A new process generalizes geometric Brownian motion with asymmetry.
problem Creating a positive process with asymmetry parameter.
method Introducing asymmetry parameter α to describe volatility at new lows.
result Preserves GBM properties while expressing volatility as weighted mean.
The paper ensures positivity of solutions to stochastic equations with positive initial data.
problem Ensuring positivity of solutions to stochastic equations with positive initial data.
method Providing sufficient conditions on coefficients for positivity of mild solutions.
result Sufficient conditions for positivity of solutions to stochastic equations.
Study adaptive sensing of Cox processes using posterior sampling and positive bases.
problem Adaptive sensing of Cox point processes with intensity function modeling.
method Model intensity function as truncated Gaussian process in positive basis, use Langevin dynamics and posterior sampling.
result Demonstrated improved sensing compared to classical Bayesian experimental design.
The paper introduces new processes for modeling multivariate volatility.
problem Developing new stochastic processes for multivariate volatility modeling.
method Introducing Volterra Wishart and Volterra pure jump processes with fractional kernels.
result Affine covariance processes for multivariate volatility modeling.
We constructively prove the existence of time-discrete consumption processes for stochastic money accounts that fulfill a pre-specified positively homogeneous projection property (PHPP) and let the account always be positive and exactly zero at the end. One possible example is consumption rates forming a martingale und…
The paper finds optimal threshold strategies for insurance companies with a positive terminal value at creeping ruin.
problem Optimizing dividend payments in an insurance company's surplus process with a positive terminal value at creeping ruin.
method Using fluctuation theory, the paper derives explicit formulas for the objective function and shows the optimality of threshold strategies.
result Threshold strategies are optimal for the dividend optimization problem under certain conditions.
Extends Gaussian process theory to Banach spaces.
problem Extending Gaussian process theory to Banach spaces.
method Investigates the connection between Gaussian processes and Gaussian random elements in reproducing kernel Banach spaces.
result Characterizes positive definite functions that arise from covariance operators in Banach space setting.
In this paper we consider a modified version of the classical optimal dividends problem of de Finetti in which the dividend payments subject to a penalty at ruin. We assume that the risk process is modeled by a general spectrally positive Levy process before dividends are deducted. Using the fluctuation theory of spect…
NP-PROV separates mean and variance spaces to improve function uncertainty.
problem Neural Processes fail on out-of-domain tasks due to shared latent space uncertainty.
method Separates mean and variance into function-value-related and position-related latent spaces.
result NP-PROV achieves state-of-the-art likelihood with bounded variance in drifts.
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…
New DKPP family controls positive and negative dependence in random subsets.
problem Challenges in seamlessly bridging probabilistic models for positive and negative dependence.
method Introduced DKPP family and developed computational methods for probabilistic operations and inference.
result Controllability of positive and negative dependence demonstrated through numerical experiments.
A new method for deep Wishart processes improves kernel-based models.
problem Inference in deep Wishart processes is challenging due to the need for flexible distributions over positive semi-definite matrices.
method Developed a novel approach to flexible distributions over positive semi-definite matrices using the Bartlett decomposition of the Wishart probability density. Used this to create an approximate posterior for the DWP.
result Improved performance of inference in the DWP compared to DGP with equivalent prior.
Paper measures cognitive bias in positive feedback trading using diffusion process estimates.
problem Measuring cognitive bias in positive feedback trading behavior.
method Conditional estimates of diffusion processes to quantify bias, proving asymptotic properties.
result Bias in positive feedback trading converges to zero over time, leading to adaptive expectations.
Paper introduces a new method for Transformers with linear complexity.
problem No efficient relative positional encoding for linear Transformer models.
method Stochastic Positional Encoding (SPE) that replaces classical RPE.
result SPE behaves like RPE and performs well on benchmarks.
Paper proposes a neural network to improve traffic flow forecasting.
problem Forecasting future traffic flow distribution in an area.
method Position-aware convolutional neural network integrating data features and position information.
result Our approach outperforms previous methods even with fewer data sources.
The Dirichlet random walk on manifolds has a positive escape rate if the cover is non-amenable.
problem Analyzing the stochastic behavior of Dirichlet random walks on manifolds.
method Defining a recursive process on Galoisian covers and proving a theorem about the escape rate.
result The escape rate is positive if and only if the cover is non-amenable.
