DIFFERENTIAL GAME-THEORETIC THOUGHTS ON OPTION PRICING AND TRANSACTION COSTS

Geert Jan Olsder ()
Additional contact information
Geert Jan Olsder: Faculty of Information Technology and Systems, Delft University of Technology, P.O. Box 5031, 2600 GA Delft, The Netherlands

International Game Theory Review (IGTR), 2000, vol. 02, issue 02n03, 209-228

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.

JEL-codes: B4 C0 C6 C7 D5 D7 M2 (search for similar items in EconPapers)
Date: 2000
References: Add references at CitEc
Citations: View citations in EconPapers (3)

Downloads: (external link)
http://www.worldscientific.com/doi/abs/10.1142/S0219198900000135
Access to full text is restricted to subscribers

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:wsi:igtrxx:v:02:y:2000:i:02n03:n:s0219198900000135

Ordering information: This journal article can be ordered from

DOI: 10.1142/S0219198900000135

Access Statistics for this article

International Game Theory Review (IGTR) is currently edited by David W K Yeung

More articles in International Game Theory Review (IGTR) from World Scientific Publishing Co. Pte. Ltd.
Bibliographic data for series maintained by Tai Tone Lim ().