Stochastic Finance: An Introduction in Discrete Time

Description

This book is an introduction to financial mathematics. The first part of the book studies a simple one-period model which 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 risk. In the second part, the idea of dynamic hedging of contingent claims is developed in a multiperiod framework. Such models are typically incomplete: They involve intrinsic risks which cannot be hedged away completely. Topics include martingale measures, pricing formulas for derivatives, American options, superhedging, and hedging strategies with minimal shortfall risk. In addition to many corrections and improvements, this second edition contains several new sections, including a systematic discussion of law-invariant risk measures and of the connections between American options, superhedging, and dynamic risk measures. Standard refence book for stochastic finance in discrete time Now with exercises Suitable for students, researchers and practioneers Preface to the second edition Preface to the first edition Contents Part I. Mathematical finance in one period Chapter 1. Arbitrage theory Chapter 2. Preferences Chapter 3. Optimality and equilibrium Chapter 4. Monetary measures of risk Part II. Dynamic hedging Chapter 5. Dynamic arbitrage theory Chapter 6. American contingent claims Chapter 7. Superhedging Chapter 8. Efficient hedging Chapter 9. Hedging under constraints Chapter 10. Minimizing the hedging error Appendix Notes Bibliography List of symbols Index