2012/11/06 by Salvatore Federico, Federico, Salvatore, Paul Gassiat +3
Decision Sciences · Economics, Econometrics and Finance · #Economic theories and models #FOS: Economics and business #Portfolio Management (q-fin.PM) #Risk and Portfolio Optimization #Stochastic processes and financial applications #q-fin.PM
paper · pdf · doi:10.48550/arxiv.1211.1285
openalex publication_date 2012/11/06 · arxiv created 2015/03/19 · arxiv updated 2015/03/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study a problem of optimal investment/consumption over an infinite horizon in a market consisting of two possibly correlated assets: one liquid and one illiquid. The liquid asset is observed and can be traded continuously, while the illiquid one can be traded only at discrete random times corresponding to the jumps of a Poisson process with intensity λ, is observed at the trading dates, and is partially observed between two different trading dates. The problem is a nonstandard mixed discrete/continuous optimal control problem which we face by the dynamic programming approach. When the utility has a general form we prove that the value function is the unique viscosity solution of the HJB equation and, assuming sufficient regularity of the value function, we give a verification theorem that describes the optimal investment strategies for the illiquid asset. In the case of power utility, we prove the regularity of the value function needed to apply the verification theorem, providing the complete theoretical solution of the problem. This allows us to perform numerical simulation, so to analyze the impact of time illiquidity in this mixed market and how this impact is affected by the degree of observation.