Related papers: Asymptotic Static Hedge via Symmetrization
The aim of this paper is to provide a mathematical contribution on the semi-static hedge of timing risk associated to positions in American-style options under a multi-dimensional market model. Barrier options are considered in the paper…
In the present paper, we introduce a numerical scheme for the price of a barrier option when the price of the underlying follows a diffusion process. The numerical scheme is based on an extension of a static hedging formula of barrier…
In this work, we study the optimal discretization error of stochastic integrals, in the context of the hedging error in a multidimensional It\^{o} model when the discrete rebalancing dates are stopping times. We investigate the convergence,…
In this manuscript, we present a novel approach for sampling from a continuous multivariate probability distribution, which may either be explicitly known (up to a normalization factor) or represented via empirical samples. Our method…
In this work we propose a nonlinear stabilization technique for convection-diffusion-reaction and pure transport problems discretized with space-time isogeometric analysis. The stabilization is based on a graph-theoretic artificial…
In this study, we investigate the Shallow Water Equations incorporating source terms accounting for Manning friction and a non-flat bottom topology. Our primary focus is on developing and validating numerical schemes that serve a dual…
The latter author, together with collaborators, proposed a numerical scheme to calculate the price of barrier options. The scheme is based on a symmetrization of diffusion process. The present paper aims to give a mathematical credit to the…
This thesis develops a mathematical framework for the analysis of continuous-time trading strategies which, in contrast to the classical setting of continuous-time finance, does not rely on stochastic integrals or other probabilistic…
In this paper we study the stochastic area swept by a regular time-homogeneous diffusion till a stopping time. This unifies some recent literature in this area. Through stochastic time change we establish a link between the stochastic area…
This paper investigates the simultaneous identification of a spatially dependent potential and the initial condition in a subdiffusion model based on two terminal observations. The existence, uniqueness, and conditional stability of the…
In this paper, we consider an inverse problem for a time-fractional diffusion equation with a nonlinear source. We prove that the considered problem is ill-posed, i.e. the solution does not depend continuously on the data. The problem is…
Many processes in chemistry, physics, and biology depend on thermally activated events in which the system changes its state by surmounting an activation barrier. Examples range from chemical reactions, protein folding, and nucleation…
We revisit the asymptotic bias analysis of the distributed Pareto optimization algorithm developed based on the diffusion strategies. We propose an alternative way to analyze the asymptotic bias of this algorithm at small step-sizes and…
In this work, high order asymptotic preserving schemes are constructed and analysed for kinetic equations under a diffusive scaling. The framework enables to consider different cases: the diffusion equation, the advection-diffusion equation…
The purpose of this work is to develop and study a distributed strategy for Pareto optimization of an aggregate cost consisting of regularized risks. Each risk is modeled as the expectation of some loss function with unknown probability…
We propose and analyze a stabilizing iteration scheme for the algorithmic implementation of model predictive control for linear discrete-time systems. Polytopic input and state constraints are considered and handled by means of so-called…
The paper presents a generalization of the local limit theorem on the convergence of inhomogeneous Markov chains to the diffusion limit for the case where the corresponding process coefficients satisfy weak regularity conditions and…
We present a semi-static hedging algorithm for callable interest rate derivatives under an affine, multi-factor term-structure model. With a traditional dynamic hedge, the replication portfolio needs to be updated continuously through time…
In incomplete financial markets not every contingent claim can be replicated by a self-financing strategy. The risk of the resulting shortfall can be measured by convex risk measures, recently introduced by F\"ollmer, Schied (2002). The…
We study the long-time dynamics of the nonlinear processes modeled by diffusion-transport partial differential equations in non-divergence form with drifts. The solutions are subject to some inhomogeneous Dirichlet boundary condition.…