Optimal Consumption and Investment Choice with Bounded Memory and Recursive Preferences in a Multi-Asset Setting

This paper studies an optimal consumption–investment problem in a multi-asset financial market where risky assets returns incorporate returns history. Preferences are modelled using Epstein–Zin recursive utility, allowing a separation between risk aversion and intertemporal substitution. Using the well-known martingale optimality principle and forward–backward stochastic differential equations (FBSDEs), we obtain explicit closed-form solutions for the optimal strategy and value function. A sensitivity analysis illustrates the dependence of optimal policies and value function on key parameters, including risk aversion, elasticity of intertemporal substitution (EIS), memory horizon, learning intensity, and wealth-history parameters. The findings provide new insights into the interaction between behavioural features and dynamic portfolio choice in a multi-asset setting.