This article provides the mathematical foundation for stochastically continuous affine processes on the cone of positive semidefinite symmetric matrices. This analysis has been motivated by a large and growing use of matrix-valued affine processes in finance, including multi-asset option pricing with stochastic volatil…
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A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
168,657 papers · 148 categories
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48 results for “correlated stochastic processes”
We propose a correlated stochastic process of which the novel non-Gaussian probability mass function is constructed by exactly solving moment generating function. The calculation of cumulants and auto-correlation shows that the process is convergent and scale invariant in the large but finite number limit. We demonstra…
Develops diffusion models for time-varying correlation on the circle.
problem Time-varying correlation modeling on the circle.
method Stochastic processes on the unit circle, specifically Brownian motion and von Mises diffusion.
result Derives an accurate analytical approximation to the transition density of the von Mises diffusion.
We conduct an empirical study using the quantile-based correlation function to uncover the temporal dependencies in financial time series. The study uses intraday data for the S\&P 500 stocks from the New York Stock Exchange. After establishing an empirical overview we compare the quantile-based correlation function to…
MTNPs jointly model multiple correlated tasks from various sources.
problem Naive NPs can only model a single stochastic process and infer tasks independently.
method MTNPs are a hierarchical extension of NPs that jointly infer tasks from multiple stochastic processes, considering inter-task correlation and handling incomplete data.
result MTNPs successfully model multiple tasks jointly, discovering and exploiting their correlations in various real-world data.
It is known that the implied volatility skew of FX options demonstrates a stochastic behavior which is called stochastic skew. In this paper we create stochastic skew by assuming the spot/instantaneous variance correlation to be stochastic. Accordingly, we consider a class of SLV models with stochastic correlation wher…
We propose a stochastic process driven by the memory effect with novel distributions which include both exponential and leptokurtic heavy-tailed distributions. A class of the distributions is analytically derived from the continuum limit of the discrete binary process with the renormalized auto-correlation. The moment …
We investigate how simultaneously recorded long-range power-law correlated multi-variate signals cross-correlate. To this end we introduce a two-component ARFIMA stochastic process and a two-component FIARCH process to generate coupled fractal signals with long-range power-law correlations which are at the same time lo…
The Gaussian Neural Processstat.ML
GNP models predictive correlations and outperforms NPs.
problem Training and understanding of Neural Processes.
method Proposed a new model, Gaussian Neural Process (GNP), which incorporates translation equivariance and provides universal approximation guarantees.
result Demonstrates encouraging performance and provides universal approximation guarantees.
Optimal insurance and investment strategy under exponential preferences in a correlated market model.
problem Optimal investment and reinsurance strategy for an insurance company under exponential preferences.
method Stochastic control techniques to construct a forward dynamic exponential utility and characterize the optimal strategy.
result Characterization of the optimal investment and reinsurance strategy in a correlated market model.
Modeling correlated mutations in cancer for personalized treatment.
problem Identifying mutations for personalized cancer therapy in heterogeneous profiles.
method Proposed correlated zero-inflated negative binomial process with mixed beta-Bernoulli and variational inference.
result Identified biologically relevant correlations between somatic mutations.
Multiple time scales in volatility and leverage correlations: An stochastic volatility modelcond-mat.stat-mech
Financial time series exhibit two different type of non linear correlations: (i) volatility autocorrelations that have a very long range memory, on the order of years, and (ii) asymmetric return-volatility (or `leverage') correlations that are much shorter ranged. Different stochastic volatility models have been propos…
Stochastic Multiplicative Processes for Financial Marketscond-mat.stat-mech
We study a stochastic multiplicative system composed of finite asynchronous elements to describe the wealth evolution in financial markets. We find that the wealth fluctuations or returns of this system can be described by a walk with correlated step sizes obeying truncated Levy-like distribution, and the cross-correla…
From Target Tracking to Targeting Track -- Part III: Stochastic Process Modeling and Online Learningeess.SY
This study models target trajectories using stochastic processes for efficient tracking.
problem Efficiently modeling and predicting target trajectories in continuous time.
method Decomposes trajectory modeling into deterministic and stochastic components using Gaussian or Student's- processes.
result Demonstrates superior performance in tracking maneuvering targets compared to existing methods.
Local signature-based expansionsq-fin.MF
Study local expansions of continuous-time processes using Ito signature properties.
problem Analyzing local expansions of continuous-time processes and their moments.
method Using the Ito signature, a basis of iterated integrals, to conduct expansions of the process' characteristic function.
result Explicit coefficients and stochastic representations for asymptotics as time shrinks or diverges.
