Framework for asset-liability management with fixed-term securities

ArXiv ID: 2502.19213 “View on arXiv”

Authors: Unknown

Abstract

We consider an optimal investment-consumption problem for a utility-maximizing investor who has access to assets with different liquidity and whose consumption rate as well as terminal wealth are subject to lower-bound constraints. Assuming utility functions that satisfy standard conditions, we develop a methodology for deriving the optimal strategies in semi-closed form. Our methodology is based on the generalized martingale approach and the decomposition of the problem into subproblems. We illustrate our approach by deriving explicit formulas for agents with power-utility functions and discuss potential extensions of the proposed framework. In numerical studies, we substantiate how the parameters of our framework impact the optimal proportion of initial capital allocated to the illiquid asset, the monetary value that the investor subjectively assigns to the fixed-term asset, and the potential of the illiquid asset to increase terminal the terminal value of liabilities without loss in the investor’s expected utility.

Keywords: Portfolio Optimization, Utility Maximization, Illiquidity, Investment-Consumption, Martingale Approach

Complexity vs Empirical Score

• Math Complexity: 9.0/10
• Empirical Rigor: 3.0/10
• Quadrant: Lab Rats
• Why: The paper involves advanced stochastic calculus (martingale approach, decomposition into subproblems) and derives semi-closed-form solutions for constrained utility maximization problems, indicating high mathematical density. However, the empirical portion is limited to illustrative numerical studies and conceptual discussion of parameters without mention of backtesting or real-world data analysis.

  flowchart TD
    A["Research Goal<br>Optimal investment-consumption<br>with illiquid assets & constraints"] --> B["Methodology<br>Generalized Martingale Approach &<br>Problem Decomposition"]
    B --> C["Data/Inputs<br>Utility function parameters,<br>liquidity constraints, asset returns"]
    C --> D["Computational Process<br>Solve subproblems & derive<br>semi-closed form optimal strategies"]
    D --> E["Key Outcomes<br>Explicit formulas for power utility<br>Optimal allocation to illiquid asset<br>Value of fixed-term securities"]