Asymptotic analysis for a downside risk minimization problem under partial information

作者：Watanabe Yusuke^*

来源：Stochastic Processes and Their Applications, 2013, 123(3): 1046-1082.

DOI：10.1016/j.spa.2012.11.005

• Large deviations
• Risk-sensitive control
• Degenerate ergodic HJB equation
• Nonlinear filtering equation
• Hidden Markov model

We give an analytic characterization of a large-time "downside risk" probability associated with an investor's wealth. We assume that risky securities in our market model are affected by "hidden" economic factors, which evolve as a finite-state Markov chain. We formalize and prove a duality relation between downside risk minimization and the related risk-sensitive optimization. The proof is based on an analysis of an ergodic-type Hamilton-Jacobi-Bellman equation with large (exponentially growing) drift.

• 出版日期2013-3