Proposes a new model to better handle correlation risk in credit risk calculations.
problem Empirical evidence shows correlation risk is significant in credit risk models.
method Introduces a stochastic correlation extension of the Vasicek model using circular diffusion.
result Demonstrates how correlation volatility and persistence affect joint default and survival probabilities.
Target search optimization by threshold resettingcond-mat.stat-mech
Optimizes search times by resetting agents when a threshold is reached.
problem Improving search efficiency in systems with thresholds.
method Develops a framework for correlated stochastic processes with threshold resetting.
result Optimal resetting can prevent larger losses and is applicable to various stochastic systems.
New PEMs improve network inference from time-series data.
problem Causal inference from time-series data with trade-off between accuracy and feasibility.
method Infer networks via process motifs for lagged correlation in linear stochastic processes.
result Proposed PEMs achieve high accuracy and efficiency in network inference.
Study on network-valued processes with asynchronous updates, proving consistency in community and changepoint estimation.
problem Understanding the behavior of network-valued stochastic processes with asynchronous updates.
method Analysis of concentration properties of aggregated adjacency and Laplacian matrices for lazy network-valued stochastic processes.
result Demonstrates consistency of estimators in community and changepoint estimation problems.
The generalized correlation approach, which has been successfully used in statistical radio physics to describe non-Gaussian random processes, is proposed to describe stochastic financial processes. The generalized correlation approach has been used to describe a non-Gaussian random walk with independent, identically d…
Artificial market model based on deterministic agents and derivation of limit of GARCH type processcond-mat.stat-mech
We propose an artificial market model based on deterministic agents. The agents modify their ask/bid price depending on past price changes. The temporal development of market price fluctuations is calculated numerically. A probability density function of market price changes has power law tails. Autocorrelation coeffic…
Empirical studies show that the volatility may exhibit correlations that decay as a fractional power of the time offset. The paper presents a rigorous analysis for the case when the stationary stochastic volatility model is constructed in terms of a fractional Ornstein Uhlenbeck process to have such correlations. It is…
Mean-correction and Higher Order Moments for a Stochastic Volatility Model with Correlated Errorsstat.ME
In an efficient stock market, the log-returns and their time-dependent variances are often jointly modelled by stochastic volatility models (SVMs). Many SVMs assume that errors in log-return and latent volatility process are uncorrelated, which is unrealistic. It turns out that if a non-zero correlation is included in …
Study on martingale property and moment explosions in signature volatility models.
problem Analyzing the martingale property and moment explosions in signature volatility models.
method Fine analysis of the explosion time of a signature stochastic differential equation.
result The price process is a true martingale if and only if the order of the linear form is odd and a correlation parameter is negative.
This paper considers the case of pricing discretely-sampled variance swaps under the class of equity-interest rate hybridization. Our modeling framework consists of the equity which follows the dynamics of the Heston stochastic volatility model, and the stochastic interest rate is driven by the Cox-Ingersoll-Ross (CIR)…
Efficient algorithm for matching graphs with community structure.
problem Graph matching between correlated stochastic block models with constant correlation.
method Partition trees rooted from each vertex, comparing edge statistics to different communities.
result First low-order polynomial-time algorithm achieving exact matching with high probability in dense graphs.
In an incomplete market, with incompleteness stemming from stochastic factors imperfectly correlated with the underlying stocks, we derive representations of homothetic (power, exponential and logarithmic) forward performance processes in factor-form using ergodic BSDE. We also develop a connection between the forward …
We investigate aspects of semimartingale decompositions, approximation and the martingale representation for multidimensional correlated Markov processes. A new interpretation of the dependence among processes is given using the martingale approach. We show that it is possible to represent, in both continuous and discr…
Removing noise from correlations in multivariate stock price datacond-mat.stat-mech
This paper examines the applicability of Random Matrix Theory to portfolio management in finance. Starting from a group of normally distributed stochastic processes with given correlations we devise an algorithm for removing noise from the estimator of correlations constructed from measured time series. We then apply t…
Paper proves minibatch SGD for GP inference converges and improves generalization.
problem Theoretical understanding and practical use of SGD for correlated samples in Gaussian process inference.
method Proves minibatch SGD converges to a critical point with rate O(1/K) for K iterations, under certain kernel conditions.
result Minibatch SGD for GP inference improves generalization and reduces computational burden.
