arXiv research

The paper solves optimal control problems for stochastic delay equations.

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…

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…

The paper models financial asset prices with jumps and evaluates European option prices using numerical methods.

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…

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

New method solves stochastic control problems with delays using deep learning.

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…

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…

BayTiDe discovers time-delayed differential equations from noisy data.

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…

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…

Delay-SDE-net models time series with memory and uncertainty, outperforming other models.

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…

Study on synchronization in financial markets with time delays.

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…

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…

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

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

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…

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

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

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

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…

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

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…

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…

HS-FNO models non-Markovian PDEs by learning history and future states.

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 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 algorithm tackles delayed feedback in Lipschitz bandits with sublinear regret.

Neural networks can approximate complex stochastic equations well.

New algorithm tackles stochastic bandits with varying arm-dependent delays.

Develops a stochastic approach to financial market delays.

We formulate stochastic partial differential equations on Riemannian manifolds, moving surfaces, general evolving Riemannian manifolds (with appropriate assumptions) and Riemannian manifolds with random metrics, in the variational setting of the analysis to stochastic partial differential equations. Considering mainly …

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…

The adjoint sensitivity method scalably computes gradients of solutions to ordinary differential equations. We generalize this method to stochastic differential equations, allowing time-efficient and constant-memory computation of gradients with high-order adaptive solvers. Specifically, we derive a stochastic differen…

We provide tight finite-time convergence bounds for gradient descent and stochastic gradient descent on quadratic functions, when the gradients are delayed and reflect iterates from $τ$ rounds ago. First, we show that without stochastic noise, delays strongly affect the attainable optimization error: In fact, the error…

DASA speeds up SA with delayed agents, achieving N-fold speedup.

Deep neural networks solve stochastic control problems with delay.

This paper presents a novel approach to numerically solve stochastic differential games for nonlinear systems. The proposed approach relies on the nonlinear Feynman-Kac theorem that establishes a connection between parabolic deterministic partial differential equations and forward-backward stochastic differential equat…

Extend classical theory of affine processes to path-dependent setting

Bayesian inference for stochastic differential equations using Wishart diffusions.

Algorithm samples constrained stochastic differential equations.

Paper uses second-order differential geometry to study stochastic mechanics.

Proposes a method to reduce parallel complexity of MLMC in SGD.

We study a variant of the stochastic $K$-armed bandit problem, which we call "bandits with delayed, aggregated anonymous feedback". In this problem, when the player pulls an arm, a reward is generated, however it is not immediately observed. Instead, at the end of each round the player observes only the sum of a number…