Framework for asset-liability management with fixed-term securities
Yevhen Havrylenko
TL;DR
The paper develops an asset-liability management framework that allows an investor to choose between liquid assets and a fixed-term illiquid asset while imposing lower bounds on consumption and terminal wealth. It employs a generalized martingale approach and a two-step initial-wealth separation to decompose the problem into a utility-from-consumption subproblem and a utility-from-wealth subproblem, then merges the solutions to obtain semi-closed-form strategies. For power utilities, explicit formulas are derived for both random and deterministic fixed-term assets, with detailed analysis of non-redundancy and case distinctions that arise from the fixed-term asset’s risk-return profile. The authors provide numerical studies showing how the illiquid allocation, the subjective value of the fixed-term asset, and potential improvements to liabilities depend on horizon, risk aversion, and asset characteristics, offering practical guidance for insurers and investors. The framework extends prior work by integrating fixed-term illiquid assets into the Lakner–KornDesmettre lineage and by quantifying the trade-offs between liquidity, guarantees, and consumption sustainability in a tractable, analytically grounded setting.
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.