Paper: arXiv 2511.02158

Authors: Wilfried Kuissi-Kamdem

Abstract

This paper solves a consumption-investment choice problem with Epstein-Zin recursive utility under partial information–unobservable market price of risk. The main novelty is the introduction of a terminal liability constraint, a feature directly motivated by practical portfolio management and insurance applications but absent from the recursive utility literature. Such constraint gives rise to a coupled forward-backward stochastic differential equation (FBSDE) whose well-posedness has not been addressed in earlier work. We provide an explicit solution to this FBSDE system–contrasting with the typical existence and uniqueness results with no closed-form expressions in the literature. Under mild additional assumptions, we also establish the Malliavin differentiability of the solution allowing the optimal investment strategy to be expressed as a conditional expectation of random variables that can be efficiently simulated. These results allows us to obtain the explicit expressions of the optimal controls and the value function. Finally, we quantify the utility loss from ignoring learning about the market price of risk, highlighting the economic significance of partial information.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 3.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents a rigorous theoretical framework combining Epstein-Zin recursive utility, partial information, Malliavin calculus, and FBSDEs to solve an ALM problem with explicit closed-form solutions. However, it is primarily theoretical and lacks real-world empirical validation or extensive backtesting beyond basic numerical illustrations.

Research Flowchart

  flowchart TD
    A[Research Goal: Solve ALM with Epstein-Zin Utility under Partial Info & Terminal Liability] --> B[Model Inputs: Stochastic Interest Rate, Unobservable Market Price of Risk, Liability Constraint]
    B --> C[Formulate Stochastic Control Problem & Derive Coupled FBSDE System]
    C --> D[Solve FBSDE Explicitly & Apply Malliavin Calculus for Optimal Strategies]
    D --> E[Simulate Optimal Portfolio Controls & Quantify Economic Utility Loss]
    E --> F[Outcomes: Explicit Value Function, Optimal Controls & Value of Learning Unobservable Risk]

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2 of 61 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.