Framework for asset-liability management with fixed-term securities

TL;DR

This paper develops a methodology for optimal asset-liability management involving fixed-term securities, accounting for liquidity constraints and utility maximization, with explicit solutions and numerical analysis of asset allocation impacts.

Contribution

It introduces a generalized martingale approach for deriving semi-closed form optimal strategies in a complex asset-liability setting with liquidity and lower-bound constraints.

Findings

Explicit formulas for power-utility investors.

Impact of parameters on asset allocation and utility.

Potential for illiquid assets to enhance terminal wealth.

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.