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On The Singularities Of An Impulsive Differential Game Arising In Mathematical Finance

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  • PIERRE BERNHARD

    (I3S, University of Nice-Sophia Antipolis and CNRS, France)

Abstract

We investigate an impulse control differential game arising in a problem of option pricing in mathematical finance. In a previous paper, it was shown that its Value function in ℝ3could be described as a pair of functions affine in one of the variables, joined on a 2D manifold. Depending on the regions of the state space, this manifold is either a dispersal one, an equivocal one or a 2D focal manifold. A pair of PDE's were derived for the focal part. Here we show that irrespective of the nature of this manifold, it has to satisfy this same set of PDE's.

Suggested Citation

  • Pierre Bernhard, 2006. "On The Singularities Of An Impulsive Differential Game Arising In Mathematical Finance," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 8(02), pages 219-229.
    • Handle: RePEc:wsi:igtrxx:v:08:y:2006:i:02:n:s0219198906000874
    DOI: 10.1142/S0219198906000874
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    Citations

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    Cited by:

    1. Sadana, Utsav & Reddy, Puduru Viswanadha & Zaccour, Georges, 2021. "Nash equilibria in nonzero-sum differential games with impulse control," European Journal of Operational Research, Elsevier, vol. 295(2), pages 792-805.
    2. Naïma El Farouq & Pierre Bernhard, 2015. "Proportional Transaction Costs in the Robust Control Approach to Option Pricing: The Uniqueness Theorem," Post-Print hal-01090616, HAL.
    3. Seydel, Roland C., 2009. "Existence and uniqueness of viscosity solutions for QVI associated with impulse control of jump-diffusions," Stochastic Processes and their Applications, Elsevier, vol. 119(10), pages 3719-3748, October.
    4. Dmitry Gromov & Ekaterina Gromova, 2017. "On a Class of Hybrid Differential Games," Dynamic Games and Applications, Springer, vol. 7(2), pages 266-288, June.

    More about this item

    Keywords

    Differential games; robust control; impulse control; option pricing;
    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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