BayTiDe discovers time-delayed differential equations from noisy data.
problem Discovering time-delayed differential equations from data with large delays and noise.
method Bayesian inference with a sparsity-promoting prior.
result BayTiDe accurately identifies time-delayed differential equations with accuracy proportional to data resolution.
Derives a Feynman-Kac formula for a fixed delay CIR model.
problem Modeling financial processes with fixed delay.
method Proves existence and uniqueness of a strong solution for a specific SDDE.
result Derives a Feynman-Kac type formula leading to an affine bond pricing formula.
The paper solves optimal control problems for stochastic delay equations.
problem Optimal control of stochastic delay differential equations.
method Rewriting the problem in an infinite-dimensional Hilbert space, using dynamic programming and viscosity solutions.
result Characterizes the value function as the unique viscosity solution of the Hamilton-Jacobi-Bellman equation.
Study on synchronization in financial markets with time delays.
problem Understanding market dynamics and synchronization in financial systems with time delays.
method Examined a system of coupled non-linear delay-differential equations, linearized for small delays, and analyzed collective dynamics using bifurcation diagrams and numerical solutions.
result Demonstrated that limit cycles can be maintained in coupled N-asset models with appropriate parameterization, leading to market synchronization.
In this article we propose a model for stochastic delay differential equation with jumps (SDDEJ) in a differentiable manifold M endowed with a connection ∇. In our model, the continuous part is driven by vector fields with a fixed delay and the jumps are assumed to come from a distinct source of (càdlàg) noise…
We consider that the price of a firm follows a non linear stochastic delay differential equation. We also assume that any claim value whose value depends on firm value and time follows a non linear stochastic delay differential equation. Using self-financed strategy and replication we are able to derive a Random Partia…
The paper models financial asset prices with jumps and evaluates European option prices using numerical methods.
problem Modeling and pricing European options with jumps in delayed stochastic systems.
method Existence, uniqueness, and positivity of solutions to delayed stochastic differential equations with jumps. Application of Fourier transformation for analytical pricing and Monte-Carlo simulation with a logarithmic Euler-Maruyama scheme for numerical approximation.
result The logarithmic Euler-Maruyama scheme provides a positive and convergent method for approximating the solution to the delayed stochastic differential equations with jumps.
Proposes neural delay differential equations for stable system identification with partially observed states.
problem Learning stable models for systems with partial or delayed observations.
method Augments states with history, uses neural delay differential equations, and ensures stability through time delay analysis.
result The approach ensures stability of learned models for partially observed systems.
Improved GRU model with weighted time-delay feedback for long-term dependencies.
problem Modeling long-term dependencies in sequential data.
method Introducing a gated recurrent unit (GRU) with a weighted time-delay feedback mechanism.
result τ-GRU outperforms state-of-the-art models on various tasks.
Paper develops Euler scheme for fractional delay diff. eqs with additive noise.
problem Developing a consistent Euler-Maruyama scheme for fractional stochastic delay diff. eqs.
method Euler-Maruyama scheme for fractional Brownian motion with additive noise.
result Achieved convergence rate of H+1/2 for smooth delays when H>1/2.
A new transform links rotating calorons to solutions of a differential equation.
problem Existence and characterization of rotating calorons.
method Formulated a Nahm transform to relate rotating calorons to solutions of a delayed-differential equation.
result Existence of an eight-parameter family of rotating calorons with nontrivial holonomy.
Derives relationship between interest rates and inflation in a two-component system.
problem Understanding the relationship between interest rates and inflation in a two-component economic system.
method Used the Fisher relation to derive a delay differential equation and provided computer simulations.
result Obtained a delay differential equation and provided solutions for it over different interest regimes.
DiffEqFlux.jl integrates neural networks with differential equations.
problem Combining machine learning and differential equations for modeling complex systems.
method Fusing neural networks and differential equations using DiffEqFlux.jl.
result Demonstrates the integration of differential equations into neural networks and vice versa.
In this paper we investigate novel applications of a new class of equations which we call time-delayed backward stochastic differential equations. Time-delayed BSDEs may arise in finance when we want to find an investment strategy and an investment portfolio which should replicate a liability or meet a target depending…
This article is a sequel to [A.H.M.P]. In [A.H.M.P], we develop an explicit formula for pricing European options when the underlying stock price follows a non-linear stochastic delay equation with fixed delays in the drift and diffusion terms. In this article, we look at models of the stock price described by stochasti…
HS-FNO models non-Markovian PDEs by learning history and future states.
problem Non-Markovian dynamics where future states depend on past history.
method History-Space Fourier Neural Operator (HS-FNO) for delay and memory-driven PDEs.
result HS-FNO achieves lowest aggregate errors across various PDE families.
