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The Interval Market Model in Mathematical Finance: Game-Theoretic Methods
Paperback
Series: Static & Dynamic Game Theory: Foundations & Applications
Business GeneralInvesting & Finance
ISBN13: 9781489985804
Publisher: Springer Pg
Published: Jan 28 2015
Pages: 348
Weight: 1.12
Height: 0.75 Width: 6.14 Depth: 9.21
Language: English
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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