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

Résumé/Abstract: We consider a risk minimization problem in a continuous-time Markovian regimeswitching financial model modulated by a continuous-time, observable and finitestate 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 proxy of risk. The riskminimization problem is formulated as a Markovian regime-switching version of a two-player, zerosum 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 games and stochastic control. A verification theorem for the Hamilton-Jacobi-Bellman (HJB) solution of the game is provided and some particular cases are discussed. (joint work with Tak Kuen Siu, Curtin University of Technology)