The Interval Market Model in Mathematical Finance: Game-Theoretic Methods

by Patrick Saint-Pierre, Jean-Pierre Aubin, Vassili Kolokoltsov, et al.

Book Overview

General introduction.-Part 1: Two classical problems revisited.- Merton's optimal dynamic portfolio revisited.- Probability free Black and Scholes theory.- Part 2: Robust control approach to option pricing.- Option pricing and the interval market model.- Vanilla options.- Digital options.- Validation: robustness and calibration.- Extensions.- Part 3: Tychastic approach to mathematical finance.- Some drawbacks of the stochastic approach.- Other mathematical models of uncertainty.- Example: cushion approach of asset-liability management of a portfolio.- Capture basin algorithm and application to option pricing.- Impulsive capture basin algorithm and applications to barrier options and the GARCH market model.- Part 4: Hedging in Interval Models.- Introduction: why hedging?.- The risk neutral valuation principle for options.- A numerical valuation procedure: the binomial tree model.- The fair price interval of an option.- Characterization of fair price intervals in terms of strategies and Martingale measures.-A case study: a comparison with the binomial tree model.- Some computational issues.- Part 5: Explicit Formulae for Rainbow Options and related topics.- Introduction: CRR and BS formulae via game theory.- Rainbow options depending on two or three underlying stocks.- Probabilistic interpretation.- Numerical algorithms.

• Format: Paperback
• Language: English
• ISBN: 1489985808
• ISBN13: 9781489985804
• Release Date: January 2015
• Publisher: Springer PG
• Length: 348 Pages
• Weight: 1.12 lbs.
• Dimensions: 0.8" x 6.1" x 9.2"