Asymptotics of the probability of minimizing 'down-side' risk under partial information

作者：Nagai Hideo^*

来源：Quantitative Finance, 2011, 11(5): 789-803.

DOI：10.1080/14697680903341814

• Multi-factor models
• Stochastic analysis
• Stochastic control
• Downside risk
• Portfolio management
• Dynamic programming
• Mathematics of finance
• Kalnman filters

We consider minimizing the probability of falling below a target growth rate of the wealth process up to a time horizon T in an incomplete market model under partial information and then study the asymptotic behavior of the minimizing probability as T . This problem is closely related to an ergodic risk-sensitive stochastic control problem under partial information in the risk-averse case. Indeed, in our main theorem we relate the former problem to the latter as its dual. As a result we obtain an explicit expression for the limit value of the former problem in the case of linear Gaussian models.

• 出版日期2011