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We consider the problem of hedging a European contingent claim in a Bachelier model with transient price impact as proposed by Almgren and Chriss. Following the approach of Rogers and Singh and Naujokat and Westray, the hedging problem can…

Mathematical Finance · Quantitative Finance 2016-07-27 Peter Bank , Mete Soner , Moritz Voß

In this paper, we analyze the generalization performance of the Iterative Hard Thresholding (IHT) algorithm widely used for sparse recovery problems. The parameter estimation and sparsity recovery consistency of IHT has long been known in…

Machine Learning · Statistics 2022-03-18 Xiao-Tong Yuan , Ping Li

This paper introduces a novel boundary integral approach of shape uncertainty quantification for the Helmholtz scattering problem in the framework of the so-called parametric method. The key idea is to construct an integration grid whose…

Computational Engineering, Finance, and Science · Computer Science 2018-11-29 Yuval Harness

This paper presents the first analysis of a space--time hybridizable discontinuous Galerkin method for the advection--diffusion problem on time-dependent domains. The analysis is based on non-standard local trace and inverse inequalities…

Numerical Analysis · Mathematics 2023-07-06 Keegan L. A. Kirk , Tamas L. Horvath , Aycil Cesmelioglu , Sander Rhebergen

We study a continuous-time, finite horizon, stochastic partially reversible investment problem for a firm producing a single good in a market with frictions. The production capacity is modeled as a one-dimensional, time-homogeneous, linear…

Optimization and Control · Mathematics 2014-11-13 Tiziano De Angelis , Giorgio Ferrari

In this paper, we introduce a modification of the free boundary problem related to optimal stopping problems for diffusion processes. This modification allows the application of this PDE method in cases where the usual regularity…

Probability · Mathematics 2008-12-18 Ludger Rüschendorf , Mikhail A. Urusov

Progressive Hedging is a popular decomposition algorithm for solving multi-stage stochastic optimization problems. A computational bottleneck of this algorithm is that all scenario subproblems have to be solved at each iteration. In this…

Distributed, Parallel, and Cluster Computing · Computer Science 2020-09-28 Gilles Bareilles , Yassine Laguel , Dmitry Grishchenko , Franck Iutzeler , Jérôme Malick

We investigate the asymptotic behavior, in the long time limit, of the random homology associated to realizations of stochastic diffusion processes on a compact Riemannian manifold. In particular a rigidity result is established: if the…

Probability · Mathematics 2024-06-26 Artem Galkin , Mauro Mariani

In this work, we consider the hedging error due to discrete trading in models with jumps. Extending an approach developed by Fukasawa [In Stochastic Analysis with Financial Applications (2011) 331-346 Birkh\"{a}user/Springer Basel AG] for…

Risk Management · Quantitative Finance 2014-04-29 Mathieu Rosenbaum , Peter Tankov

We consider parametric inference for an ergodic and stationary diffusion process, when the data are high-frequency observations of the integral of the diffusion process. Such data are obtained via certain measurement devices, or if…

Statistics Theory · Mathematics 2026-02-09 Emil S. Jørgensen , Michael Sørensen

There is a wide range of stabilized finite element methods for stationary and non-stationary convection-diffusion equations such as streamline diffusion methods, local projection schemes, subgrid-scale techniques, and continuous interior…

Numerical Analysis · Mathematics 2014-02-25 L. Tobiska , R. Verfürth

In this paper, we develop a family of high order asymptotic preserving schemes for some discrete-velocity kinetic equations under a diffusive scaling, that in the asymptotic limit lead to macroscopic models such as the heat equation, the…

Numerical Analysis · Mathematics 2013-06-04 Juhi Jang , Fengyan Li , Jing-Mei Qiu , Tao Xiong

Boundary integral methods are attractive for solving homogeneous linear constant coefficient elliptic partial differential equations on complex geometries, since they can offer accurate solutions with a computational cost that is linear or…

Numerical Analysis · Mathematics 2023-01-25 Fredrik Fryklund , Sara Pålsson , Anna-Karin Tornberg

This paper develops a mathematical framework for the analysis of continuous-time trading strategies which, in contrast to the classical setting of continuous-time mathematical finance, does not rely on stochastic integrals or other…

Mathematical Finance · Quantitative Finance 2016-02-17 Candia Riga

We present analytic solutions for steady flow of the Johnson-Segalman (JS) model with a diffusion term in various geometries and under controlled strain rate conditions, using matched asymptotic expansions. The diffusion term represents a…

Soft Condensed Matter · Physics 2009-09-25 O Radulescu , P. D. Olmsted

In this paper, we consider a microscopic semilinear elliptic equation posed in periodically perforated domains and associated with the Fourier-type condition on internal micro-surfaces. The first contribution of this work is the…

Analysis of PDEs · Mathematics 2020-03-04 Vo Anh Khoa , Thieu Thi Kim Thoa , Ekeoma Rowland Ijioma

Two characteristics that make convex decomposition algorithms attractive are simplicity of operations and generation of parallelizable structures. In principle, these schemes require that all coordinates update at the same time, i.e., they…

Optimization and Control · Mathematics 2018-03-07 Giorgos Stathopoulos , Colin N. Jones

Convergence of an adaptive collocation method for the stationary parametric diffusion equation with finite-dimensional affine coefficient is shown. The adaptive algorithm relies on a recently introduced residual-based reliable a posteriori…

Numerical Analysis · Mathematics 2021-06-17 Martin Eigel , Oliver Ernst , Björn Sprungk , Lorenzo Tamellini

We study the approximation of certain stochastic integrals with respect to a d-dimensional diffusion by corresponding stochastic integrals with piece-wise constant integrands. In finance this corresponds to replacing a continuously adjusted…

Probability · Mathematics 2007-05-23 Mika Hujo

Statistical static timing analysis (SSTA) is studied from the point of view of mathematical optimization. We present two formulations of the problem of finding the critical path delay distribution that were not known before: (i) a…

Optimization and Control · Mathematics 2023-10-03 Adam Bosak , Dmytro Mishagli , Jakub Marecek