Framework for asset-liability management with fixed-term securities

2025-02-26

AI Summary

This paper investigates the optimal investment-consumption problem for a utility-maximizing investor facing tiered asset liquidity and dual hard constraints: a minimum consumption rate and a floor on terminal wealth. Methodologically, it innovatively integrates the generalized martingale approach with problem decomposition techniques to achieve, for the first time, a semi-closed-form solution to the asset-liability management (ALM) problem under multiple binding constraints. For power utility, explicit optimal portfolio and consumption policies are derived; their feasibility—given the constraints—and robustness are rigorously established. The results provide a scalable theoretical framework for fixed-income security allocation and lay a methodological foundation for extending the analysis to more sophisticated utility specifications and market frictions, including transaction costs and information asymmetry.

Technology Category

• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization
• Search and Optimization: Mixed Discrete/Continuous Search
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Security and Privacy: Large-scale security measurements
• Systems and Infrastructure for Web, Mobile and WoT: Energy management for devices in mobile Web and WoT environments

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.

Problem

• Optimize investment-consumption with liquidity constraints
• Derive semi-closed optimal strategies using martingale approach
• Analyze impact of illiquid assets on terminal wealth

Innovation

• Generalized martingale approach for optimal strategies
• Decomposition into subproblems for solution derivation
• Explicit formulas for power-utility functions