Novel GP-modulated Cox process framework with linear inequality constraints.
problem Modeling point patterns with positiveness and inequality constraints.
method Directly impose positiveness and inequality constraints on the Gaussian process without restrictions on covariance functions.
result Accurate inference of intensity functions with improved results for monotonic processes.
We simplify Volterra process predictions by reducing dimensionality and using a tailored deep learning model.
problem Predicting the conditional law of Volterra processes with stochastic volatility is challenging due to high dimensionality and non-smoothness.
method We developed a stable dimension reduction technique onto a low-dimensional statistical manifold of non-positive curvature and introduced a sequentially deep learning model tailored to this geometry.
result Our model can approximate the conditional law of Volterra processes with approximation rates achievable only with very large networks.
Paper introduces a new pricing model for Uniswap V3 positions.
problem Valuation of Uniswap V3 liquidity positions.
method Stochastic processes and Martingale Stopping Theorem.
result Model provides significant insights into risk exposure and hedging strategies.
Study optimal periodic dividend strategies for risky businesses with transaction costs.
problem Optimal periodic dividend strategies for spectrally positive Lévy risk processes with fixed transaction costs.
method Investigates periodic (bu,bl) strategies for a Poisson arrival process of decision times. result A periodic (bu,bl) strategy is optimal with lump sum dividends net of transaction costs. Model predicts jump risk premia influencing cryptocurrency futures and option performance.
problem Capturing asymmetric and time-varying skewness in cryptocurrency returns.
method Bivariate Hawkes process with positive and negative jump premia.
result Inferred jump risk premia predict futures cost of carry and option performance.
GP-ND avoids obstacles in trajectory planning using Gaussian Process regression.
problem Avoiding obstacles in trajectory planning for real-world systems.
method GP-ND models negative data pairs using Gaussian distributions and maximizes their KL divergence from the GP to avoid them.
result GP-ND outperforms traditional GP learning in obstacle-aware trajectory planning.
We consider a version of the stochastic inventory control problem for a spectrally positive Lévy demand process, in which the inventory can only be replenished at independent exponential times. We show the optimality of a periodic barrier replenishment policy that restocks any shortage below a certain threshold at each…
Order positions are key variables in algorithmic trading. This paper studies the limiting behavior of order positions and related queues in a limit order book. In addition to the fluid and diffusion limits for the processes, fluctuations of order positions and related queues around their fluid limits are analyzed. As a…
We propose an approach to reduce both computational complexity and data storage requirements for the online positioning stage of a fingerprinting-based indoor positioning system (FIPS) by introducing segmentation of the region of interest (RoI) into sub-regions, sub-region selection using a modified Jaccard index, and …
IDPGs extend RDPGs with a Poisson process for random latent positions.
problem Modeling randomness in latent positions for graph structure.
method Introduce IDPGs using Poisson point processes on latent Euclidean space.
result Continuous analogues of adjacency matrices link latent structure to observed graphs.
We model messaging activities as a hierarchical doubly stochastic point process with three main levels, and develop an iterative algorithm for inferring actors' relative latent positions from a stream of messaging activity data. Each of the message-exchanging actors is modeled as a process in a latent space. The actors…
A wealth-process set is abstractly defined to consist of nonnegative càdlàg processes containing a strictly positive semimartingale and satisfying an intuitive re-balancing property. Under the condition of absence of arbitrage of the first kind, it is established that all wealth processes are semimartingales and that t…
New process explains asset volatility patterns.
problem Explains statistical relationship between asset volatility and returns.
method Uses multiplicative Langevin process with adjustable coherence time.
result Exactly equivalent to Inverse Gamma distribution for volatility.
Study on prescribing positive curvature with conical singularities on a sphere.
problem Prescribing positive curvature with conical singularities on a sphere.
method Fine analysis of bubble trees and an area identity in the convergence process.
result Criterion for nonexistence in an open region of the prescribing data.
In this paper we study the optimal dividend problem for a company whose surplus process evolves as a spectrally positive Levy process. This model including the dual model of the classical risk model and the dual model with diffusion as special cases. We assume that dividends are paid to the shareholders according to ad…
Optimal stopping strategy for a Lévy process near its supremum.
problem Predicting optimal stopping distance for a Lévy process.
method Characterization using scale functions and threshold analysis.
result Non-trivial stopping strategy based on a threshold.
