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.
Optimal dividend strategy found for risk models with regime switching.
Paper generalizes Bakry-Émery calculus for curvature and applies to Markov chains.
New empirical PAC-Bayes bound for Markov chains with finite state space.
The past decade has seen substantial work on the use of non-negative matrix factorization and its probabilistic counterparts for audio source separation. Although able to capture audio spectral structure well, these models neglect the non-stationarity and temporal dynamics that are important properties of audio. The re…
The paper advances U-statistics in dependent settings, improving spectral estimation and goodness-of-fit tests.
Estimates Markov chain mixing time from a single trajectory.
This paper considers magnitude, asymptotics and duration of drawdowns for some Lévy processes. First, we revisit some existing results on the magnitude of drawdowns for spectrally negative Lévy processes using an approximation approach. For any spectrally negative Lévy process whose scale functions are well-behaved at …
In most sampling algorithms, including Hamiltonian Monte Carlo, transition rates between states correspond to the probability of making a transition in a single time step, and are constrained to be less than or equal to 1. We derive a Hamiltonian Monte Carlo algorithm using a continuous time Markov jump process, and ar…
Researchers calculate the price of a perpetual put option in Lévy models.
Model reduction of Markov processes is a basic problem in modeling state-transition systems. Motivated by the state aggregation approach rooted in control theory, we study the statistical state compression of a discrete-state Markov chain from empirical trajectories. Through the lens of spectral decomposition, we study…
The paper defines and analyzes Poissonian occupation times for negative Lévy processes.
A simple linear algebraic explanation of the algorithm in "A Spectral Algorithm for Learning Hidden Markov Models" (COLT 2009). Most of the content is in Figure 2; the text just makes everything precise in four nearly-trivial claims.
Method estimates number of clusters in Block Markov Chain trajectories.
Paper proposes a new method for training diffusion models using Markov operators.
The study proves inequalities on curved spaces without global curvature bounds.
Non-negative curvature affects Markov chains' mixing and expansion properties.
The optimal dividend problem by De Finetti (1957) has been recently generalized to the spectrally negative Lévy model where the implementation of optimal strategies draws upon the computation of scale functions and their derivatives. This paper proposes a phase-type fitting approximation of the optimal strategy. We con…
Next-generation sequencing (NGS) to profile temporal changes in living systems is gaining more attention for deriving better insights into the underlying biological mechanisms compared to traditional static sequencing experiments. Nonetheless, the majority of existing statistical tools for analyzing NGS data lack the c…
A new model BGAR(1) improves temporal NMF for time series data.
A novel method relaxes binary constraints to non-negative spheres for multi-matching and clustering.
The paper constructs Markov partitions for geodesic flow on hyperbolic surfaces.
The paper bounds generalization errors for deep neural networks with Markov datasets.
The study finds sparse sets that uniquely determine metrics on negatively curved manifolds.
Study of multi-armed bandits with state-switching rewards using Markov models.
Electroencephalographic (EEG) monitoring of neural activity is widely used for sleep disorder diagnostics and research. The standard of care is to manually classify 30-second epochs of EEG time-domain traces into 5 discrete sleep stages. Unfortunately, this scoring process is subjective and time-consuming, and the defi…
New proof shows certain 3D spaces are essentially like infinite space.
In this note we give, for a spectrally negative Levy process, a compact formula for the Parisian ruin probability, which is defined by the probability that the process exhibits an excursion below zero, with a length that exceeds a certain fixed period r. The formula involves only the scale function of the spectrally ne…
A new method simulates a lazy version of a Markov chain for empirical inference.
The study proves Strichartz and spectral projection theorems on specific types of curved surfaces.
Consider a random vector with finite second moments. If its precision matrix is an M-matrix, then all partial correlations are non-negative. If that random vector is additionally Gaussian, the corresponding Markov random field (GMRF) is called attractive. We study estimation of M-matrices taking the role of inverse sec…
We propose a new reinforcement learning algorithm for partially observable Markov decision processes (POMDP) based on spectral decomposition methods. While spectral methods have been previously employed for consistent learning of (passive) latent variable models such as hidden Markov models, POMDPs are more challenging…
Paper improves spectral learning of HMMs to avoid local optima and improve robustness.
Sharp spectral estimates for negatively curved foliations.
We propose a new reinforcement learning algorithm for partially observable Markov decision processes (POMDP) based on spectral decomposition methods. While spectral methods have been previously employed for consistent learning of (passive) latent variable models such as hidden Markov models, POMDPs are more challenging…
In machine learning, a nonparametric forecasting algorithm for time series data has been proposed, called the kernel spectral hidden Markov model (KSHMM). In this paper, we propose a technique for short-term wind-speed prediction based on KSHMM. We numerically compared the performance of our KSHMM-based forecasting tec…
Algorithm learns mixtures of Markov chains and MDPs from short trajectories.
Extended Gauss-Markov theorem for linear estimation with bounded bias.
Hidden semi-Markov models (HSMMs) are latent variable models which allow latent state persistence and can be viewed as a generalization of the popular hidden Markov models (HMMs). In this paper, we introduce a novel spectral algorithm to perform inference in HSMMs. Unlike expectation maximization (EM), our approach cor…
Hidden Markov Models (HMMs) can be accurately approximated using co-occurrence frequencies of pairs and triples of observations by using a fast spectral method in contrast to the usual slow methods like EM or Gibbs sampling. We provide a new spectral method which significantly reduces the number of model parameters tha…
Proposes RNSE for clustering with adaptive similarity matrix learning.
Paper calculates the distribution of time spent below zero in risk models.
Study minimizes risk in MDPs with spectral measures.
Efficient private matrix analysis algorithms for recent variants.
Continuous Hidden Markov Models for Equity Returns
We study a portfolio selection problem in a continuous-time Itô-Markov additive market with prices of financial assets described by Markov additive processes which combine Lévy processes and regime switching models. Thus the model takes into account two sources of risk: the jump diffusion risk and the regime switching …
In the spirit of [Surya07'], we develop an average problem approach to prove the optimality of threshold type strategies for optimal stopping of Lévy models with a continuous additive functional (CAF) discounting. Under spectrally negative models, we specialize this in terms of conditions on the reward function and ran…
The optimal capital structure model with endogenous bankruptcy was first studied by Leland (1994) and Leland and Toft (1996), and was later extended to the spectrally negative Levy model by Hilberink and Rogers (2002) and Kyprianou and Surya (2007). This paper incorporates the scale effects by allowing the values of ba…
The paper finds optimal threshold strategies for insurance companies with a positive terminal value at creeping ruin.