非自融资策略下信用债券的最优投资策略:以DC型企业年金为例

Optimal investment strategy for the defaultable bond under non-self-financing strategy:A case study of DC enterprise annuity

以往对信用债券最优投资策略的研究,均是基于投资者的自融资策略展开的。本文放松了这一假设,研究了当工资为一个随机过程时,确定缴费型(DC)企业年金如何对信用债券、股票以及银行存款进行最优资产配置的问题。假设企业年金的投资目标为基于最终财富的期望效用最大化,利用鞅方法给出了此优化问题的解。

The existing literature about the optimal investment strategy for the defaultable bond assumes that investors have a self-financial strategy. This key assumption is obviously not suitable for enterprise annuities, pension funds, open-end funds, insurance companies, and other institutional investors. In view of this, this paper removes the assumption of self-financing strategy, and studies the optimal investment strategy for the defaultable bond under non-self-financing strategy by using enterprise annuities. This study can enrich and improve the theory of defaultable bond optimal investment. We assume that enterprise annuity is defined-contribution （DC）, the salary is a stochastic process, and its investment set is a defaultable bond, a stock, and a bank account. The goal of DC enterprise annuity investment is to maximize the expected utility of terminal wealth by optimally allocating the wealth among these three securities. Using the martingale approach, we derive the general solutions for this optimal problem. In addition, we assume that the utility is constant absolute risk aversion utility （CARA）, and derives the close form solution of optimal investment strategy. From the solution, it is clear that enterprise annuity＇s optimal investment strategy for the defaultable bond is an increasing function of the jump-risk premium and the time to maturity. Enterprise annuity＇s optimalinvestment strategy for the defaultable bond is a decreasing function of the loss rate, the default intensity, and salary volatility. Through the simulation study, we find that there is a positive relationship between optimal investment in defaultable bond and jump-risk premium. By holding other factors constant, enterprise annuity purchases more defaultable bonds when the price of the jump-risk is greater. The optimal investment in the defaultable bond is increasing with an increasing rate when the jump-risk premium increases. When the loss rate is low, the marginal increase of the optimal investment strategy for the defaultable bond is huge. We can interpret this result as saying that enterprise annuity responds more to investment return when the loss rate is low, and enterprise annuity responds more to investment risk when the loss rate is high. The optimal investment strategy for the defaultable bond is a decreasing function of the loss rate. The greater loss rate means the smaller rate of investor recovery. Enterprise annuity allocates smaller amount of wealth to the defaultable bond. The optimal investment strategy for the defaultable bond is an increasing function of the time to maturity. Enterprise annuity allocates more when it has longer investment horizon. When the time to maturity is long, the marginal increase of the optimal investment strategy for the defauitable bond is huge, and vice versa. The reason is that the enterprise annuity may choose a more aggressive investment policy when the time to maturity is long. Enterprise annuity chooses a more conservative investment policy as the deadline is approaching.