169,291 papers · 148 categories

Trend · papers per month

count % of corpus

48 results for “Stochastic Rates”

Extensions of Dupire Formula: Stochastic Interest Rates and Stochastic Local Volatilityq-fin.MF

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.

Dupire formula stochastic interest rates stochastic local volatility implied variance fixed-point iteration

2020-05-12abs ↗pdf ↗

Calibrating Local Volatility Models with Stochastic Drift and Diffusionq-fin.MF

Proposes new Monte Carlo methods for calibrating local volatility models with stochastic components.

problem Calibrating local volatility models with stochastic drift and diffusion.

method Developed Monte Carlo algorithms for three models: local volatility with stochastic interest rates, stochastic local volatility with deterministic interest rates, and stochastic local volatility with stochastic interest rates.

result Conditions for the existence of local volatility given European option prices, stochastic interest rate model parameters, and correlations.

Monte Carlo methods Local volatility models Stochastic drift Stochastic diffusion Calibration algorithms

2020-09-30abs ↗pdf ↗

Improved Learning Rates for Stochastic Optimizationcs.LG

Paper improves learning rates for SGD and NAG.

problem Generalization performance of stochastic optimization algorithms.

method Establishes new learning rates for SGD and NAG.

result Improved guarantees in some settings or comparable rates under weaker assumptions.

stochastic optimization learning rates SGD NAG

2021-07-19abs ↗pdf ↗

An extension of Heston's SV model to Stochastic Interest Ratesq-fin.CP

This paper extends Heston's SV model to include stochastic interest rates.

problem Modeling options with stochastic interest rates.

method Developed a new SV model with stochastic interest rates and derived a semi-explicit formula.

result Derived a semi-explicit formula for option pricing with stochastic interest rates.

Stochastic Volatility Stochastic Interest Rates Option Pricing Heston Model Bond Options

2018-09-24abs ↗pdf ↗

Unbiased estimators for the Heston model with stochastic interest ratesq-fin.CP

Developed unbiased estimators for Heston model with stochastic interest rates.

problem Estimating the Heston model with stochastic interest rates.

method Combined unbiased estimators with the Heston model and developed a semi-exact log-Euler scheme.

result Convergence rate of

O(h)

in the

L^2

norm for a wide range of models.

Heston model stochastic interest rates unbiased estimators log-Euler scheme convergence rate

2023-01-28abs ↗pdf ↗

Understanding Stochastic Natural Gradient Variational Inferencecs.LG

Improves understanding of stochastic NGVI convergence rates.

problem Lack of knowledge about non-asymptotic convergence rates in stochastic NGVI.

method Proved non-asymptotic convergence rates for conjugate likelihoods and showed implicit optimization for non-conjugate likelihoods.

result First

\mathcal{O}(\frac{1}{T})

non-asymptotic convergence rate for stochastic NGVI in conjugate likelihoods.

stochastic natural gradient variational inference convergence rate non-asymptotic stochastic gradient descent

2024-06-04abs ↗pdf ↗

Stochastic Modified Flows, Mean-Field Limits and Dynamics of Stochastic Gradient Descentmath.PR

New dynamics for SGD in small learning rate regime.

problem Improving stochastic gradient descent in small learning rate regime.

method Introducing stochastic modified flows and distribution dependent stochastic modified flows.

result Captures fluctuating dynamics of SGD in small learning rate - infinite width scaling regime.

stochastic gradient descent small learning rate fluctuating dynamics cylindrical Brownian motion

2023-02-14abs ↗pdf ↗

Statistical Adaptive Stochastic Gradient Methodsstat.ML

SALSA automatically adjusts learning rates in stochastic gradient methods.

problem Automatic adjustment of learning rates in stochastic gradient methods.

method SALSA uses a line-search procedure to gradually increase the learning rate, then a statistical test to decrease it.

result SALSA matches the performance of best hand-tuned learning rate schedules in deep learning tasks.

learning rate stochastic gradient line search stationarity test deep learning

2020-02-25abs ↗pdf ↗

Almost Sure Convergence Rates and Concentration of Stochastic Approximation and Reinforcement Learning with Markovian Noisecs.LG

