Model approximates market prices and returns without prior market dynamics.
problem Simultaneously approximate market prices and log returns.
method GDN model of Kratsios and Papon (2022) for generalized Ornstein-Uhlenbeck process.
result Universal approximation guarantees for conditional distributions and contingent claims.
Modeling horse race betting odds with Ornstein-Uhlenbeck process.
problem Analyzing how herding and informed bettors affect odds movements.
method Deriving an Ornstein-Uhlenbeck process from vote shares and odds movements data.
result Identified microscopic and macroscopic patterns in odds convergence.
The paper addresses optimal execution for multi-asset portfolios using Ornstein-Uhlenbeck dynamics.
problem Optimal execution for multi-asset portfolios with Ornstein-Uhlenbeck dynamics.
method Stochastic optimal control and simplification of Hamilton-Jacobi-Bellman equation to ODEs.
result Existence and uniqueness of solution to the execution problem using extit{a priori} estimates.
Study optimal futures trading strategies for assets with multiscale central tendency price model.
problem Optimal dynamic trading of futures with multiscale central tendency price model.
method Derive no-arbitrage futures prices, solve HJB equations for optimal strategies.
result Optimal trading strategies depend on asset parameters and futures risk premia.
The paper models financial markets using information theory to minimize information.
problem Understanding the dynamics of financial markets.
method Modeling financial market dynamics with independent stationary scalar diffusions, interpreting the market as a communication system, and minimizing information-theoretical joint information.
result Financial market dynamics are represented by squared radial Ornstein-Uhlenbeck processes with additivity and self-similarity properties.
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.
We propose a strategy for automated trading, outline theoretical justification of the profitability of this strategy and overview the hypothetical results in application to currency pairs trading. The proposed methodology relies on the assumption that processes reflecting the dynamics of currency exchange rates are in …
The paper prices energy spread options using a complex stochastic model.
problem Pricing energy spread options with specific stochastic dynamics.
method Uses an exponential Ornstein-Uhlenbeck process driven by variance gamma processes, applying the Esscher transform and FFT method.
result Derives an analytical formula for pricing forwards and spread options.
The paper models exchange rate risk premium using mean-reverting dynamics.
problem Empirical failure of uncovered interest parity (UIP).
method Modeling risk premium using Ornstein-Uhlenbeck (OU) process embedded in stochastic differential equation for exchange rate.
result The model shows strong predictive performance at short and long horizons, but underperforms at intermediate horizons.
The paper analyzes SGD in high-dimensional networks, revealing new scaling limits.
problem Understanding SGD dynamics in high-dimensional networks.
method Analyzing the effective dynamics of SGD using recent work on the subject.
result A new correction term emerges at the critical scaling regime, changing the phase diagram.
We consider a spread financial market defined by the multidimensional Ornstein--Uhlenbeck (OU) process. We study the optimal consumption/investment problem for logarithmic utility functions in the base of stochastic dynamical programming method. We show a special Verification Theorem for this case. We find the solution…
We study the pricing problem for a European call option when the volatility of the underlying asset is random and follows the exponential Ornstein-Uhlenbeck model. The random diffusion model proposed is a two-dimensional market process that takes a log-Brownian motion to describe price dynamics and an Ornstein-Uhlenbec…
Study prices energy derivatives using specific stochastic processes.
problem Pricing energy derivatives in markets driven by specific stochastic processes.
method Calculated characteristic functions, derived non-arbitrage conditions, and developed efficient algorithms for simulation.
result Developed methods for pricing various energy contracts.
The paper explores how score-driven models can approximate rough volatility.
problem Modeling rough volatility with long memory structures.
method Extending score-driven models to include infinite-lag structures and heavy-tailed decay.
result Score-driven models converge to fractional Ornstein-Uhlenbeck processes under appropriate scaling.
In this paper we study the pricing of exchange options under a dynamic described by stochastic correlation with random jumps. In particular, we consider a Ornstein-Uhlenbeck covariance model with Levy Background Noise Process driven by Inverse Gaussian subordinators. We use expansion in terms of Taylor polynomials and …
Modeling price dynamics in response to order flow imbalance in Chinese futures markets.
problem Understanding price dynamics in markets with order flow imbalance.
method Modeling order flow imbalance as an Ornstein-Uhlenbeck process with memory and mean-reverting characteristics.
result Horizon-dependent heterogeneity in conventional metrics' interaction with order flow imbalance.
Study optimal investment strategies for an insurer in two currency markets.
problem Maximizing expected exponential utility of terminal wealth for an insurer in two currency markets.
method Dynamic programming method applied to solve Hamilton-Jacobi-Bellman equations.
result Optimal investment strategies and value functions are derived.
