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Models and Methods in Economics and Management Science pp 17–25Cite as

Linear-Quadratic Stochastic Differential Games with General Noise Processes

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Part of the book series: International Series in Operations Research & Management Science ((ISOR,volume 198))

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.

Research supported by NSF grants DMS 0808138 and DMS 1108884, AFOSR grants FA9550-09-12-1-0384 and FA9550-12-1-0384, and ARO grant W911NF-10-1-0248.

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Kansas, Lawrence, KS, 66045, USA

    Tyrone E. Duncan

Authors
  1. Tyrone E. Duncan
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Correspondence to Tyrone E. Duncan .

Editor information

Editors and Affiliations

  1. ESSEC Business School, Cergy Pontoise, France

    Fouad El Ouardighi

  2. Department of Management, Bar-Ilan University, Ramat-Gan, Israel

    Konstantin Kogan

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Duncan, T.E. (2014). Linear-Quadratic Stochastic Differential Games with General Noise Processes. In: El Ouardighi, F., Kogan, K. (eds) Models and Methods in Economics and Management Science. International Series in Operations Research & Management Science, vol 198. Springer, Cham. https://doi.org/10.1007/978-3-319-00669-7_2

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