Paper establishes convergence rates and concentration bounds for stochastic approximation and reinforcement learning with Markovian noise.

problem Analyzing convergence rates and concentration bounds for stochastic approximation and reinforcement learning with Markovian noise.

method Novel discretization of the mean ODE of stochastic approximation algorithms using intervals with diminishing length.

result First almost sure convergence rate and maximal concentration bound with exponential tails for contractive stochastic approximation algorithms with Markovian noise.

stochastic approximation reinforcement learning Markovian noise convergence rates concentration bounds

2024-11-20abs ↗pdf ↗

An analytic multi-currency model with stochastic volatility and stochastic interest ratesq-fin.PR

We introduce a tractable multi-currency model with stochastic volatility and correlated stochastic interest rates that takes into account the smile in the FX market and the evolution of yield curves. The pricing of vanilla options on FX rates can be performed effciently through the FFT methodology thanks to the affinit…

2013-02-28abs ↗pdf ↗

Calibration of a Hybrid Local-Stochastic Volatility Stochastic Rates Model with a Control Variate Particle Methodq-fin.MF

Calibrates hybrid LSV models with stochastic rates using particle method and control variates.

problem Calibrating complex foreign exchange models with stochastic volatility and stochastic rates.

method Combines particle method with variance reduction techniques and control variates.

result Accelerates convergence in calibration process for a wide class of hybrid LSV models.

Calibration Hybrid LSV models Stochastic Volatility Stochastic Rates Particle Method

2017-01-21abs ↗pdf ↗

Almost sure convergence rates for Stochastic Gradient Descent and Stochastic Heavy Ballcs.LG

The paper analyzes convergence rates for SGD and SHB methods.

problem Analyzing convergence rates for stochastic gradient descent and heavy ball methods.

method Stochastic gradient descent and stochastic heavy ball method for general stochastic approximation problems.

result The last iterate of SHB converges almost surely to a minimizer and has faster convergence rates than SGD.

stochastic gradient descent stochastic heavy ball convergence rates asymptotic convergence nonconvex optimization

2020-06-14abs ↗pdf ↗

Variance and interest rate risk in unit-linked insurance policiesq-fin.PR

The paper analyzes insurance risks using stochastic models.

problem Interest rate and variance risks in unit-linked insurance policies.

method General stochastic volatility models and stochastic interest rates are used to price unit-linked life insurance contracts.

result A perfect hedging strategy is provided and compared with the Black-Scholes model.

insurance stochastic volatility interest rates unit-linked hedging

2020-06-26abs ↗pdf ↗

Quantitative Weak Convergence for Discrete Stochastic Processesmath.ST

Paper shows convergence rates for stochastic processes.

problem Analyzing convergence rates for stochastic processes.

method Quantitative convergence in

W_2

for Langevin-like processes.

result Iterates converge to an invariant distribution at rate

O(1/\sqrt{k})

stochastic processes quantitative convergence Langevin-like processes invariant distribution convergence rate

2019-02-03abs ↗pdf ↗

Learning Rate Annealing Improves Tuning Robustness in Stochastic Optimizationcs.LG

Learning rate annealing improves robustness in stochastic optimization.

problem Tuning learning rates in large-scale models is costly and prone to errors.

method We analyze and demonstrate the benefits of learning rate annealing schemes.

result Stochastic gradient descent with annealed schedules converges more robustly to the optimal solution.

learning rate stochastic optimization annealing robustness hyperparameter tuning

2025-03-12abs ↗pdf ↗

Conditional Accelerated Lazy Stochastic Gradient Descentcs.LG

Improved SGD algorithm with faster convergence.

problem Optimization of machine learning models.

method Conditional accelerated lazy stochastic gradient descent.

result Convergence rate of $O\left(\frac{1}{\varepsilon^2} ight)$, faster than previous methods.

