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

Pierre Bernhard, et al
Publisher: 
Birkhäuser
Publication Date: 
2013
Number of Pages: 
346
Format: 
Hardcover
Series: 
Static and Dynamic Game Theory: Foundations and Applications
Price: 
129.00
ISBN: 
9780817683870
Category: 
Monograph
We do not plan to review this book.

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.

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