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.
Introduces a new class of hybrid processes combining Markov chains and Hawkes processes.
problem Characterize and ensure existence and uniqueness of complex hybrid marked point processes.
method Defines hybrid marked point processes implicitly via intensity and state process interactions, proving existence and uniqueness under general assumptions.
result Proves existence and uniqueness of hybrid marked point processes, extending existing results.
Modeling time series with jumps using neural networks and stochastic processes.
problem Capturing the dynamics of time series with both continuous flows and discrete jumps.
method Introducing Neural Jump Stochastic Differential Equations (Neural JSDEs) that extend Neural Ordinary Differential Equations (Neural ODEs) with a stochastic process term.
result Demonstrated the model's predictive capabilities on various datasets, including Hawkes processes, Stack Overflow awards, medical records, and earthquake monitoring.
A new method for pricing derivatives using self-exciting dynamics and finite-difference transforms.
problem Pricing derivatives with accumulated marks using a self-exciting marked point process.
method Derive discounted pricing equation as a PIDE, transform to one-dimensional PIDEs, use Laplace/Fourier transform, approximate jump term, solve using finite difference scheme.
result Efficiently price derivatives with accumulated marks using a novel finite-difference and transform approach.
We study the stochastic control problem of maximizing expected utility from terminal wealth under a non-bankruptcy constraint. The wealth process is subject to shocks produced by a general marked point process. The problem of the agent is to derive the optimal insurance strategy which allows "lowering" the level of the…
We classify GL(2,R) invariant point markings over components of strata of Abelian differentials. Such point markings exist only when the component is hyperelliptic and arise from marking Weierstrass points or two points exchanged by the hyperelliptic involution. We show that these point markings can be used to determin…
This paper deals with numerical solutions of maximizing expected utility from terminal wealth under a non-bankruptcy constraint. The wealth process is subject to shocks produced by a general marked point process. The problem of the agent is to derive the optimal insurance strategy which allows "lowering" the level of t…
This paper models how features influence event triggers in high-dimensional networks.
problem Estimating context-dependent networks in high-dimensional marked point processes.
method Leveraging compositional time series and regularization methods, the paper considers autoregressive multinomial and logistic-normal models for network estimation.
result The logistic-normal model leads to a convex negative log-likelihood objective and captures dependence across categories.
We explore martingale and convex duality techniques to study optimal investment strategies that maximize expected risk-averse utility from consumption and terminal wealth. We consider a market model with jumps driven by (multivariate) marked point processes and so-called non-linear wealth dynamics which allows to take …
We introduce a new model in order to describe the fluctuation of tick-by-tick financial time series. Our model, based on marked point process, allows us to incorporate in a unique process the duration of the transaction and the corresponding volume of orders. The model is motivated by the fact that the "excitation" of …
We study body-and-hinge and panel-and-hinge chains in R^d, with two marked points: one on the first body, the other on the last. For a general chain, the squared distance between the marked points gives a Morse-Bott function on a torus configuration space. Maximal configurations, when the distance between the two marke…
The aim of this paper is to define a chain level refinement of the Batalin-Vilkovisky (BV) algebra structure on the homology of the free loop space of a closed, oriented C∞-manifold. For this purpose, we define a (nonsymmetric) cyclic dg operad which consists of "de Rham chains" of free loops with marked points…
We derive generalized estimators for a number of spatial statistics that have been used in the analysis of spatially resolved omics data, such as Ripley's K, H and L functions, clustering index, and degree of clustering, which allow these statistics to be calculated on data modelled by arbitrary random measures (RMs). …
Optimizes learning schedules for better memory retention.
problem Finding the best review schedule for spaced repetition.
method Flexible representation of spaced repetition using marked temporal point processes and optimal control for stochastic differential equations with jumps.
result Optimal reviewing schedule is the recall probability of content.
We introduce a new model for describing the fluctuations of a tick-by-tick single asset price. Our model is based on Markov renewal processes. We consider a point process associated to the timestamps of the price jumps, and marks associated to price increments. By modeling the marks with a suitable Markov chain, we can…
In this work we present a new approach on studying dynamical systems. Combining the two ways of expressing the uncertainty, using probabilistic theory and credibility theory, we have research the generalized fractional hybrid equations. We have introduced the concepts of generalized fractional Wiener process, generaliz…
It has been suggested that marked point processes might be good candidates for the modelling of financial high-frequency data. A special class of point processes, Hawkes processes, has been the subject of various investigations in the financial community. In this paper, we propose to enhance a basic zero-intelligence o…