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

Robert J. Elliott, Tak Kuen Siu

Research output: Contribution to journalArticlepeer-review

68 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)271-291
Number of pages21
JournalAnnals of Operations Research
Issue number1
Publication statusPublished - Mar 2010
Externally publishedYes


  • Change of measures
  • Convex risk measure
  • Regime-switching HJB equation
  • Risk minimization
  • Stochastic differential game


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