This paper tackles tweet classification by identifying purpose and position.
problem Difficulties in determining user intention and attitude in short, informal tweets.
method Transformed tweet classification into a multi-label problem and applied a multi-label classification method with post-processing.
result The method effectively classifies tweet purpose and position, outperforming individual classification methods.
In this paper we want to exploit further the semi-discrete method appeared in Halidias and Stamatiou (2015). We are interested in the numerical solution of mean reverting CEV processes that appear in financial mathematics models and are described as non negative solutions of certain stochastic differential equations wi…
We put forward a complete theory on moment explosion for fairly general state-spaces. This includes a characterization of the validity of the affine transform formula in terms of minimal solutions of a system of generalized Riccati differential equations. Also, we characterize the class of positive semidefinite process…
Defines a new process for financial modeling.
problem Developing a new stochastic process for financial applications.
method Introduces a fractional Cox-Ingersoll-Ross process and proves its properties.
result The process has unique solutions and is strictly positive for certain Hurst parameters.
Study on measure-valued CARMA processes in Banach spaces.
problem Modeling dynamics of functionals of spatio-temporal random fields.
method Defined measure-valued CARMA processes and derived conditions for stationarity.
result Positive measure-valued CARMA processes can model spatio-temporal random fields.
DEDPUL improves PU learning by estimating proportions and classifying unlabeled data.
problem Analog to supervised binary classification with only positive samples clean and unlabeled mixtures of positive and negative.
method Applies a post-processing procedure to any classifier trained to distinguish positive and unlabeled data, estimating proportions alongside classification.
result Outperforms state-of-the-art in both proportion estimation and PU classification.
Study optimizes trading strategies in markets with transaction costs and uncertain models.
problem Optimizing trading strategies in markets with transaction costs and model uncertainty.
method Maximizing worst-case expected utility over a class of models on a filtered probability space.
result Existence of optimal trading strategies for general càdlàg price processes and incomplete filtrations.
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 …
Introduces a new Hawkes model with CARMA(p,q) intensity to better model dependence structures.
problem Modeling dependence structures in time series data with realistic autocorrelation functions.
method Develops a Hawkes process with CARMA(p,q) intensity to capture more complex dependencies.
result The CARMA(p,q)-Hawkes model can reproduce more realistic dependence structures and is stationary and positive.
We consider a heat kernel approach for the development of stochastic pricing kernels. The kernels are constructed by positive propagators, which are driven by time-inhomogeneous Markov processes. We multiply such a propagator with a positive, time-dependent and decreasing weight function, and integrate the product over…
Let $({\M}, g(t))$ be a Kähler Ricci flow with positive first Chern class. We prove a uniform isoperimetric inequality for all time. In the process we also prove a Cheng-Yau type log gradient bound for positive harmonic functions on $({\M}, g(t))$, and a Poincaré inequality without assuming the Ricci curvature is bound…
It is well known that neural networks with rectified linear units (ReLU) activation functions are positively scale-invariant. Conventional algorithms like stochastic gradient descent optimize the neural networks in the vector space of weights, which is, however, not positively scale-invariant. This mismatch may lead to…
In a semimartingale financial market model, it is shown that there is equivalence between absence of arbitrage of the first kind (a weak viability condition) and the existence of a strictly positive process that acts as a local martingale deflator on nonnegative wealth processes.
Derives RL framework for systems without velocity or acceleration measurements.
problem Learning control for systems with limited sensor data.
method Gaussian Process Regression with a novel derivative-free kernel.
result Improved estimation performance and data-efficiency compared to traditional methods.
A pair trade is a portfolio consisting of a long position in one asset and a short position in another, and it is a widely applied investment strategy in the financial industry. Recently, Ekström, Lindberg and Tysk studied the problem of optimally closing a pair trading strategy when the difference of the two assets is…
Positive paths connect diffeomorphisms on contact manifolds.
problem Defining and analyzing positivity in diffeomorphism groups of manifolds with contact structures.
method By examining paths of diffeomorphisms that are positively transverse to the contact distribution, showing flexibility and connecting diffeomorphisms.
result Any two diffeomorphisms on standard contact structure of R^(2n+1) can be connected by a positive path.