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

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  • Wilfried Kuissi-Kamdem

    (Department of Mathematical Stochastics, University of Freiburg, 79104 Freiburg, Germany
    Department of Mathematics, University of Rwanda, Kigali 4285, Rwanda
    African Institute for Mathematical Sciences, 1 Shoppers Street, Accra, Ghana)

  • Marcel Ndengo

    (Department of Mathematics, University of Rwanda, Kigali 4285, Rwanda)

Abstract

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.

Suggested Citation

  • Wilfried Kuissi-Kamdem & Marcel Ndengo, 2026. "Optimal Consumption and Investment Choice with Bounded Memory and Recursive Preferences in a Multi-Asset Setting," Risks, MDPI, vol. 14(6), pages 1-19, June.
    • Handle: RePEc:gam:jrisks:v:14:y:2026:i:6:p:140-:d:1969669
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