Portfolio Optimization with Asset-Liability Ratio Regulation Constraints

De-Lei Sheng,Peilong Shen

doi:10.1155/2020/1435356

Abstract

This paper considers both a top regulation bound and a bottom regulation bound imposed on the asset-liability ratio at the regulatory time T to reduce risks of abnormal high-speed growth of asset price within a short period of time (or high investment leverage), and to mitigate risks of low assets’ return (or a sharp fall). Applying the stochastic optimal control technique, a Hamilton–Jacobi–Bellman (HJB) equation is derived. Then, the effective investment strategy and the minimum variance are obtained explicitly by using the Lagrange duality method. Moreover, some numerical examples are provided to verify the effectiveness of our results.

Highlights

Taking liabilities into the traditional portfolio models, Sharpe and Tint [1] put forward the asset-liability problem for pension fund management under the mean-variance framework
Kell and Muller [2] point out that liabilities affect the efficient frontier of this asset-liability problem
Early research on asset-liability problems was limited to the standard single-period mean-variance criterion; Leippold et al [3] obtain an analytical optimal strategy and efficient frontier for asset-liability problems by using embedding technique proposed by Li and Ng [4] under a multiperiod mean-variance framework

Summary

Introduction

Taking liabilities into the traditional portfolio models, Sharpe and Tint [1] put forward the asset-liability problem for pension fund management under the mean-variance framework. Considering a financial market consists of a risk-free bond, a stock, and a derivative, Li et al [8] give the optimal investment strategies of a continuous-time mean-variance asset-liability management in presence of stochastic volatility. In accordance with the need of practice, this paper considers the asset-liability problem with the constraints imposed at the regulatory time T to find the optimal investment strategy, in order to reduce the risk of abnormal high-speed growth of asset price within a short period of time or high investment leverage and to lessen the risk of too low return rate or a sharp fall. Problem (10) is a dynamic quadratic convex optimization problem, and it has an unique solution

Solutions of the Problem

Findings

Conclusion