On risk minimizing portfolios under a Markovian regime-switching Black-Scholes economy

Robert Elliott () and Tak Kuen Siu

Annals of Operations Research, 2010, vol. 176, issue 1, 291 pages

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. Copyright Springer Science+Business Media, LLC 2010

Keywords: Risk minimization; Convex risk measure; Stochastic differential game; Regime-switching HJB equation; Change of measures (search for similar items in EconPapers)
Date: 2010
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Citations: View citations in EconPapers (22)

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DOI: 10.1007/s10479-008-0448-5

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