A Markovian regime-switching stochastic differential game for portfolio risk minimization
Date
2008
Authors
Elliott, R.
Siu, T.
Editors
Advisors
Journal Title
Journal ISSN
Volume Title
Type:
Conference paper
Citation
Proceedings of the American Control Conference, 2008: pp.1017-1022
Statement of Responsibility
Robert J. Elliott and Tak Kuen Siu
Conference Name
American Control Conference (2008 : Seattle, Washington)
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.