Research Catalog

Title

Change of time and change of measure / Ole E. Barndorff-Nielsen, Albert Shiryaev.

Author

Barndorff-Nielsen, O. E. (Ole E.)

Publication

Singapore ; London : World Scientific, ©2010.

Items in the Library & Off-site

Details

Additional Authors

Shiri︠a︡ev, A. N. (Alʹbert Nikolaevich)

Description

xvi, 305 pages; 24 cm

Summary

A comprehensive account of two topics that are of particular significance in both theoretical and applied stochastics: random change of time and change of probability law. The book comprehensively collects and integrates results from a number of scattered sources in the literature and discusses the importance of the results.

Series Statement

Advanced series on statistical science & applied probability ; v. 13

Uniform Title

Advanced series on statistical science & applied probability ; v. 13.

Subject

• Stochastic processes
• Stochastic Processes
• Diskreter stochastischer Prozess
• Lévy-Prozess
• Stetigkeit
• Stochastischer Prozess
• Wahrscheinlichkeitstheorie

Bibliography (note)

• Includes bibliographical references (p. 291-300) and index.

Contents

• Machine generated contents note: 1.1. Basic Definitions -- 1.2. Some Properties of Change of Time -- 1.3. Representations in the Weak Sense (X law = X o T), in the Strong Sense (X = X o T) and the Semi-strong Sense (Xa.s. = X o T). I. Constructive Examples -- 1.4. Representations in the Weak Sense (X law = X o T), Strong Sense (X = X o T) in the Semi-strong Sense (X a.s. = X o T). II. The Case of Continuous Local Martingales and Processes of Bounded Variation -- 2.1. Integral Representations of Local Martingales in the Strong Sense -- 2.2. Integral Representations of Local Martingales in a Semi-strong Sense -- 2.3. Stochastic Integrals Over the Stable Processes and Integral Representations -- 2.4. Stochastic Integrals with Respect to Stable Processes and Change of Time -- 3.1. Basic Definitions and Properties -- 3.2. Canonical Representation. Triplets of Predictable Characteristics -- 3.3. Stochastic Integrals with Respect to a Brownian Motion, Square-integrable Martingales, and Semimartingales -- 3.4. Stochastic Differential Equations -- 4.1. Stochastic Exponential and Stochastic Logarithm -- 4.2. Fourier Cumulant Processes -- 4.3. Laplace Cumulant Processes -- 4.4. Cumulant Processes of Stochastic Integral Transformation Xφ = φ·X -- 5.1. Processes with Independent Increments and Semimartingales -- 5.2. Processes with Stationary Independent Increments (Lévy Processes) -- 5.3. Sonic Properties of Sample Paths of Processes with Independent Increments -- 5.4. Some Properties of Sample Paths of Processes with Stationary Independent Increments (Lévy Processes) -- 6.1. Basic Definitions. Density Process -- 6.2. Discrete Version of Girsanov's Theorem -- 6.3. Semimartingale Version of Girsanov's Theorem -- 6.4. Esscher's Change of Measure -- 7.1. Linear and Exponential Lévy Models under Change of Measure -- 7.2. On the Criteria of Local Absolute Continuity of Two Measures of Lévy Processes -- 7.3. On the Uniqueness of Locally Equivalent Martingale-type Measures for the Exponential Lévy Models -- 7.4. On the Construction of Martingale Measures with Minimal Entropy in the Exponential Lévy Models -- 8.1. Some General Facts about Change of Time for Semimartingale Models -- 8.2. Change of Time in Brownian Motion. Different Formulations -- 8.3. Change of Time Given by Subordinators. I. Some Examples -- 8.4. Change of Time Given by Subordinators. II. Structure of the Triplets of Predictable Characteristics -- 9.1. Deviation from the Gaussian Property of the Returns of the Prices -- 9.2. Martingale Approach to the Study of the Returns of the Prices -- 9.3. Conditionally Gaussian Models. I. Linear (AR, MA, ARMA) and Nonlinear (ARCH, GARCH) Models for Returns -- 9.4. Conditionally Gaussian Models. II. IG- and GIG-distributions for the Square of Stochastic Volatility and GH-distributions for Returns -- 10.1. Basic Notions and Summary of Results of the Theory of Arbitrage. I. Discrete Time Models -- 10.2. Basic Notions and Summary of Results of the Theory of Arbitrage. II. Continuous-Time Models -- 10.3. Arbitrage in a Model of Buying/Selling Assets with Transaction Costs -- 10.4. Asymptotic Arbitrage: Some Problems -- 11.1. Overview of the Pricing Formulae for European Options -- 11.2. Overview of the Pricing Formulae for American Options -- 11.3. Duality and Symmetry of the Semimartingale Models -- 11.4. Call-Put Duality in Option Pricing Lévy Models -- 12.1. From Black[-]Scholes Theory of Pricing of Derivatives to the Implied Volatility, Smile Effect and Stochastic Volatility Models -- 12.2. Generalized Inverse Gaussian Subordinator and Generalized Hyperbolic Lévy Motion: Two Methods of Construction, Sample Path Properties -- 12.3. Distributional and Sample-path Properties of the Lévy Processes L(GIG) and L(GH) -- 12.4. On Some Others Models of the Dynamics of Prices. Comparison of the Properties of Different Models.
• Random change of time -- Integral representations and change of time in stochastic integrals -- Semi.

ISBN

• 9789814324472
• 9814324477

OCLC

• ocn644676674
• 644676674
• SCSB-9177973

Owning Institutions

Princeton University Library