[图书][B] Malliavin calculus for Lévy processes with applications to finance

GD Nunno, B Øksendal, F Proske - 2008 - Springer
The purpose of this chapter is to present an overview of recent results on stochastic control,
in particular, portfolio optimization, achieved via techniques of Malliavin calculus and …

[图书][B] Differentiable measures and the Malliavin calculus

VI Bogachev - 2010 - books.google.com
This book provides the reader with the principal concepts and results related to differential
properties of measures on infinite dimensional spaces. In the finite dimensional case such …

[图书][B] Stochastic calculus of variations in mathematical finance

P Malliavin - 2006 - Springer
Stochastic Calculus of Variations (or Malliavin Calculus) consists, in brief, in constructing
and exploiting natural differentiable structures on abstract probability spaces; in other words …

[图书][B] Stochastic Analysis in discrete and Continuous settings: with normal martingales

N Privault - 2009 - books.google.com
This monograph is an introduction to some aspects of stochastic analysis in the framework of
normal martingales, in both discrete and continuous time. The text is mostly self-contained …

Integration by parts formula for locally smooth laws and applications to sensitivity computations

V Bally, MP Bavouzet, M Messaoud - 2007 - projecteuclid.org
We consider random variables of the form F= f (V 1,…, V n), where f is a smooth function and
V i, i∈ ℕ, are random variables with absolutely continuous law pi (y) dy. We assume that pi …

Malliavin Calculus and Its Application to Robust Optimal Investment for an Insider

C Yu, Y Cheng - Mathematics, 2023 - mdpi.com
In the theory of portfolio selection, there are few methods that effectively address the
combined challenge of insider information and model uncertainty, despite numerous …

[HTML][HTML] Sensitivity analysis and density estimation for finite-time ruin probabilities

S Loisel, N Privault - Journal of computational and applied mathematics, 2009 - Elsevier
The goal of this paper is to obtain probabilistic representation formulas that are suitable for
the numerical computation of the (possibly non-continuous) density functions of infima of …

Grid-free computation of probabilistic safety with malliavin calculus

F Cosentino, H Oberhauser… - IEEE Transactions on …, 2023 - ieeexplore.ieee.org
This article concerns continuous-time, continuous-space stochastic dynamical systems
described by stochastic differential equations (SDE). It presents a new approach to compute …

A representation theorem and a sensitivity result for functionals of jump diffusions

G Di Nunno, B Øksendal - Mathematical analysis of random …, 2007 - World Scientific
We use white noise calculus for Lévy processes to obtain a representation formula for the
functionals of a jump diffusion. Then we use this to find an explicit formula for the Donsker …

Integration by parts for point processes and Monte Carlo estimation

N Privault, X Wei - Journal of applied probability, 2007 - cambridge.org
We develop an integration by parts technique for point processes, with application to the
computation of sensitivities via Monte Carlo simulations in stochastic models with jumps …