Optimal Asset Allocation Subject to Withdrawal Risk and Solvency Constraints

Areski Cousin,Olivier David Zerbib,Ying Jiao,Christian Yann Robert

doi:10.3390/risks10010015

Abstract

This paper investigates the optimal asset allocation of a financial institution whose customers are free to withdraw their capital-guaranteed financial contracts at any time. In accounting for the asset-liability mismatch risk of the institution, we present a general utility optimization problem in a discrete-time setting and provide a dynamic programming principle for the optimal investment strategies. Furthermore, we consider an explicit context, including liquidity risk, interest rate, and credit intensity fluctuations, and show by numerical results that the optimal strategy improves both the solvency and asset returns of the institution compared to a standard institutional investor’s asset allocation.

Highlights

Recent financial turmoil and market stresses following the sub-prime crisis or the COVID-19 pandemic had a double impact on asset management: massive withdrawals accompanied by violent and persistent liquidity shocks
The sharp increase in redemptions generally occurs in two main cases: (i) when customers consider the financial institution to be at risk, usually during a financial crisis when default risk increases; or (ii) when customers find more attractive investment opportunities, usually during periods of rising interest rates
This study examined an optimal investment allocation problem for a financial institution offering capital-guaranteed contracts that incorporate the option of withdrawal at any time

Summary

Introduction

Recent financial turmoil and market stresses following the sub-prime crisis or the COVID-19 pandemic had a double impact on asset management: massive withdrawals accompanied by violent and persistent liquidity shocks. The financial institution, given its risk aversion, searches to optimize the asset allocation of the investment portfolio by using the expected utility maximization upon the wealth value at a final horizon. The financial institution who is exposed to the risk of potentially massive withdrawals aims at finding the optimal investment strategies according to its risk preference or aversion under the expected utility maximization criterion of the final wealth value of the investment portfolio at a time horizon T > 0. The above constraint is given in form of conditional probability and is called the “next-period constraint” in Jiao et al (2017) In this case, the asset-liability requirement is imposed by considering two successive dates and accounting for the financial situations of the previous date.

General Formulation and Dynamic Programming Principle

An Alternative Dynamic Program with Exponential Utility Function

Application and Numerical Illustrations in the Presence of Liquidity Risk

Conclusions

Findings

Solving the Bellman equation on the discretized state space