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On risk minimizing portfolios under a Markovian regime-switching Black-Scholes economy. (English) Zbl 1233.91242

Summary: 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.

MSC:

91G10 Portfolio theory
93E20 Optimal stochastic control
91A23 Differential games (aspects of game theory)
91B30 Risk theory, insurance (MSC2010)

Software:

RiskMetrics
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