Stochastic Gradient Descent Optimization Convergence Rate Lazy Algorithm Conditional Acceleration

2017-03-16abs ↗pdf ↗

Joint Calibration of Local Volatility Models with Stochastic Interest Rates using Semimartingale Optimal Transportq-fin.MF

Method calibrates local volatility and stochastic short rate models for equity-rate dynamics.

problem Joint calibration of local volatility and stochastic short rate models.

method Iterative approach using semimartingale optimal transport.

result Demonstrated performance on market data using European SPX options and cap interest rate options.

local volatility stochastic short rate semimartingale optimal transport equity-rate dynamics European options

2023-08-28abs ↗pdf ↗

Optimal Dividends in the Dual Risk Model under a Stochastic Interest Rateq-fin.MF

Study optimal dividends in dual risk model with stochastic interest rate.

problem Optimal dividend strategy in dual risk model with stochastic interest rate.

method Geometric Brownian motion or exponential Lévy process for discounting factor.

result Closed form solutions can be obtained for optimal dividends.

dividends dual risk model stochastic interest rate optimal strategy geometric Brownian motion

2017-05-23abs ↗pdf ↗

Term structure modelling with overnight rates beyond stochastic continuityq-fin.MF

This work models overnight rates with jumps and discontinuities, extending classical short-rate models.

problem Capturing the jump behavior and discontinuities in overnight rates for accurate modeling.

method Developed a term structure modeling framework based on overnight rates, accommodating stochastic discontinuities.

result Simple specifications can capture the jump behavior of overnight rates, and explicit valuation formulas are provided.

overnight rates stochastic discontinuities term structure modeling Heath-Jarrow-Morton affine semimartingales

2022-02-02abs ↗pdf ↗

Acceleration and Averaging in Stochastic Mirror Descent Dynamicsmath.OC

Study of accelerated dynamics for convex function minimization with noisy gradients.

problem Minimizing smooth convex functions with noisy gradients.

method Formulate and study continuous-time stochastic dynamics, prove convergence rates.

result Derive estimates of convergence rates for function values, both persistent and asymptotic.

stochastic dynamics accelerated mirror descent convex optimization stochastic differential equation convergence rates

2017-07-19abs ↗pdf ↗

Positivity of mild solution to stochastic evolution equations with an application to forward ratesmath.AP

Maximum principle proves positivity of forward rates in stochastic models.

problem Proving positivity of forward rates in stochastic models.

method Maximum principle for mild solutions to SPDEs with Lipschitz coefficients and Wiener noise.

result Sufficient conditions for positivity of forward rates in the Heath-Jarrow-Morton model.

maximum principle stochastic evolution equations forward rates Heath-Jarrow-Morton model Musíla SPDE

2019-12-28abs ↗pdf ↗

Variance swaps under Lévy process with stochastic volatility and stochastic interest rate in incomplete marketsq-fin.PR

The paper prices variance swaps in incomplete markets with stochastic interest rate and volatility.

problem Pricing variance swaps in markets with stochastic interest rates and volatility.

method Equilibrium framework and joint moment generating function.

result Closed-form solution for fair delivery price of variance swaps.

Variance Swaps Incomplete Markets Stochastic Interest Rate Stochastic Volatility Cox-Ingersoll-Ross Model

2017-12-29abs ↗pdf ↗

Parameter-Free Locally Differentially Private Stochastic Subgradient Descentcs.LG

New algorithm reduces privacy loss in SGD without learning rate tuning.

problem Locally differentially private stochastic optimization with high privacy loss.

method BANCO (Betting Algorithm for Noisy COins) for

ε

-LDP SGD.

result Matches convergence rate of tuned SGD without learning rate tuning.

locally differential privacy stochastic optimization private SGD convergence rate privacy loss

2019-11-21abs ↗pdf ↗

Optimal Asymptotic Rates for (Stochastic) Gradient Descent under the Local PL-Condition: A Geometric Approachmath.OC

SGD and stochastic gradient descent converge at optimal rates for certain non-convex functions.

problem Optimal convergence rates for non-convex functions under gradient noise.

method Geometric interpretation of the PL-condition to analyze convergence rates.

result Convergence rates of SGD and stochastic gradient descent match those of strongly convex quadratics.