In this paper we show that there are applications that transform the movement of a pendulum into movements in R3. This can be done using Euler top system of differential equations. On the constant level surfaces, Euler top system reduces to the equation of a pendulum. Those properties are also considered in…
New method solves stochastic control problems with delays using deep learning.
problem Stochastic control problems with delayed control in drift and diffusion.
method Characterization via Riccati PDEs and deep learning scheme.
result Illustrates effect of delay on Markowitz portfolio allocation problem.
The paper introduces a new short rate model with memory components.
problem Modeling short rate dynamics with past values.
method Integrates memory (delay) components into Merton or Vasiček models.
result Analytical solutions for bond prices and forward rates.
Modeling inter-bank lending and borrowing with delays to assess systemic risk.
problem Assessing systemic risk in a network of banks with delayed interactions.
method Linear-quadratic stochastic differential game with delay, open-loop and close-loop Nash equilibria.
result The delay in controls affects liquidity and systemic risk, leading to a higher likelihood of defaults.
In this paper we consider backward stochastic differential equations with time-delayed generators of a moving average type. The classical framework with linear generators depending on (Y(t),Z(t)) is extended and we investigate linear generators depending on (t1∫0tY(s)ds,t1∫0tZ(s)ds). We…
Approximate Bayesian computation (ABC) using a sequential Monte Carlo method provides a comprehensive platform for parameter estimation, model selection and sensitivity analysis in differential equations. However, this method, like other Monte Carlo methods, incurs a significant computational cost as it requires explic…
In this article we develop an explicit formula for pricing European options when the underlying stock price follows a non-linear stochastic differential delay equation (sdde). We believe that the proposed model is sufficiently flexible to fit real market data, and is yet simple enough to allow for a closed-form represe…
Delay-SDE-net models time series with memory and uncertainty, outperforming other models.
problem Accurately modeling time series with memory and uncertainty.
method Stochastic delay differential equations (SDDEs) neural network model with aleatoric and epistemic uncertainty.
result The Delay-SDE-net consistently outperforms other models in predicting time series values and uncertainties.
Optimizes portfolios with delayed economic factors.
problem Optimizing portfolios in markets with delayed economic factors.
method Maximizing power utility through QFBSDEs, verified by super-martingale argument.
result Existence and uniqueness of solutions to QFBSDEs.
Neural Laplace models diverse DEs in the Laplace domain for better dynamics.
problem Inadequate ODEs for long-range dependencies and discontinuities.
method Unified framework in Laplace domain, using stereographic map for smoothness.
result Superior performance in diverse DEs, including complex history dependency and abrupt changes.
Quantum machine learning without measurements using time-delayed equations.
problem Efficiently solving problems encoded in quantum controlled unitary operations.
method Iteration of a time-delayed equation for feedback in dynamics, eliminating measurements.
result Performance comparison with classical machine learning methods shows enhanced efficiency.
Unified framework connects physical laws and machine learning.
problem Combining physical laws and machine learning for scientific applications.
method Universal Differential Equations (UDEs) as a unifying framework.
result Wide variety of applications can be efficiently handled through UDE formalism.
Proposes a deep learning method for solving complex financial games with delays.
problem Financial modeling with multi-agent interactions and delayed effects.
method Parameterizes controls using recurrent neural networks and trains them with modified fictitious play.
result Demonstrates effectiveness on finance problems with known solutions and new problems with derived Nash equilibria.
A new algorithm tackles delayed combinatorial semi-bandit with causal relations.
problem Optimizing decisions in a non-stationary environment with delayed and causally related rewards.
method Formalized as a non-stationary delayed combinatorial semi-bandit problem, the approach models causal relations with a directed graph in a stationary structural equation model. The agent learns these relations from delayed feedback to optimize decisions.
result Proved a regret bound for the proposed algorithm's performance.
This paper analyzes ASGD using SDEs for a more intuitive convergence rate.
problem Theoretical analysis of ASGD is limited by discrete methods and complex proofs.
method Continuous approximation of ASGD using SDDEs and convergence rate analysis methods.
result Continuous view provides better convergence rates and insights into ASGD.
EPD method accurately captures parameter distributions from RCS data.
problem Limitations of traditional methods in estimating parameter distributions from RCS data.
method EPD method generates synthetic trajectories, estimates parameters, and selects parameters based on discrepancy.
result EPD provides accurate distribution of parameters without data loss.
Paper presents a novel method to assess boundedness and stability of nonlinear systems with variable delays.
problem Challenges in assessing boundedness and stability of vector nonlinear systems with variable delays and coefficients.
method Develops a novel framework to evaluate the evolution of solution norms in such systems by constructing scalar counterparts.
result Introduces new criteria for boundedness and stability and estimates the radii of containing balls for history functions.
