VIABLE CAPTURE BASIN FOR STUDYING DIFFERENTIAL AND HYBRID GAMES: APPLICATION TO FINANCE

Patrick Saint-Pierre
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Patrick Saint-Pierre: Centre de Recherche Viabilité, Jeux, Contrôle Université, Paris-Dauphine, F-75016 Paris, France

International Game Theory Review (IGTR), 2004, vol. 06, issue 01, 109-136

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.

Keywords: Viability; capturability; tychastic control; dynamical games; hedging portfolio (search for similar items in EconPapers)
JEL-codes: B4 C0 C6 C7 D5 D7 M2 (search for similar items in EconPapers)
Date: 2004
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DOI: 10.1142/S0219198904000101

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