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Stochastic Analysis with Financial Applications

Part of the Progress in Probability Book Series (volume 65)

Editors: Kohatsu-Higa, Arturo; Privault, Nicolas; Sheu, Shuenn-Jyi

DOI: 10.1007/978-3-0348-0097-6

ISBN: 978-3-0348-0096-9

Publisher: Springer Basel - Springer Journals

Jul 12, 2011

11 - 20 of 22 Chapters

LitStream

Exponentially Stable Stationary Solutions for Delay Stochastic Evolution Equations

Luo, Jiaowan

Pages: 169 –178

[We establish some sufficient conditions ensuring existence, uniqueness and exponential stability of non-trivial stationary mild solutions for a class of delay stochastic partial differential equations. Some known results are generalized and improved.]
LitStream

Robust Stochastic Control and Equivalent Martingale Measures

Øksendal, Bernt; Sulem, Agnès

Pages: 179 –189

[We study a class of robust, or worst case scenario, optimal control problems for jump diffusions. The scenario is represented by a probability measure equivalent to the initial probability law. We show that if there exists a control that annihilates the noise coefficients in the state equation...
LitStream

Multi-valued Stochastic Differential Equations Driven by Poisson Point Processes

Ren, Jiagang; Wu, Jing

Pages: 191 –205

[We prove the existence and uniqueness of solutions of multi-valued stochastic differential equations driven by Poisson point processes when the domain of the multi-valued maximal monotone operator is the whole space Rd.]
LitStream

Sensitivity Analysis for Jump Processes

Takeuchi, Atsushi

Pages: 207 –219

[Consider stochastic differential equations with jumps. The goal in this paper is to study the sensitivity of the solution with respect to the initial point, under the conditions on the Lévy measure and the uniformly elliptic condition on the coefficients. The key tool is the martingale property...
LitStream

Quantifying Model Uncertainties in Complex Systems

Yang, Jiarui; Duan, Jinqiao

Pages: 221 –252

[Uncertainties are abundant in complex systems. Appropriate mathematical models for these systems thus contain random effects or noises. The models are often in the form of stochastic differential equations, with some parameters to be determined by observations. The stochastic differential...
LitStream

Convertible Bonds in a Defaultable Diffusion Model

Bielecki, Tomasz R.; Crépey, Stéphane; Jeanblanc, Monique; Rutkowski, Marek

Pages: 255 –298

[In this paper, we study convertible securities (CS) in a primary market model consisting of: a savings account, a stock underlying a CS, and an associated CDS contract (or, alternatively to the latter, a rolling CDS more realistically used as an hedging instrument). We model the dynamics of...
LitStream

A Convexity Approach to Option Pricing with Transaction Costs in Discrete Models

Chiang, Tzuu-Shuh; Sheu, Shuenn-Jyi

Pages: 299 –315

[We study the option pricing problems under transaction costs in a discrete financial model with a riskless bond and one risky asset. For general models with a transaction fee, a perfectly replicating portfolio (if it exists) may not be optimal, i.e., a perfectly replicating portfolio may cost...
LitStream

Completeness and Hedging in a Lévy Bond Market

Corcuera, José M.

Pages: 317 –330

[In this paper we analyze the completeness problem in a bond market where the short rate is driven by a non-homogeneous Lé process. Even though it is known that under certain conditions we have a kind of uniqueness of the risk neutral measure, little is known about how to hedge in this market. We...
LitStream

Asymptotically Efficient Discrete Hedging

Fukasawa, Masaaki

Pages: 331 –346

[The notion of asymptotic efficiency for discrete hedging is introduced and a discretizing strategy which is asymptotically efficient is given explicitly. A lower bound for asymptotic risk of discrete hedging is given, which is attained by a simple discretization scheme. Numerical results for...
LitStream

Efficient Importance Sampling Estimation for Joint Default Probability:The First Passage Time Problem

Han, Chuan-Hsiang

Pages: 347 –359

[Motivated from credit risk modeling, this paper extends the twodimensional first passage time problem studied by Zhou (2001) to any finite dimension by means of Monte Carlo simulation. We provide an importance sampling method to estimate the joint default probability, and apply the large...

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