# The Role of Inflation-Indexed Bond in Optimal Management of Defined Contribution Pension Plan During the Decumulation Phase

^{*}

^{†}

## Abstract

**:**

## 1. Introduction and Motivation

## 2. Model Assumptions and Notations

#### 2.1. The Financial Market

**Remark**

**1.**

**Lemma**

**1.**

**Proof.**

#### 2.2. The Demographic Pattern

**Remark**

**2.**

## 3. DC Pension Fund Management with Investment of Inflation-Indexed Bond

- ${u}^{BI}(t)$ is progressively measurable with respect to ${\left(\right)}_{{\mathcal{F}}_{t}}$;
- $\mathbb{E}\left\{{\displaystyle {\int}_{0}^{T}\left(\right)open="["\; close="]">{\left(\right)}^{X}{\nabla}_{R}^{B}\phantom{\rule{0.277778em}{0ex}}{\sigma}_{R}2},+,{\left(\right)}^{X},2\right\}+{\left(\right)}^{X}2dt$
- Equation (16) has a unique strong solution for the initial value $({t}_{0},{R}_{0},{X}_{0})\in [0,T]\times {(0,\infty )}^{2}$.

**Remark**

**3.**

**Theorem**

**1.**

**Proof.**

## 4. DC Pension Fund Management without the Investment of Inflation-indexed Bond

**Theorem**

**2.**

**Proof.**

## 5. Sensitivity Analysis

## 6. Comparative Statics and Conclusions

**Theorem**

**3.**

**Proof.**

**Remark**

**4.**

**Remark**

**5.**

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Abbreviations

DC | Defined contribution |

DB | Defined benefit |

CRRA | Constant relative risk aversion |

HJB | Hamilton-Jacobi-Bellman |

PAYG | Pay-as-you-go |

## Appendix A

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**MDPI and ACS Style**

Zhang, X.; Guo, J.
The Role of Inflation-Indexed Bond in Optimal Management of Defined Contribution Pension Plan During the Decumulation Phase. *Risks* **2018**, *6*, 24.
https://doi.org/10.3390/risks6020024

**AMA Style**

Zhang X, Guo J.
The Role of Inflation-Indexed Bond in Optimal Management of Defined Contribution Pension Plan During the Decumulation Phase. *Risks*. 2018; 6(2):24.
https://doi.org/10.3390/risks6020024

**Chicago/Turabian Style**

Zhang, Xiaoyi, and Junyi Guo.
2018. "The Role of Inflation-Indexed Bond in Optimal Management of Defined Contribution Pension Plan During the Decumulation Phase" *Risks* 6, no. 2: 24.
https://doi.org/10.3390/risks6020024