This paper analyzes a hybrid reinsurance and investment game with bounded memory.
problem A hybrid stochastic differential reinsurance and investment game between reinsurer and insurers.
method Stochastic Stackelberg differential subgame and non-zero-sum stochastic differential subgame, using backward induction and dynamic programming.
result Derive equilibrium strategy and value functions explicitly, showing how delay and competition affect strategies.
The paper examines financial trading models and proves conditions for positive solutions.
problem Analyzing conditions for positive solutions in a financial trading model.
method Introduced thresholds α− and α+ to prove state positivity or bankruptcy. result For α<α−, state positivity is guaranteed for all time; for α>α+, state positivity is not guaranteed. This paper improves ABC-SMC by using a cheap simulator to reduce computational cost.
problem High computational cost of exact simulators in ABC.
method Delayed acceptance Markov chain Monte Carlo (MCMC) within ABC-SMC.
result The approach reduces computational cost without sacrificing accuracy.
Extend classical theory of affine processes to path-dependent setting
problem Path-dependent affine processes
method Introduce path-dependent coefficients and provide analytic formulas for their Fourier--Laplace transform
result Define path-dependent affine processes through their exponential-affine Fourier--Laplace transform and establish a characterization theorem
We present a stochastic analysis of a data set consisiting of 10^6 quotes of the US Doller - German Mark exchange rate. Evidence is given that the price changes x(tau) upon different delay times tau can be described as a Markov process evolving in tau. Thus, the tau-dependence of the probability density function (pdf) …
New method speeds up Bayesian inverse problem solving with neural operators.
problem Solving infinite-dimensional Bayesian inverse problems with high computational cost.
method Delayed-acceptance geometric MCMC driven by derivative-informed neural operator surrogates.
result Significant speedup in generating posterior samples (3-9 times faster).
Proposes a new method combining Reservoir Computing and Normalizing Flow for predicting stochastic dynamical systems.
problem Predicting and capturing long-term behaviors of stochastic dynamical systems.
method Data-driven framework combining Reservoir Computing and Normalizing Flow, integrating error modeling and both approaches virtues.
result Successfully predicts the long-term evolution of stochastic dynamical systems and replicates dynamical behaviors.
Paper optimizes insurer's investment strategy in a fluctuating market with memory effects.
problem Optimizing insurer's investment in a market with regime switching and noisy memory.
method Formulated as a stochastic differential delay game, solved using BSDE approach.
result Derives analytical solutions for a specific case of a quadratic penalty function.
Modeling air pollutants using data-driven techniques and sparse identification of nonlinear dynamics.
problem Predicting concentrations of air pollutants using hidden physical laws.
method Sparse identification of nonlinear dynamics (SINDy) for parsimonious systems of ordinary differential equations.
result More than half of the critical points are saddle points, indicating system instability.
Improved modeling of chaotic systems using time-delay embeddings and Frenet-Serret frame.
problem Identifying effective coordinate systems for nonlinear dynamical systems.
method Developed a new algorithm to identify more stable and accurate models from less data, leveraging the connection between HAVOK and Frenet-Serret frame.
result The sub- and super-diagonal entries of the linear model correspond to intrinsic curvatures in Frenet-Serret frame.
New Hessian estimates for heat equations on manifolds.
problem Estimating Hessian matrices for heat-type equations on Riemannian manifolds.
method Using Bismut-Stroock Hessian formula, with explicit coefficients and delay/growth rate functions.
result Novel backward weak Harnack inequality and precise pointwise Hessian estimates for eigenfunctions.
New strategy improves liquidity takers' performance in markets with latency.
problem Latency affects liquidity takers' ability to execute limit orders effectively.
method Modelled LOB and MLOs as a marked point process, used variational analysis and FBSDEs to find optimal price limits.
result Optimal trading strategy improves marksmanship in markets with latency.
New model reveals balance crucial for robust neural coding.
problem Efficient neural coding in noisy, chaotic networks.
method Analytical model of balanced predictive coding with dissociated balance and weight disorder.
result Superclassical scaling in coding accuracy, independent of balance and weight disorder.
Continuous time random walks (CTRWs) are used in physics to model anomalous diffusion, by incorporating a random waiting time between particle jumps. In finance, the particle jumps are log-returns and the waiting times measure delay between transactions. These two random variables (log-return and waiting time) are typi…
DSPG improves SPSA for distributed optimization with wireless delays.
problem Optimizing global functions in multi-agent systems with wireless delays and errors.
method Cross-entropy based distributed stochastic approximation algorithm (DSPG) using simultaneous perturbation.
result DSPG reduces biases due to communication delays and maintains convergence rate.