Illiquid Assets Allocation with Jumps and Lock-in Periods under General Utility Function

The asset allocation problem of illiquid assets is an important issue in the study of financial mathematics. Due to the trading restrictions, market inefficiency and illiquidity of illiquid assets, such illiquid assets (such as real estate, private equity, etc.) rely on uninsurable risk sources and provide certain liquidity dividends. In addition, the liquidity of illiquid assets will not remain unchanged over time, so illiquid assets will have a lock-up period during which investors cannot trade illiquid assets. The paper considers the asset allocation problem under the general utility function when the trading time of illiquid assets follows a Poisson process. In this case, the agent can only trade illiquid assets at discrete moments, and the agent can only obtain price information on the trading day of illiquid assets. Finally, this paper selects the daily data of NASDAQ-100 (NDX) Index and MSCI US Real Estate Investment Trust Index (REITs) as numerical analysis objects to compare the optimal investment strategies.