Solving statistical learning problems often involves nonconvex optimization. Despite the empirical success of nonconvex statistical optimization methods, their global dynamics, especially convergence to the desirable local minima, remain less well understood in theory. In this paper, we propose a new analytic paradigm …
Study simulates Variance Gamma processes for energy derivatives pricing.
problem Simulating Variance Gamma processes for accurate energy derivative pricing.
method Three-step procedure to relate self-decomposability to increments, derived from Qu et al. (2019). Exact simulation of skeleton of Variance Gamma and symmetric Variance Gamma driven Ornstein-Uhlenbeck processes.
result Exact simulation of Variance Gamma and related processes without numerical inversion.
This paper optimizes DC pension plan investments using O-U process and loan.
problem Optimizing investment strategy for DC pension plans under specific market conditions.
method Dynamic programming and Hamilton-Jacobi-Bellman equation to derive optimal investment strategy.
result Explicit expression for optimal investment strategy derived.
Modeling joint log-volatility dynamics with multivariate fractional Ornstein-Uhlenbeck process.
problem Empirical evidence of joint behavior in realized volatility time series.
method Multivariate fractional Ornstein-Uhlenbeck process with different Hurst exponents and non-trivial interdependencies.
result Model accurately captures asymmetries and spillover effects in realized-volatility time series.
Model captures SPX and VIX volatility surfaces and skew-stickiness ratio.
problem Capturing volatility dynamics in financial markets.
method Two-factor Quintic Ornstein-Uhlenbeck (OU) model with polynomial volatility.
result Model accurately represents SPX and VIX volatility surfaces and SSR.
TCNF models SDEs using time deformation of Brownian motion.
problem Modeling SDEs with existing methods.
method Time-changed normalizing flows (TCNF) based on time deformation of Brownian motion.
result Improved modeling of SDEs, including Ornstein-Uhlenbeck process.
Novel AMM model for pegged cryptoassets using nested OU processes.
problem Liquidity and risk management in markets for pegged cryptoassets.
method Multi-level nested Ornstein-Uhlenbeck (OU) processes for exchange rate dynamics, calibrated and filtered AMM model.
result Consistent efficient quotes and improved liquidity provision for pegged cryptoassets.
Characterizes Lévy-driven Ornstein-Uhlenbeck processes linked to tempered stable distributions.
problem Understanding Lévy-driven Ornstein-Uhlenbeck processes and their properties.
method Characterizes the Lévy triplet and deduces transition laws for finite variation Ornstein-Uhlenbeck processes associated with tempered stable distributions.
result Provides algorithms for generating skeleton of Ornstein-Uhlenbeck processes related to exponentially-modulated tempered stable laws.
This paper studies the problem of trading futures with transaction costs when the underlying spot price is mean-reverting. Specifically, we model the spot dynamics by the Ornstein-Uhlenbeck (OU), Cox-Ingersoll-Ross (CIR), or exponential Ornstein-Uhlenbeck (XOU) model. The futures term structure is derived and its conne…
Stochastic bridges are commonly used to impute missing data with a lower sampling rate to generate data with a higher sampling rate, while preserving key properties of the dynamics involved in an unbiased way. While the generation of Brownian bridges and Ornstein-Uhlenbeck bridges is well understood, unbiased generatio…
Reducing volatility proxy improves apparent market correlation dynamics.
problem Attributing apparent slow collective market dynamics to intrinsic or driver inheritance.
method Coupled Ornstein-Uhlenbeck model with VIX proxy, decomposing and controlling for autocorrelation.
result VIX-coupled model reduces effective relaxation time from 298 to 61 trading days, improving fit over bare mean reversion.
Pairs trading strategy improved using Ornstein-Uhlenbeck process.
problem Improving pairs trading strategy effectiveness.
method Used Ornstein-Uhlenbeck process to model stock price spreads.
result OU model captures signals and trends effectively but underperforms compared to naive model.
Entropy-minimal measure calculated for a stochastic volatility model.
problem Calculating the entropy-minimal equivalent martingale measure in a stochastic volatility model.
method Revised related theory, calculated entropy-minimal measure.
result Entropy-minimal measure for the exponential Ornstein-Uhlenbeck model.
New simulation technique speeds up Lévy-driven OU process pricing.
problem Inefficient Monte Carlo simulations of Lévy-driven OU processes.
method Numerical inversion of characteristic function combined with FFT for fast and accurate simulations.
result The proposed technique is at least one order of magnitude faster than existing methods.
