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Viable Capture Basin For Studying Differential And Hybrid Games: Application To Finance

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  • PATRICK SAINT-PIERRE

    (Centre de Recherche Viabilité, Jeux, Contrôle Université, Paris-Dauphine, F-75016 Paris, France)

Abstract

Viability theory can be applied for determining viable capture basin for control problem in presence of uncertainty. We first recall the concepts of viability theory which allow to develop numerical methods for computing viable capture basin for control problems and guaranteed control problems. Recent developments of option pricing in the framework of dynamical games with constraints lead to the formulation of guaranteed valuation in terms of guaranteed viable-capture basin of a dynamical game. As an application we show how the viability/capturability algorithm evaluates and manages portfolios. Regarding viability/capturability issues, stochastic control is a particular use of tychastic control. We replace the standard translation of uncertainty by stochastic control problem by tychastic ones and the concept of stochastic viability by the one of guaranteed viability kernel. Considering the Cox–Rubinstein model, we extend algorithms for hedging portfolios in the presence of transaction costs and dividends using recent developments on hybrid calculus.

Suggested Citation

  • Patrick Saint-Pierre, 2004. "Viable Capture Basin For Studying Differential And Hybrid Games: Application To Finance," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 6(01), pages 109-136.
    • Handle: RePEc:wsi:igtrxx:v:06:y:2004:i:01:n:s0219198904000101
    DOI: 10.1142/S0219198904000101
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    More about this item

    Keywords

    Viability; capturability; tychastic control; dynamical games; hedging portfolio;
    All these keywords.

    JEL classification:

    • B4 - Schools of Economic Thought and Methodology - - Economic Methodology
    • C0 - Mathematical and Quantitative Methods - - General
    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D5 - Microeconomics - - General Equilibrium and Disequilibrium
    • D7 - Microeconomics - - Analysis of Collective Decision-Making
    • M2 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Economics

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