SGD stochastic gradient descent convergence rates non-convex functions PL-condition

2026-05-14abs ↗pdf ↗

Stochastic gradient descent with random learning ratecs.LG

Random learning rate improves neural network training without extra cost.

problem Optimizing neural networks with stochastic gradient descent.

method Uniformly-distributed random learning rate in SGD.

result Random learning rate yields better regularization without extra computational cost.

neural networks stochastic gradient descent random learning rate Fokker-Planck temperature

2020-03-15abs ↗pdf ↗

Using Statistics to Automate Stochastic Optimizationstat.ML

Automates learning rate tuning in machine learning.

problem Difficulty in tuning the learning rate of stochastic gradient methods.

method Automates the learning rate tuning by using a statistical test to determine when to decrease the learning rate.

result Statistical adaptive stochastic approximation (SASA) method can automatically find good learning rate schedules and match hand-tuned methods.

learning rate stochastic optimization machine learning statistical testing adaptive methods

2019-09-21abs ↗pdf ↗

Pricing variance swaps with stochastic volatility and stochastic interest rate under full correlation structureq-fin.PR

This paper develops a semi-closed form formula for pricing variance swaps with stochastic volatility and interest rate correlation.

problem Pricing variance swaps with stochastic volatility and interest rate correlation under full correlation structure.

method Developed an efficient semi-closed form pricing formula for variance swaps using characteristic functions.

result The correlation between the underlying and interest rate significantly impacts the pricing of variance swaps.

Variance Swaps Stochastic Volatility Stochastic Interest Rate Full Correlation Characteristic Functions

2016-10-30abs ↗pdf ↗

On Learning Rates and Schrödinger Operatorscs.LG

The paper analyzes how learning rate affects SGD and provides insights into optimal rates.

problem Understanding the impact of learning rate on stochastic gradient descent.

method Developed a learning-rate-dependent stochastic differential equation (lr-dependent SDE) to analyze SGD.

result Established a linear rate of convergence for SGD and found the optimal linear rate by analyzing the spectrum of the Witten-Laplacian.

learning rate stochastic gradient descent Schrödinger operator nonconvex optimization convex optimization

2020-04-15abs ↗pdf ↗

A novel approach to rating transition modelling via Machine Learning and SDEs on Lie groupsq-fin.RM

A novel approach models rating transitions using Lie groups and Deep Learning.

problem Modeling rating transitions with geometric properties and stochastic processes.

method Introducing Itô-SDEs on Lie groups, using TimeGAN for calibration, and examining rating matrix properties.

result The geometric approach using Lie groups and Deep Learning generates a good fit for rating transitions.

Machine Learning Deep Learning SDEs Lie groups Rating transitions

2022-05-31abs ↗pdf ↗

Stochastic Recursive Gradient Algorithm for Nonconvex Optimizationstat.ML

Paper analyzes SARAH for nonconvex optimization with mini-batches.

problem Solving nonconvex optimization problems with mini-batches.

method Stochastic Recursive Gradient Algorithm (SARAH) for nonconvex losses.

result Sublinear and linear convergence rates for different types of nonconvex functions.

SARAH Stochastic Recursive Gradient Nonconvex Optimization Mini-batches Convergence Rates

2017-05-20abs ↗pdf ↗

How To Make the Gradients Small Stochastically: Even Faster Convex and Nonconvex SGDcs.LG

New algorithms improve SGD's efficiency in convex and nonconvex optimization.

problem Optimizing gradient size in stochastic optimization.

method Designing SGD3 for convex objectives and SGD5 for nonconvex objectives.

result Near-optimal rates for gradient size reduction in both convex and nonconvex settings.

stochastic gradient descent convex optimization nonconvex optimization gradient norm optimization rates

2018-01-08abs ↗pdf ↗

Optimal Surplus Management for Insurers under Stochastic Interest Rates and Jump-Driven Liabilitiesq-fin.RM

Optimal insurance surplus management under stochastic interest rates and jumps.

problem Managing insurance surplus with stochastic interest rates and jump-driven liabilities.

