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

By: Contributor(s): Material type: TextTextSeries: De Gruyter TextbookPublisher: Berlin ; Boston : De Gruyter, [2016]Copyright date: ©2016Edition: 4th rev. edDescription: 1 online resource (596 p.)Content type:
Media type:
Carrier type:
ISBN:
  • 9783110463446
  • 9783110463460
  • 9783110463453
Subject(s): DDC classification:
  • 332/.01/519232 21
Other classification:
  • online - DeGruyter
Online resources:
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
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
Holdings
Item type Current library Call number URL Status Notes Barcode
eBook eBook Biblioteca "Angelicum" Pont. Univ. S.Tommaso d'Aquino Nuvola online online - DeGruyter (Browse shelf(Opens below)) Online access Not for loan (Accesso limitato) Accesso per gli utenti autorizzati / Access for authorized users (dgr)9783110463453

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

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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

Mode of access: Internet via World Wide Web.

In English.

Description based on online resource; title from PDF title page (publisher's Web site, viewed 30. Aug 2021)