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Differential Game-Theoretic Thoughts On Option Pricing And Transaction Costs

Author

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  • GEERT JAN OLSDER

    (Faculty of Information Technology and Systems, Delft University of Technology, P.O. Box 5031, 2600 GA Delft, The Netherlands)

Abstract

This paper investigates some differential game applications to option pricing mechanisms and related problems. Two players, an investor and "Nature", play a zero-sum game. The usual uncertainty modelling (log-normality for instance) in systems describing the price evolution of stocks is replaced by "Nature", a player who counteracts the investor as much as possible. A relationship between a restricted version of the Black-Scholes and the Hamilton-Jacobi-Bellman partial differential equations is given. This paper, is a first step to possibly solve various option pricing problems (with constraints and/or transactions costs for instance) by means of the available numerical software for optimal control problems. In the second part of the paper, another model, now with three players, is considered. The third player is the bank interested in maximising its own profits by choosing the right formula for transaction costs. Thus a three-person nonzero-sum game, with a special kind of Stackelberg information structure, results. Some simple examples hint in the direction that the bank will be a clear winner.

Suggested Citation

  • Geert Jan Olsder, 2000. "Differential Game-Theoretic Thoughts On Option Pricing And Transaction Costs," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 2(02n03), pages 209-228.
    • Handle: RePEc:wsi:igtrxx:v:02:y:2000:i:02n03:n:s0219198900000135
    DOI: 10.1142/S0219198900000135
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    Citations

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    Cited by:

    1. G. J. Olsder, 2009. "Phenomena in Inverse Stackelberg Games, Part 1: Static Problems," Journal of Optimization Theory and Applications, Springer, vol. 143(3), pages 589-600, December.
    2. Guang Zhu & Hu Liu & Mining Feng, 2018. "Sustainability of Information Security Investment in Online Social Networks: An Evolutionary Game-Theoretic Approach," Mathematics, MDPI, vol. 6(10), pages 1-19, September.
    3. G. J. Olsder, 2009. "Phenomena in Inverse Stackelberg Games, Part 2: Dynamic Problems," Journal of Optimization Theory and Applications, Springer, vol. 143(3), pages 601-618, December.

    More about this item

    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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