Optimal consumption and portfolio selection with quadratic utility and a subsistence consumption constraint

An Optimal Consumption and Investment Problem With Quadratic Utility and Subsistence Consumption Constraints: A Dynamic Programming Approach

“…where θ := (µ − r)/σ is the market price of risk, x is the threshold wealth level which corresponds to a subsistence consumption level Γ , andx = 1/(2rR) is the wealth level that can support the bliss level of consumptionc (for the concrete forms of the boundary wealth levels, refer to Koo et al [8]).…”

“…In this section, we provide properties of the optimal policies without the assumption ρ − 2r + θ 2 > 0 given in Koo et al [8]. Proof.…”

“…The existence of a subsistence consumption constraint has a significant impact on the agent's optimal consumption and investment policies, especially when the constraints are binding. Cox and Huang [2], Gong and Li [4], Huang and Pagès [6], Koo et al [8], Lakner and Nygren [9], Lee and Shin [10], Lim et al [11], Shim and Shin [15], Shin and Lim [16], Shin et al [17], and Yuan and Hu [18] have studied optimal consumption and portfolio selection problems with subsistence consumption constraints.…”

“…Koo et al [8] also solved an optimal consumption and portfolio selection problem for an agent with quadratic utility and subsistence consumption constraints. However, Koo et al [8] solved the problem using the martingale method, while we use the dynamic programming method. More significantly, we can replicate the results of Koo et al [8] without the assumption ρ − 2r + θ 2 > 0.…”

“…However, Koo et al [8] solved the problem using the martingale method, while we use the dynamic programming method. More significantly, we can replicate the results of Koo et al [8] without the assumption ρ − 2r + θ 2 > 0. We further provide a verification theorem that shows that the value function obtained using the dynamic programming method is the same as the value function obtained using the martingale method in Koo et al [8].…”