Viscosity Characterization of the Value Function of an Investment-Consumption Problem in Presence of an Illiquid Asset

摘要: We study a problem of optimal investment/consumption over an infinite horizon in market consisting liquid and illiquid asset. The asset is observed can be traded continuously, while the one only at discrete random times corresponding to jumps Poisson process. nonstandard mixed discrete/continuous control problem, which we face by dynamic programming approach. main goal paper characterization value function as unique viscosity solution associated Hamilton–Jacobi–Bellman equation. then use such result build numerical algorithm, allowing approximate so measure cost illiquidity.