A Markovian regime-switching stochastic differential game for portfolio risk minimization

Robert J. Elliott; Tak Kuen Siu

doi:10.1109/ACC.2008.4586625

A Markovian regime-switching stochastic differential game for portfolio risk minimization

Robert J. Elliott, Tak Kuen Siu

Research output: Chapter in Book/Report/Conference proceeding › Conference proceeding contribution › peer-review

4 Citations (Scopus)

53 Downloads (Pure)

Abstract

A risk minimization problem is considered in a continuous-time Markovian regime-switching financial model modulated by a continuous-time, finite-state Markov chain. We interpret the states of the chain as different market regimes. A convex risk measure is used as a measure of risk and an optimal portfolio is determined by minimizing the convex risk measure of the terminal wealth. We explore the state of the art of the stochastic differential game to formulate the problem as a Markovian regime-switching version of a two-player, zero-sum stochastic differential game. A verification theorem for the Hamilton-Jacobi-Bellman (HJB) solution of the game is provided.

Original language	English
Title of host publication	Proceedings of the 2008 American Control Conference
Subtitle of host publication	Seattle, WA, USA, July 11-13, 2008
Editors	Naira Hovakimyan
Place of Publication	New York
Publisher	Institute of Electrical and Electronics Engineers (IEEE)
Pages	1017-1022
Number of pages	6
ISBN (Print)	9781424420797
DOIs	https://doi.org/10.1109/ACC.2008.4586625
Publication status	Published - 2008
Externally published	Yes
Event	2008 American Control Conference, ACC - Seattle, WA, United States Duration: 11 Jun 2008 → 13 Jun 2008

Other

Other	2008 American Control Conference, ACC
Country/Territory	United States
City	Seattle, WA
Period	11/06/08 → 13/06/08

Bibliographical note

Copyright 2008 IEEE. Reprinted from Proceedings of the 2008 American Control Conference. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Macquarie Universityâ€™s products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.

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10.1109/ACC.2008.4586625

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Elliott, R. J., & Siu, T. K. (2008). A Markovian regime-switching stochastic differential game for portfolio risk minimization. In N. Hovakimyan (Ed.), Proceedings of the 2008 American Control Conference: Seattle, WA, USA, July 11-13, 2008 (pp. 1017-1022). Article 4586625 Institute of Electrical and Electronics Engineers (IEEE). https://doi.org/10.1109/ACC.2008.4586625

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abstract = "A risk minimization problem is considered in a continuous-time Markovian regime-switching financial model modulated by a continuous-time, finite-state Markov chain. We interpret the states of the chain as different market regimes. A convex risk measure is used as a measure of risk and an optimal portfolio is determined by minimizing the convex risk measure of the terminal wealth. We explore the state of the art of the stochastic differential game to formulate the problem as a Markovian regime-switching version of a two-player, zero-sum stochastic differential game. A verification theorem for the Hamilton-Jacobi-Bellman (HJB) solution of the game is provided.",

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Elliott, RJ & Siu, TK 2008, A Markovian regime-switching stochastic differential game for portfolio risk minimization. in N Hovakimyan (ed.), Proceedings of the 2008 American Control Conference: Seattle, WA, USA, July 11-13, 2008., 4586625, Institute of Electrical and Electronics Engineers (IEEE), New York, pp. 1017-1022, 2008 American Control Conference, ACC, Seattle, WA, United States, 11/06/08. https://doi.org/10.1109/ACC.2008.4586625

A Markovian regime-switching stochastic differential game for portfolio risk minimization. / Elliott, Robert J.; Siu, Tak Kuen.
Proceedings of the 2008 American Control Conference: Seattle, WA, USA, July 11-13, 2008. ed. / Naira Hovakimyan. New York: Institute of Electrical and Electronics Engineers (IEEE), 2008. p. 1017-1022 4586625.

Research output: Chapter in Book/Report/Conference proceeding › Conference proceeding contribution › peer-review

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A Markovian regime-switching stochastic differential game for portfolio risk minimization

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