Stochastic Finance : An Introduction in Discrete Time / Hans Föllmer, Alexander Schied.

Format:

Book

Author/Creator:

Föllmer, Hans, author.

Schied, Alexander, author.

Series:

De Gruyter Textbook

Language:

English

Subjects (All):

Finance--Statistical methods.

Finance.

Stochastic analysis.

Probabilities.

Physical Description:

1 online resource (608 p.)

Edition:

4th rev. ed.

Place of Publication:

Berlin ; Boston : De Gruyter, [2016]

Language Note:

English

Summary:

This book is an introduction to financial mathematics. It is intended for graduate students in mathematics and for researchers working in academia and industry.The focus on stochastic models in discrete time has two immediate benefits. First, the probabilistic machinery is simpler, and one can discuss right away some of the key problems in the theory of pricing and hedging of financial derivatives. Second, the paradigm of a complete financial market, where all derivatives admit a perfect hedge, becomes the exception rather than the rule. Thus, the need to confront the intrinsic risks arising from market incomleteness appears at a very early stage.The first part of the book contains a study of a simple one-period model, which also serves as a building block for later developments. Topics include the characterization of arbitrage-free markets, preferences on asset profiles, an introduction to equilibrium analysis, and monetary measures of financial risk.In the second part, the idea of dynamic hedging of contingent claims is developed in a multiperiod framework. Topics include martingale measures, pricing formulas for derivatives, American options, superhedging, and hedging strategies with minimal shortfall risk.This fourth, newly revised edition contains more than one hundred exercises. It also includes material on risk measures and the related issue of model uncertainty, in particular a chapter on dynamic risk measures and sections on robust utility maximization and on efficient hedging with convex risk measures. Contents:Part I: Mathematical finance in one periodArbitrage theoryPreferencesOptimality and equilibriumMonetary measures of riskPart II: Dynamic hedgingDynamic arbitrage theoryAmerican contingent claimsSuperhedgingEfficient hedgingHedging under constraintsMinimizing the hedging errorDynamic risk measures

Contents:

Frontmatter

Preface to the fourth edition

Preface to the third edition

Preface to the second edition

Preface to the first edition

Contents

Part I: Mathematical finance in one period

1. Arbitrage theory

2. Preferences

3. Optimality and equilibrium

4. Monetary measures of risk

Part II: Dynamic hedging

5. Dynamic arbitrage theory

6. American contingent claims

7. Superhedging

8. Efficient hedging

9. Hedging under constraints

10. Minimizing the hedging error

11. Dynamic risk measures

Appendix

Bibliographical notes

References

List of symbols

Index

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

Description based on online resource; title from PDF title page (publisher's Web site, viewed 26. Mrz 2019)

ISBN:

9783110463460

3110463466

9783110463453

3110463458

OCLC:

1001426503