2011/12/13 by Xiang Yu, Yu, Xiang
Decision Sciences · Economics, Econometrics and Finance · #91G10 (Primary) 93E11 #93E20 (Secondary) #Economic theories and models #FOS: Economics and business #FOS: Mathematics #Optimization and Control (math.OC) #Portfolio Management (q-fin.PM) #Risk and Portfolio Optimization #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1112.2939
openalex publication_date 2011/12/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider a model of optimal investment and consumption with both habit\nformation and partial observations in incomplete It o processes market. The\ninvestor chooses his consumption under the addictive habits constraint while\nonly observing the market stock prices but not the instantaneous rate of\nreturn. Applying the Kalman-Bucy filtering theorem and the Dynamic Programming\narguments, we solve the associated Hamilton-Jacobi-Bellman (HJB) equation\nexplicitly for the path dependent stochastic control problem in the case of\npower utilities. We provide the optimal investment and consumption policies in\nexplicit feedback forms using rigorous verification arguments.\n