On risk minimizing portfolios under a Markovian regime-switching Black-Scholes economy
On risk minimizing portfolios under a Markovian regime-switching Black-Scholes economy
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DOI：
10.1007/s10479-008-0448-5
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发表时间：
2010-04
影响因子：
4.8
通讯作者：
R. Elliott;T. Siu
中科院分区：
文献类型：
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作者：
R. Elliott;T. Siu
考虑了一个连续时间马尔可夫状态转换金融模型中的风险最小化问题，该模型由一个连续时间、可观测的有限状态马尔可夫链调制，其状态代表不同的市场状态.我们采用一种特殊形式的凸风险测度作为风险的测度，它包括熵风险测度作为一种特殊情况。风险最小化问题被制定为一个马尔可夫政权切换版本的两个球员，零和随机微分游戏。我们的模型的一个重要特点是允许灵活控制代表金融风险的扩散过程和代表宏观经济风险的马尔可夫链。从随机微分对策和随机控制的角度来看，这是新颖而有趣的。给出了该博弈的Hamilton-Jacobi-Bellman（HJB）解的验证定理，并讨论了一些特殊情况。
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.