Stochastic Finance: An Introduction in Discrete Time / Edition 2

Stochastic Finance: An Introduction in Discrete Time / Edition 2

by Hans Follmer, Alexander Schied
     
 

ISBN-10: 3110183463

ISBN-13: 9783110183467

Pub. Date: 11/28/2004

Publisher: De Gruyter, Walter, Inc.

Intended for graduate students in mathematics, this textbook is an introduction to probabilistic methods in finance that focuses on stochastic models in real time. It is based on courses taught by the authors at Humboldt U. and Technical U. in Germany. The core of the work is a dynamic arbitrage theory presented in the second section, but they first explain some of

Overview

Intended for graduate students in mathematics, this textbook is an introduction to probabilistic methods in finance that focuses on stochastic models in real time. It is based on courses taught by the authors at Humboldt U. and Technical U. in Germany. The core of the work is a dynamic arbitrage theory presented in the second section, but they first explain some of the main arguments in a more transparent one-period model. For the new edition they have simplified and clarified some of the material regarding robust representations of risk measures, arbitrage-free pricing of contingent claims, convergence to Black-Scholes prices, and stability under pasting with its connections to dynamically consistent coherent risk measures. They have also added several new sections discussing of law-invariant risk measures, concave distortions, and the relations between risk measures and Choquet integration. Annotation ©2005 Book News, Inc., Portland, OR

Product Details

ISBN-13:
9783110183467
Publisher:
De Gruyter, Walter, Inc.
Publication date:
11/28/2004
Series:
De Gruyter Studies in Mathematics Series
Edition description:
2nd rev. and extend. ed.
Pages:
470
Product dimensions:
6.80(w) x 9.60(h) x 1.10(d)
Age Range:
18 Years

Table of Contents

Introductionv
IMathematical finance in one period1
1Arbitrage theory3
1.1Assets, portfolios, and arbitrage opportunities3
1.2Absence of arbitrage and martingale measures6
1.3Derivative securities13
1.4Complete market models22
1.5Geometric characterization of arbitrage-free models26
1.6Contingent initial data30
2Preferences43
2.1Preference relations and their numerical representation44
2.2Von Neumann-Morgenstern representation50
2.3Expected utility60
2.4Uniform preferences74
2.5Robust preferences on asset profiles89
2.6Probability measures with given marginals103
3Optimality and equilibrium112
3.1Portfolio optimization and the absence of arbitrage112
3.2Exponential utility and relative entropy121
3.3Optimal contingent claims130
3.4Microeconomic equilibrium141
4Monetary measures of risk157
4.1Risk measures and their acceptance sets158
4.2Robust representation of convex risk measures163
4.3Convex risk measures on L[infinity]175
4.4Value at Risk179
4.5Measures of risk in a financial market191
4.6Shortfall risk198
IIDynamic hedging207
5Dynamic arbitrage theory209
5.1The multi-period market model209
5.2Arbitrage opportunities and martingale measures213
5.3European contingent claims219
5.4Complete markets231
5.5The binomial model234
5.6Convergence to the Black-Scholes price245
6American contingent claims257
6.1Hedging strategies for the seller257
6.2Stopping strategies for the buyer262
6.3Arbitrage-free prices272
6.4Lower Snell envelopes277
7Superhedging284
7.1P-supermartingales and upper Snell envelopes284
7.2Uniform Doob decomposition286
7.3Superhedging of American and European claims289
7.4Superhedging with derivatives298
8Efficient hedging309
8.1Quantile hedging309
8.2Hedging with minimal shortfall risk315
9Hedging under constraints326
9.1Absence of arbitrage opportunities326
9.2Uniform Doob decomposition333
9.3Upper Snell envelopes338
9.4Superhedging and risk measures345
10Minimizing the hedging error348
10.1Local quadratic risk348
10.2Minimal martingale measures358
10.3Variance-optimal hedging368
Appendix375
A.1Convexity375
A.2Absolutely continuous probability measures379
A.3The Neyman-Pearson lemma382
A.4The essential supremum of a family of random variables385
A.5Spaces of measures386
A.6Some functional analysis394

Customer Reviews

Average Review:

Write a Review

and post it to your social network

     

Most Helpful Customer Reviews

See all customer reviews >