New model learns graph spectra accurately, outperforming existing methods.
problem Graph diffusion models struggle to distinguish certain graph families and their spectra.
method Leveraged random matrix theory to analytically extract spectral properties, introducing Dyson Diffusion Model.
result Dyson Diffusion Model learns graph spectra accurately and outperforms existing models.
The paper proposes estimators for bid-ask spreads with and without serial dependence.
problem Estimating bid-ask spreads in financial markets with and without serial dependence.
method The authors propose moment-based estimators for bid-ask spreads, considering both geometric Brownian motion and geometric fractional Brownian motion for price dynamics, and Ornstein-Uhlenbeck process for microstructure noise.
result The estimators are consistent and asymptotically normal, and perform well compared to existing approaches on simulated data.
New method reconstructs non-equilibrium stochastic systems from data.
problem Reconstructing non-equilibrium stochastic systems from ensemble measurements.
method Schrödinger bridge problem with multivariate Ornstein-Uhlenbeck process.
result Simulation-free algorithm achieves higher accuracy than competing methods.
A new fast method simulates stochastic volatility models.
problem Simulating stochastic volatility models efficiently.
method Karhunen-Loève expansions to express stochastic volatility as sine series, followed by analytical derivation of integrals.
result Simulation is several hundred times faster than existing methods.
We start by showing that the finite-time absolute ruin probability in the classical risk model with constant interest force can be expressed in terms of the transition probability of a positive Ornstein-Uhlenbeck type process, say X. Our methodology applies to the case when the dynamics of the aggregate claims process …
Develops European power option pricing under correlated interest rate and asset processes.
problem Pricing European power options under correlated interest rate and asset processes.
method Martingale method and Girsannov transform.
result Derives European power option pricing formulae under two market assumptions.
We prove sharp bounds for the growth rate of eigenfunctions of the Ornstein-Uhlenbeck operator and its natural generalizations. The bounds are sharp even up to lower order terms and have important applications to geometric flows.
Paper models non-maturing deposits using a Lévy-driven Ornstein-Uhlenbeck process.
problem Managing non-maturing deposits as a major funding source for banks.
method Develops a multivariate Lévy-driven Ornstein-Uhlenbeck process with three sources of randomness.
result Models rare but severe events in deposit volumes with positive probability.
Study optimal strategy for maximizing exponential utility in financial market with linear price impact.
problem Maximizing exponential utility in financial market with linear price impact.
method Purely probabilistic approach using duality.
result Computed optimal portfolio strategy and value for Ornstein-Uhlenbeck process.
We consider the problem of option pricing under stochastic volatility models, focusing on the linear approximation of the two processes known as exponential Ornstein-Uhlenbeck and Stein-Stein. Indeed, we show they admit the same limit dynamics in the regime of low fluctuations of the volatility process, under which we …
Phylogeny is the field of modelling the temporal discrete dynamics of speciation. Complex models can nowadays be studied using the Approximate Bayesian Computation approach which avoids likelihood calculations. The field's progression is hampered by the lack of robust software to estimate the numerous parameters of the…
Neural SVEs model complex systems with memory, outperforming traditional methods.
problem Modeling systems with memory effects and irregular behavior.
method Introducing neural stochastic Volterra equations as a physics-inspired architecture.
result Neural SVEs outperform neural SDEs and DeepONets in various applications.
We study the problem of dynamically trading futures in a regime-switching market. Modeling the underlying asset price as a Markov-modulated diffusion process, we present a utility maximization approach to determine the optimal futures trading strategy. This leads to the analysis of the associated system of Hamilton-Jac…
We consider the Black--Scholes model of financial market modified to capture the stochastic nature of volatility observed at real financial markets. For volatility driven by the Ornstein--Uhlenbeck process, we establish the existence of equivalent martingale measure in the market model. The option is priced with respec…
When stock prices are observed at high frequencies, more information can be utilized in estimation of parameters of the price process. However, high-frequency data are contaminated by the market microstructure noise which causes significant bias in parameter estimation when not taken into account. We propose an estimat…
Study on gamma-related OU processes with simulation methods.
problem Distributional properties and simulation of gamma-related OU processes.
method Investigation of gamma and bilateral gamma laws, derivation of closed-form densities and characteristic functions, and development of efficient simulation algorithms.
result Efficient algorithms for generating gamma-related OU processes with significantly faster performance than existing methods.
Method verifies if observed data fits Lévy-Driven Ornstein-Uhlenbeck process.
problem Verifying if observed data fits Lévy-Driven Ornstein-Uhlenbeck process.
method Estimating parameters and approximating the driving process to test CAR(1) Lévy-driven hypothesis.
result Demonstrates method's effectiveness through simulations and real data examples.