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We address the problem of analyzing sets of noisy time-varying signals that all report on the same process but confound straightforward analyses due to complex inter-signal heterogeneities and measurement artifacts. In particular we…
Financial markets are nonlinear with complexity, where different types of assets are traded between buyers and sellers, each having a view to maximize their Return on Investment (ROI). Forecasting market trends is a challenging task since…
A parsimonious generalization of the Heston model is proposed where the volatility-of-volatility is assumed to be stochastic. We follow the perturbation technique of Fouque et al (2011, CUP) to derive a first order approximation of the…
In this paper we assume the insurance wealth process is driven by the compound Poisson process. The discounting factor is modelled as a geometric Brownian motion at first and then as an exponential function of an integrated…
In supply chain networks, firms dynamically form or dissolve partnerships to adapt to market fluctuations, posing a challenge for predicting future supply relationships. We model the occurrence of supply edges (firm i to firm j) as a…
The growing complexity of decision-making in public health and health care has motivated an increasing use of mathematical modeling. An important line of health modeling is based on stock & flow diagrams. Such modeling elevates transparency…
This paper models stochastic process of price time series of CSI 300 index in Chinese financial market, analyzes volatility characteristics of intraday high-frequency price data. In the new generalized Barndorff-Nielsen and Shephard model,…
In this paper we derive the optimal execution trajectory for a trader who wishes to buy or sell a large position of shares which evolve as a geometric Brownian process in contrast to the arithmetic model which prevails in the existing…
This work focuses on a self-exciting point process defined by a Hawkes-like intensity and a switching mechanism based on a hidden Markov chain. Previous works in such a setting assume constant intensities between consecutive events. We…
Algorithmic trading relies on extracting meaningful signals from diverse financial data sources, including candlestick charts, order statistics on put and canceled orders, traded volume data, limit order books, and news flow. While deep…
We consider a road network represented by a directed graph. We assume to collect many measurements of traffic flows on all the network arcs, or on a subset of them. We assume that the users are divided into different groups. Each group…
The increasing richness in volume, and especially types of data in the financial domain provides unprecedented opportunities to understand the stock market more comprehensively and makes the price prediction more accurate than before.…
Continuous Time Markov Chains, Hawkes processes and many other interesting processes can be described as solution of stochastic differential equations driven by Poisson measures. Previous works, using the Stein's method, give the…
This paper presents a novel approach to pricing American options using piecewise diffusion Markov processes (PDifMPs), a type of generalised stochastic hybrid system that integrates continuous dynamics with discrete jump processes. Standard…
In sampling tasks, it is common for target distributions to be known up to a normalizing constant. However, in many situations, even evaluating the unnormalized distribution can be costly or infeasible. This issue arises in scenarios such…
Markov Chain Monte Carlo (MCMC) algorithms play an important role in statistical inference problems dealing with intractable probability distributions. Recently, many MCMC algorithms such as Hamiltonian Monte Carlo (HMC) and Riemannian…
Classical asset price forecasting methods primarily rely on numerical data, such as price time series, trading volumes, limit order book data, and technical analysis indicators. However, the news flow plays a significant role in price…
The stochastic simulation algorithm (SSA) and the corresponding Monte Carlo (MC) method are among the most common approaches for studying stochastic processes. They rely on knowledge of interevent probability density functions (PDFs) and on…
We demonstrate the application of an algorithmic trading strategy based upon the recently developed dynamic mode decomposition (DMD) on portfolios of financial data. The method is capable of characterizing complex dynamical systems, in this…
In this paper, we introduce Max Markov Chain (MMC), a novel representation for a useful subset of High-order Markov Chains (HMCs) with sparse correlations among the states. MMC is parsimony while retaining the expressiveness of HMCs. Even…