Stochastic Analysis with Financial Applications: Hong Kong 2009

✍ Scribed by Nicolas Bouleau, Laurent Denis (auth.), Arturo Kohatsu-Higa, Nicolas Privault, Shuenn-Jyi Sheu (eds.)

• Publisher: Birkhäuser Basel
• Year: 2011
• Tongue: English
• Leaves: 440
• Series: Progress in Probability 65
• Edition: 1
• Category: Library

✦ Synopsis

Stochastic 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 stochastic analysis and some of its recent theoretical developments. This includes numerical simulation, error analysis, parameter estimation, as well as control and robustness properties for stochastic equations. The book also covers the areas of backward stochastic 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.

Contributors:

T.R. Bielecki
N. Bouleau
S. Chakraborty
T.S. Chiang
S.N. Cohen
J.M. Corcuera
S. Crépey
A.B. Cruzeiro
L. Denis
J. Duan
R.J. Elliott
S. Fang
M. Fukasawa
F.Q. Gao
B. Goldys
S. Han
Y. Ishikawa
M. Jeanblanc
H. Jiang
B. Jourdain
A. Kohatsu-Higa
E.T. Kolkovska
H. Lee
L. Li
J.A. López-Mimbela
J. Luo
B. Øksendahl
J. Ren
M. Rutkowski
E. Shamarova
S.J. Sheu
A. Sulem
A. Takeuchi
N. Vaytis
R. Wang
J. Wei
J. Wu
J. Yang
H. Yang
K. Yasuda
X. Zhang

✦ Table of Contents

Front Matter....Pages i-ix
Front Matter....Pages 1-1
Dirichlet Forms for Poisson Measures and Lévy Processes: The Lent Particle Method....Pages 3-20
Stability of a Nonlinear Equation Related to a Spatially-inhomogeneous Branching Process....Pages 21-32
Backward Stochastic Difference Equations with Finite States....Pages 33-42
On a Forward-backward Stochastic System Associated to the Burgers Equation....Pages 43-59
On the Estimate for Commutators in DiPerna–Lions Theory....Pages 61-71
Approximation Theorem for Stochastic Differential Equations Driven by G -Brownian Motion....Pages 73-81
Stochastic Flows for Nonlinear SPDEs Driven by Linear Multiplicative Space-time White Noises....Pages 83-97
Optimal Stopping Problem Associated with Jump-diffusion Processes....Pages 99-120
A Review of Recent Results on Approximation of Solutions of Stochastic Differential Equations....Pages 121-144
Strong Consistency of Bayesian Estimator Under Discrete Observations and Unknown Transition Density....Pages 145-167
Exponentially Stable Stationary Solutions for Delay Stochastic Evolution Equations....Pages 169-178
Robust Stochastic Control and Equivalent Martingale Measures....Pages 179-189
Multi-valued Stochastic Differential Equations Driven by Poisson Point Processes....Pages 191-205
Sensitivity Analysis for Jump Processes....Pages 207-219
Quantifying Model Uncertainties in Complex Systems....Pages 221-252
Front Matter....Pages 253-253
Convertible Bonds in a Defaultable Diffusion Model....Pages 255-298
A Convexity Approach to Option Pricing with Transaction Costs in Discrete Models....Pages 299-315
Completeness and Hedging in a Lévy Bond Market....Pages 317-330
Asymptotically Efficient Discrete Hedging....Pages 331-346
Efficient Importance Sampling Estimation for Joint Default Probability:The First Passage Time Problem....Pages 347-359
Front Matter....Pages 253-253
Market Models of Forward CDS Spreads....Pages 361-411
Optimal Threshold Dividend Strategies under the Compound Poisson Model with Regime Switching....Pages 413-429

✦ Subjects

Probability Theory and Stochastic Processes; Quantitative Finance