method Stochastic control techniques and normalized surplus projection method.

result Optimal investment policy with myopic and hedging components.

insurance surplus management stochastic interest rates jump processes HJB equation

2026-07-23abs ↗pdf ↗

Modeling credit default swap premiums with stochastic recovery rateq-fin.PR

This study models credit default swap premiums with a stochastic recovery rate.

problem Analyzing credit default swap premiums with varying recovery rates.

method Develops a model using stochastic recovery rates.

result Models credit default swap premiums effectively with a stochastic recovery rate.

credit default swaps stochastic recovery modeling derivatives

2017-06-18abs ↗pdf ↗

Optimal portfolios with anticipating information on the stochastic interest rateq-fin.PR

Optimizes portfolios using anticipated interest rate information.

problem Maximizing utility in financial models with future interest rate trends.

method Enlargement of filtrations, affine diffusion process, Markov chain modeling.

result Explicit formulas for expected logarithmic utility.

portfolio optimization stochastic interest rate anticipating information filtration enlargement affine diffusion

2017-11-09abs ↗pdf ↗

Enhancing Valuation of Variable Annuities in Lévy Models with Stochastic Interest Rateq-fin.PR

Enhances valuation of variable annuities with stochastic interest rate models.

problem Valuation and optimal surrender strategies for variable annuities in Lévy models.

method Hybrid numerical method combining tree methods for interest rate modeling and finite difference techniques for asset price.

result Influence of stochastic interest rates on surrender decisions and contract design.

variable annuities Lévy models stochastic interest rate Hull-White model optimal surrender

2024-04-11abs ↗pdf ↗

Defining and estimating stochastic rate change in a dynamic general insurance portfolioq-fin.PM

New method estimates stochastic rate change in insurance portfolios.

problem Determining the stochastic nature of premium changes in dynamic insurance portfolios.

method Definition of rate change as a statistical parameter, various models and techniques for estimation, matched sampling to adjust for policy characteristics.

result Quantification of uncertainty in stochastic rate change estimates, application to motor premium database.

stochastic rate change insurance portfolio matched sampling genetic algorithm uncertainty quantification

2018-10-04abs ↗pdf ↗

Optimal Rates for Learning with Nyström Stochastic Gradient Methodsstat.ML

Optimal rates found for learning with Nyström stochastic gradient methods.

problem Nonparametric regression learning with improved computational efficiency.

method Combination of stochastic gradient methods with Nyström subsampling, allowing multiple passes and mini-batches.

result Derivation of optimal learning rates considering various parameters.

Nyström subsampling stochastic gradient methods nonparametric regression optimal rates mini-batches

2017-10-21abs ↗pdf ↗

Stochastic Volatility, Jumps, and Rates: A Unified Framework for Option Pricing and Term-Structure Simulationq-fin.PM

Unified model for equity option pricing and interest-rate risk assessment.

problem Pricing short and medium-term equity options and interest-rate risk.

method Developed a stochastic modeling framework using Heston, Bates, and CIR models, calibrated using Fourier inversion and FFT.

result Calibration stability and convergence of parameter sets across models.

stochastic volatility equity options interest-rate risk Fourier inversion CIR model

2026-05-27abs ↗pdf ↗

Measuring Financial Resilience Using Backward Stochastic Differential Equationsq-fin.MF

Measures financial resilience using BSDEs and their properties.

problem Measuring financial resilience in dynamic risk environments.

method Developed stochastic calculus for BSDEs with jumps, revealing resilience rate as expectation of generator.

result Resilience rate can be represented as expectation of BSDE generator, revealing properties of dynamic risk measures.

financial resilience resilience rate backward stochastic differential equations dynamic risk measure stochastic calculus

2025-05-12abs ↗pdf ↗

Expansion method for pricing foreign exchange options under stochastic volatility and interest ratesq-fin.CP

Expands method for pricing foreign exchange options under stochastic volatility and interest rates.

problem Approximating pricing of foreign exchange options with no exact formula.

method Directly expands the expectation value of payoff function with respect to the volatility of volatility, then uses it to price options in the stochastic volatility model.

