arXiv research

BayTiDe discovers time-delayed differential equations from noisy data.

The paper solves optimal control problems for stochastic delay equations.

Stochastic delay differential equations (SDDE's) have been used for financial modeling. In this article, we study a SDDE obtained by the equation of a CIR process, with an additional fixed delay term in drift; in particular, we prove that there exists a unique strong solution (positive and integrable) which we call fix…

Study on synchronization in financial markets with time delays.

In this article we propose a model for stochastic delay differential equation with jumps (SDDEJ) in a differentiable manifold $M$ endowed with a connection $\nabla$. 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.

Proposes neural delay differential equations for stable system identification with partially observed states.

Improved GRU model with weighted time-delay feedback for long-term dependencies.

Paper develops Euler scheme for fractional delay diff. eqs with additive noise.

A new transform links rotating calorons to solutions of a differential equation.

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.

In this paper we show that there are applications that transform the movement of a pendulum into movements in $\mathbb{R}^3$. 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.

The paper introduces a new short rate model with memory components.

This article is an extension of the work of one of us (Coopersmith, 2011) in deriving the relationship between certain interest rates and the inflation rate of a two component economic system. We use the well-known Fisher relation between the difference of the nominal interest rate and its inflation adjusted value to e…

We propose a model of inter-bank lending and borrowing which takes into account clearing debt obligations. The evolution of log-monetary reserves of $N$ banks is described by coupled diffusions driven by controls with delay in their drifts. Banks are minimizing their finite-horizon objective functions which take into a…

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 $(\frac{1}{t}\int_0^tY(s)ds, \frac{1}{t}\int_0^tZ(s)ds)$. We…

DiffEqFlux.jl is a library for fusing neural networks and differential equations. In this work we describe differential equations from the viewpoint of data science and discuss the complementary nature between machine learning models and differential equations. We demonstrate the ability to incorporate DifferentialEqua…

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.

Neural Laplace models diverse DEs in the Laplace domain for better dynamics.

We propose an optimal portfolio problem in the incomplete market where the underlying assets depend on economic factors with delayed effects, such models can describe the short term forecasting and the interaction with time lag among different financial markets. The delay phenomenon can be recognized as the integral ty…

Proposes a deep learning method for solving complex financial games with delays.

In the context of science, the well-known adage "a picture is worth a thousand words" might well be "a model is worth a thousand datasets." In this manuscript we introduce the SciML software ecosystem as a tool for mixing the information of physical laws and scientific models with data-driven machine learning approache…

A new algorithm tackles delayed combinatorial semi-bandit with causal relations.

This paper investigates a hybrid stochastic differential reinsurance and investment game between one reinsurer and two insurers, including a stochastic Stackelberg differential subgame and a non-zero-sum stochastic differential subgame. The reinsurer, as the leader of the Stackelberg game, can price reinsurance premium…

EPD method accurately captures parameter distributions from RCS data.

Paper presents a novel method to assess boundedness and stability of nonlinear systems with variable delays.

Asynchronous stochastic gradient descent (ASGD) is a popular parallel optimization algorithm in machine learning. Most theoretical analysis on ASGD take a discrete view and prove upper bounds for their convergence rates. However, the discrete view has its intrinsic limitations: there is no characterization of the optim…

We propose a quantum machine learning algorithm for efficiently solving a class of problems encoded in quantum controlled unitary operations. The central physical mechanism of the protocol is the iteration of a quantum time-delayed equation that introduces feedback in the dynamics and eliminates the necessity of interm…

Extend classical theory of affine processes to path-dependent setting

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.

Proposes a new method combining Reservoir Computing and Normalizing Flow for predicting stochastic dynamical systems.

Approximate Bayesian computation (ABC) is now an established technique for statistical inference used in cases where the likelihood function is computationally expensive or not available. It relies on the use of a~model that is specified in the form of a~simulator, and approximates the likelihood at a~parameter value $…

Modeling air pollutants using data-driven techniques and sparse identification of nonlinear dynamics.

Improved modeling of chaotic systems using time-delay embeddings and Frenet-Serret frame.

New Hessian estimates for heat equations on manifolds.

We consider a discrete-time, linear state equation with delay which arises as a model for a trader's account value when buying and selling a risky asset in a financial market. The state equation includes a nonnegative feedback gain $α$ and a sequence $v(k)$ which models asset returns which are within known bounds but o…

In this paper, we consider a risk-based optimal investment problem of an insurer in a regime-switching jump diffusion model with noisy memory. Using the model uncertainty modeling, we formulate the investment problem as a zero-sum, stochastic differential delay game between the insurer and the market, with a convex ris…

New model reveals balance crucial for robust neural coding.

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…

Develops a stochastic approach to financial market delays.

Paper tackles action delays in reinforcement learning, proposing a delay-aware framework.