On risk minimizing portfolios under a Markovian regime-switching Black-Scholes economy |
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Authors: | Robert J Elliott Tak Kuen Siu |
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Institution: | 1.Haskayne School of Business,University of Calgary,Calgary,Canada;2.School of Mathematical Sciences,University of Adelaide,Adelaide,Australia;3.Department of Mathematics and Statistics,Curtin University of Technology,Perth,Australia |
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Abstract: | We consider a risk minimization problem in a continuous-time Markovian regime-switching financial model modulated by a continuous-time,
observable and finite-state Markov chain whose states represent different market regimes. We adopt a particular form of convex
risk measure, which includes the entropic risk measure as a particular case, as a measure of risk. The risk-minimization problem
is formulated as a Markovian regime-switching version of a two-player, zero-sum stochastic differential game. One important
feature of our model is to allow the flexibility of controlling both the diffusion process representing the financial risk
and the Markov chain representing macro-economic risk. This is novel and interesting from both the perspectives of stochastic
differential game and stochastic control. A verification theorem for the Hamilton-Jacobi-Bellman (HJB) solution of the game
is provided and some particular cases are discussed. |
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Keywords: | |
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