result Shows numerically comparable results to Grzelak et al. (2012) using characteristic function approximation.

foreign exchange options stochastic volatility stochastic interest rates expansion method smart expansion

2019-08-26abs ↗pdf ↗

Pricing variance swaps in a hybrid model of stochastic volatility and interest rate with regime-switchingq-fin.MF

In this paper, we consider the problem of pricing discretely-sampled variance swaps based on a hybrid model of stochastic volatility and stochastic interest rate with regime-switching. Our modelling framework extends the Heston stochastic volatility model by including the CIR stochastic interest rate and model paramete…

2016-03-28abs ↗pdf ↗

Stochasticity of Deterministic Gradient Descent: Large Learning Rate for Multiscale Objective Functioncs.LG

Deterministic GD can behave stochastically in large learning rates for multiscale functions.

problem Understanding deterministic GD's stochastic behavior in large learning rates for multiscale objectives.

method Established a sufficient condition for deterministic GD to converge to a rescaled Gibbs distribution in large learning rates for multiscale functions.

result Deterministic GD can converge to a statistical distribution in large learning rates for multiscale functions.

Gradient Descent Stochasticity Multiscale Function Large Learning Rate Rescaled Gibbs Distribution

2020-02-14abs ↗pdf ↗

Two Approaches for a Dividend Maximization Problem under an Ornstein-Uhlenbeck Interest Ratemath.OC

Study optimizes dividend payout strategies under fluctuating interest rates.

problem Maximizing dividends under stochastic interest rates with negative values.

method Analytical HJB approach and backward SDEs for analysis.

result Explicit optimal strategies found for both time-dependent and strategy-independent stopping times.

dividend maximization stochastic interest rates Ornstein-Uhlenbeck negative rates optimal control

2021-07-31abs ↗pdf ↗

The Dynamics of the Forward Interest Rate Curve with Stochastic String Shockscond-mat.stat-mech

This paper offers a new class of models of the term structure of interest rates. We allow each instantaneous forward rate to be driven by a different stochastic shock, constrained in such a way as to keep the forward rate curve continuous. We term the process followed by the shocks to the forward curve ``stochastic str…

1998-01-30abs ↗pdf ↗

Numerical and analytical methods for bond pricing in short rate convergence models of interest ratesq-fin.MF

In this survey paper we discuss recent advances on short interest rate models which can be formulated in terms of a stochastic differential equation for the instantaneous interest rate (also called short rate) or a system of such equations in case the short rate is assumed to depend also on other stochastic factors. Ou…

2016-07-18abs ↗pdf ↗

Almost Sure Convergence Rates of Stochastic Approximation and Reinforcement Learning via a Poisson-Moreau Driftcs.LG

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(n^{1 - 2η})

and

o(n^{-1})

stochastic approximation reinforcement learning Markovian noise Lyapunov drift Poisson equation

2026-05-08abs ↗pdf ↗

New nonasymptotic convergence rates of stochastic proximal pointalgorithm for convex optimization problemsmath.OC

New algorithm improves convergence rates for convex optimization problems.

problem Convex optimization problems with noisy stochastic data.

method Stochastic proximal point algorithm with weak linear regularity condition.

result Achieves $\mathcal{O}\left(\frac{1}{k} ight)$ convergence rate for SPP.

stochastic optimization proximal point convex optimization weak linear regularity convergence rate

2019-01-22abs ↗pdf ↗

Weak error approximation for rough and Gaussian mean-reverting stochastic volatility modelsmath.PR

Study approximates weak error for specific stochastic models with rough and Gaussian mean-reverting volatility.

problem Approximating weak error for specific stochastic models with rough and Gaussian mean-reverting volatility.

method Used Euler type scheme with integrated kernels to study weak convergence rate.

result Obtained weak convergence rate of

\min(3α-1,1)

for discretised rough Ornstein-Uhlenbeck process and stochastic rough volatility model.

weak approximation stochastic volatility rough volatility Euler scheme fractional convolution

2026-02-20abs ↗pdf ↗