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Linear-Quadratic Stochastic Differential Games with General Noise Processes

In: Models and Methods in Economics and Management Science

Author

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  • Tyrone E. Duncan

    (University of Kansas)

Abstract

In this paper a noncooperative, two person, zero sum, stochastic differential game is formulated and solved that is described by a linear stochastic system and a quadratic cost functional for the two players. The optimal strategies for the two players are given explicitly using a relatively simple direct method. The noise process for the two player linear system can be an arbitrary square integrable stochastic process with continuous sample paths. The special case of a fractional Brownian motion noise is explicitly noted.

Suggested Citation

  • Tyrone E. Duncan, 2014. "Linear-Quadratic Stochastic Differential Games with General Noise Processes," International Series in Operations Research & Management Science, in: Fouad El Ouardighi & Konstantin Kogan (ed.), Models and Methods in Economics and Management Science, edition 127, pages 17-25, Springer.
    • Handle: RePEc:spr:isochp:978-3-319-00669-7_2
    DOI: 10.1007/978-3-319-00669-7_2
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    Cited by:

    1. Tyrone E. Duncan & Hamidou Tembine, 2018. "Linear–Quadratic Mean-Field-Type Games: A Direct Method," Games, MDPI, vol. 9(1), pages 1-18, February.

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