In this paper, optimal investment and consumption decisions for an optimal choice problem in infinite horizon are considered, for an investor who has available a bank account and a stock whose price is a log normal di...In this paper, optimal investment and consumption decisions for an optimal choice problem in infinite horizon are considered, for an investor who has available a bank account and a stock whose price is a log normal diffusion. The bank pays at an interest rate r for any deposit, and takes at a larger rate r′ for any loan. As in the paper of Xu Wensheng and Chen Shuping in JAMS(B), where an analogous problem in finite horizon is studied, optimal strategies are obtained via Hamilton Jacobi Bellman (HJB) equation which is derived from dynamic programming principle. For the specific HARA case, i.e. U(t,c)=e -βt c 1-R 1-R , this paper gets the optimal consumption and optimal investment in the form ofc * t=β-Rw t\ and \ π * t=b-γRσ 2w twith γ:= max{ r, min{ r′,b-Rσ 2 }}, =(1-R)γ+(b-γ) 22Rσ 2]. This result coincides with the classical one under condition r′≡r.展开更多
文摘In this paper, optimal investment and consumption decisions for an optimal choice problem in infinite horizon are considered, for an investor who has available a bank account and a stock whose price is a log normal diffusion. The bank pays at an interest rate r for any deposit, and takes at a larger rate r′ for any loan. As in the paper of Xu Wensheng and Chen Shuping in JAMS(B), where an analogous problem in finite horizon is studied, optimal strategies are obtained via Hamilton Jacobi Bellman (HJB) equation which is derived from dynamic programming principle. For the specific HARA case, i.e. U(t,c)=e -βt c 1-R 1-R , this paper gets the optimal consumption and optimal investment in the form ofc * t=β-Rw t\ and \ π * t=b-γRσ 2w twith γ:= max{ r, min{ r′,b-Rσ 2 }}, =(1-R)γ+(b-γ) 22Rσ 2]. This result coincides with the classical one under condition r′≡r.
