An optimal consumption and investment problem with partial information. (20th March 2018)

• Record Type: Journal Article
• Authors: Hata, Hiroaki; Sheu, Shuenn-Jyi
• Is Part Of: Advances in applied probability. Volume 50:Number 1(2018)
• Page Start: 131
• Page End: 153
• Publication Date: 2018-03-20
• Subjects: Optimal consumption and investment, -- HARA utility, -- stochastic factor model, -- partial information, -- Hamilton–Jacobi–Bellman equation; Primary 49L20, -- 60H30, -- 91G10, -- 93E20, -- Secondary 93E11; Probabilities -- Periodicals; Stochastic models -- Periodicals; Electronic journals; Periodicals; 519.2
• DOI: 10.1017/apr.2018.7
• Languages: English
• ISSNs: 0001-8678

Abstract

Abstract: We consider a finite-time optimal consumption problem where an investor wants to maximize the expected hyperbolic absolute risk aversion utility of consumption and terminal wealth. We treat a stochastic factor model in which the mean returns of risky assets depend linearly on underlying economic factors formulated as the solutions of linear stochastic differential equations. We discuss the partial information case in which the investor cannot observe the factor process and uses only past information of risky assets. Then our problem is formulated as a stochastic control problem with partial information. We derive the Hamilton–Jacobi–Bellman equation. We solve this equation to obtain an explicit form of the value function and the optimal strategy for this problem. Moreover, we also introduce the results obtained by the martingale method.