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.
The paper characterizes potential functions whose level sets are orbits in mechanical systems.
Paper proves existence and uniqueness of solutions to PIDEs in Bessel spaces for option pricing.
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…
Paper analyzes multidimensional PIDEs for financial modeling, proving existence and uniqueness in Bessel spaces.
In science and especially in economics, agent-based modeling has become a widely used modeling approach. These models are often formulated as a large system of difference equations. In this study, we discuss two aspects, numerical modeling and the probabilistic description for two agent-based computational economic mar…
Study improves parameter estimation for SDEs driven by Levy noise.
This paper studies a class of optimal multiple stopping problems driven by Lévy processes. Our model allows for a negative effective discount rate, which arises in a number of financial applications, including stock loans and real options, where the strike price can potentially grow at a higher rate than the original d…
A new model that combines economic growth rate fluctuations at the microscopic and macroscopic level is presented. At the microscopic level, firms are growing at different rates while also being exposed to idiosyncratic shocks at the firm and sector level. We describe such fluctuations as independent Lévy-stable fluctu…
Study of degenerate contrast functions on Lie groupoids and their geometric structures.
Study of manifolds with flat connections and diagonal metrics leading to vanishing Euler characteristic.
In this paper we study perpetual American call and put options in an exponential Lévy model. We consider a negative effective discount rate which arises in a number of financial applications including stock loans and real options, where the strike price can potentially grow at a higher rate than the original discount f…
The paper analyzes insurance risk with Parisian ruin and capital injection.
These lectures notes aim at introducing Lévy processes in an informal and intuitive way, accessible to non-specialists in the field. In the first part, we focus on the theory of Lévy processes. We analyze a `toy' example of a Lévy process, viz. a Lévy jump-diffusion, which yet offers significant insight into the distri…
The Levy-Levy-Solomon model (A microscopic model of the stock market: cycles, booms, and crashes, Economic Letters 45 (1))is one of the most influential agent-based economic market models. In several publications this model has been discussed and analyzed. Especially Lux and Zschischang (Some new results on the Levy, L…
The problem of an arbitrary truncated Levy flight description using the method of cumulant approach has been solved. The set of cumulants of the truncated Levy distribution given the assumption of arbitrary truncation has been found. The influence of truncation shape on the truncated Levy flight properties in the Gauss…
Develops information geometry for Lévy processes in finance.
Study of Yang-Mills fields on 4-manifolds using modified Lévy Laplacians.
New method for efficient pricing of double barrier options in Lévy models.
Study of financial models using PIDEs with and without market liquidity.
The pricing of options in exponential Levy models amounts to the computation of expectations of functionals of Levy processes. In many situations, Monte-Carlo methods are used. However, the simulation of a Levy process with infinite Levy measure generally requires either to truncate small jumps or to replace them by a …
Efficient methods for Lévy models using SINH-regular processes.
Study of Lévy flights on Zoll surfaces, revealing geometric information.
Study shows convergence rates for BSDEs approximated by compound Poisson processes.
Levy copulas are the most general concept to capture jump dependence in multivariate Levy processes. They translate the intuition and many features of the copula concept into a time series setting. A challenge faced by both, distributional and Levy copulas, is to find flexible but still applicable models for higher dim…
Motivated by the pricing of lookback options in exponential Lévy models, we study the difference between the continuous and discrete supremum of Lévy processes. In particular, we extend the results of Broadie et al. (1999) to jump-diffusion models. We also derive bounds for general exponential Lévy models.
We introduce an algorithm for the pricing of finite expiry American options driven by Lévy processes. The idea is to tweak Carr's `Canadisation' method, cf. Carr [9] (see also Bouchard et al [5]), in such a way that the adjusted algorithm is viable for any Lévy process whose law at an independent, exponentially distrib…
Study of bandit problem with Poisson decision times and Lévy processes.
The paper constructs CR manifolds with arbitrary Levi nondegeneracy.
Paper calculates perpetual American put option pricing with drawdown event in Lévy market.
In this note we apply the recently established Wiener-Hopf Monte Carlo (WHMC) simulation technique for Levy processes from Kuznetsov et al. [17] to path functionals, in particular first passage times, overshoots, undershoots and the last maximum before the passage time. Such functionals have many applications, for inst…
Study of Yamabe solitons on specific geometric manifolds.
Extends Gaussian process regression for non-Gaussian data.
Analyzes Lévy flights on manifolds for finding small targets.
The Levy Laplacian is studied on manifolds, with heat flow solutions tending to constant functionals over time.
Paper extends Lévy models with memory to better price FX double barrier options.
Sequences of Levy transformations for the Darboux system of conjugates nets in multidimensions are studied. We show that after a suitable number of Levy transformations, with at least a Levy transformation in each direction, we get closed formulae in terms of multi-Wroński determinants. These formulae are for the tange…
We construct a complete convergent normal form for a real hypersurface in $\CC{N},\,N\geq 2$ at generic Levi degeneracy. This seems to be the first convergent normal form for a Levi-degenerate hypersurface. In particular, we obtain, in the spirit of the work of Chern and Moser \cite{chern}, distinguished curves in the …
We study curvature restrictions of Levi-flat real hypersurfaces in complex projective planes, whose existence is in question. We focus on its totally real Ricci curvature, the Ricci curvature of the real hypersurface in the direction of the Reeb vector field, and show that it cannot be greater than -4 along a Levi-flat…
This brief manuscript provides an introduction to Lévy processes and their applications in finance as the random process that drives asset models. Characteristic functions and random variable generators of popular Lévy processes are presented in R.
Method extends option valuation for 2D Lévy models.
Bayesian inference for Levy density with Gibbs posterior in discrete sampling.
This is a continuation of our previous paper [14]. In [14], we introduced the first Aeppli-Chern class on compact complex manifolds, and proved that the curvature form of the Levi-Civita connection represents the first Aeppli-Chern class which is a natural link between Riemannian geometry and complex geometry. …
In this paper, we study the geometry of compact complex manifolds with Levi-Civita Ricci-flat metrics and prove that compact complex surfaces admitting Levi-Civita Ricci-flat metrics are Kahler Calabi-Yau surfaces or Hopf surfaces.
This paper presents hedging strategies for European and exotic options in a Levy market. By applying Taylor's Theorem, dynamic hedging portfolios are con- structed under different market assumptions, such as the existence of power jump assets or moment swaps. In the case of European options or baskets of European optio…
The paper constructs Levi flat structures using structure sheaves and differential complexes.
DLPM replaces Gaussian noise with α-stable noise in DDPM, improving data distribution coverage and robustness.
Universal approximation for rough paths and Lévy processes.
Calibrating a Lévy process usually requires characterizing its jump distribution. Traditionally this problem can be solved with nonparametric estimation using the empirical characteristic functions (ECF), assuming certain regularity, and results to date are mostly in 1D. For multivariate Lévy processes and less smooth …