On the martingale property in stochastic volatility models based on time-homogeneous diffusionsmath.PR
Lions and Musiela (2007) give sufficient conditions to verify when a stochastic exponential of a continuous local martingale is a martingale or a uniformly integrable martingale. Blei and Engelbert (2009) and Mijatović and Urusov (2012c) give necessary and sufficient conditions in the case of perfect correlation (ρ=1).…
In this paper, we study the problems of principal Generalized Eigenvector computation and Canonical Correlation Analysis in the stochastic setting. We propose a simple and efficient algorithm, Gen-Oja, for these problems. We prove the global convergence of our algorithm, borrowing ideas from the theory of fast-mixing M…
We consider a structural stochastic volatility model for the loss from a large portfolio of credit risky assets. Both the asset value and the volatility processes are correlated through systemic Brownian motions, with default determined by the asset value reaching a lower boundary. We prove that if our volatility model…
In the setting of polynomial jump-diffusion dynamics, we provide an explicit formula for computing correlators, namely, cross-moments of the process at different time points along its path. The formula appears as a linear combination of exponentials of the generator matrix, extending the well-known moment formula for p…
We propose an extension to Hawkes processes by treating the levels of self-excitation as a stochastic differential equation. Our new point process allows better approximation in application domains where events and intensities accelerate each other with correlated levels of contagion. We generalize a recent algorithm f…
Proposes logistic-beta process for modeling dependent probabilities with beta marginals.
problem Limited work on flexible and computationally convenient stochastic process extensions for dependent random probabilities.
method Introduces logistic-beta process with logistic transformation and beta marginals, capable of modeling dependence in discrete and continuous domains.
result Logistic-beta processes enable effective posterior inference and design of computationally tractable dependent Bayesian nonparametric models.
Model rough volatility using RDEs with correlated Brownian motion and fractional Brownian motion.
problem Modeling rough volatility with correlated stochastic processes.
method Developed a method to lift Brownian motion and rough paths, applying it to fractional Brownian motion to model rough volatility.
result Calibrated a new rough volatility model to market data.
In this paper we discuss the basket options valuation for a jump-diffusion model. The underlying asset prices follow some correlated local volatility diffusion processes with systematic jumps. We derive a forward partial integral differential equation (PIDE) for general stochastic processes and use the asymptotic expan…
We study the sample complexity of canonical correlation analysis (CCA), \ie, the number of samples needed to estimate the population canonical correlation and directions up to arbitrarily small error. With mild assumptions on the data distribution, we show that in order to achieve -suboptimality in a properly define…
Graph alignment problem solved with convex relaxations for correlated matrices.
problem Recovering hidden vertex permutations from correlated Gaussian matrices.
method Convex relaxations of the quadratic assignment problem over doubly stochastic matrices.
result The solution of the convex relaxation concentrates around the ground-truth permutation matrix for certain correlation parameters.
The paper solves investment problems with uncertain factors using game theory.
problem Optimal forward investment in an incomplete market with model uncertainty.
method Combining stochastic differential games and ergodic BSDE approach.
result Representation of robust forward performance processes in factor form.
Scale-invariant Truncated Lévy Processcond-mat.stat-mech
We develop a scale-invariant truncated Lévy (STL) process to describe physical systems characterized by correlated stochastic variables. The STL process exhibits Lévy stability for the probability density, and hence shows scaling properties (as observed in empirical data); it has the advantage that all moments are fini…
Flow Annealing Posterior Sampling unifies stochastic-process regression and PDE inverse problems.
problem Function-space posterior sampling for stochastic processes and inverse problems.
method Flow Annealing Posterior Sampling (FAPS) using pretrained function-space flow-matching priors.
result Coherent posterior samples with accurate uncertainty quantification.
Gaussian stochastic volatility models: Scaling regimes, large deviations, and moment explosionsq-fin.MF
In this paper, we establish sample path large and moderate deviation principles for log-price processes in Gaussian stochastic volatility models, and study the asymptotic behavior of exit probabilities, call pricing functions, and the implied volatility. In addition, we prove that if the volatility function in an uncor…
Model strategic interactions between market makers and traders to optimize execution.
problem Optimizing execution in markets with strategic interactions.
method Stochastic game modeling with FBSDEs and decoupling approach.
result Established Nash equilibria and global well-posedness for specific models.
Recent empirical studies suggest that the volatility of an underlying price process may have correlations that decay slowly under certain market conditions. In this paper, the volatility is modeled as a stationary process with long-range correlation properties in order to capture such a situation, and we consider Europ…
We propose a novel algorithm - Multifractal Cross-Correlation Analysis (MFCCA) - that constitutes a consistent extension of the Detrended Cross-Correlation Analysis (DCCA) and is able to properly identify and quantify subtle characteristics of multifractal cross-correlations between two time series. Our motivation for …
We analyze the properties of arguably the simplest bilinear stochastic multiplicative process, proposed as a model of financial returns and of other complex systems combining both nonlinearity and multiplicative noise. By construction, it has no linear predictability (zero two-point correlation) but a certain nonlinear…