Stochastic Analysis with Financial Applications: Hong Kong 2009

by Arturo Kohatsu-Higa (Editor), Nicolas Privault (Editor), Shuenn-Jyi Sheu (Editor)

Overview

Shastic analysis has a variety of applications to biological systems as well as physical and engineering problems, and its applications to finance and insurance have bloomed exponentially in recent times. The goal of this book is to present a broad overview of the range of applications of shastic analysis and some of its recent theoretical developments. This includes numerical simulation, error analysis, parameter estimation, as well as control and robustness properties for shastic equations. The book also covers the areas of backward shastic differential equations via the (non-linear) G-Brownian motion and the case of jump processes. Concerning the applications to finance, many of the articles deal with the valuation and hedging of credit risk in various forms, and include recent results on markets with transaction costs.

Product Details

ISBN-13:	9783034803373
Publisher:	Springer Basel
Publication date:	11/27/2013
Series:	Progress in Probability Series , #65
Edition description:	2011
Pages:	430
Product dimensions:	6.10(w) x 9.25(h) x 0.04(d)

Table of Contents

Part I: Shastic Analysis.- Dirichlet forms for Poisson measures and Lévy processes: the lent particle method.- Backward shastic difference equations with finite states.- On a forward-backward shastic system associated to the Burgers equation.- Quantifying model uncertainties in complex systems.- On the estimate for commutators in DiPerna-Lions theory.- Approximation theorem for shastic differential equations driven by G-Brownian motion.- Shastic flows for nonlinear SPDEs driven by linear multiplicative space-time white noises.- Optimal stopping problem associated with jump-diffusion processes.- A review of recent results on approximation of solutions of shastic differential equations.- Strong consistency of Bayesian estimator under discrete observations and unknown transition density.- Stability of a nonlinear equation related to a spatially-inhomogeneous branching process.- Exponentially stable stationary solutions for delay shastic evolution equations.- Robust shastic control and equivalent martingale measures.- Multivalued shastic differential questions driven by point processes.- Logarithmic derivatives of densities for jump processes.- Part II: Financial Applications.- Convertible bonds in a defaultable diffusion model.- A geometric approach to option pricing with transaction costs in discrete models.- Completeness and hedging in a Lévy bond market.- Asymptotically efficient discrete hedging.- Estimating joint default probability by efficient importance sampling with applications from bottom up.- Market models of forward CDS spreads.- Optimal threshold dividend strategies under the compound Poisson model with regime switching.