# American Institute of Mathematical Sciences

doi: 10.3934/jimo.2020015

## Mean-variance investment and contribution decisions for defined benefit pension plans in a stochastic framework

 1 School of Statistics and Information, Shanghai University of International Business and Economics, Shanghai 201620, China 2 School of Risk and Actuarial Studies, University of New South Wales, Sydney NSW 2052, Australia 3 Key Laboratory of Advanced Theory and Application in Statistics and Data Science-MOE, School of Statistics, East China Normal University, Shanghai 200241, China

* Corresponding author: Jiaqin Wei

Received  January 2019 Revised  September 2019 Published  January 2020

Fund Project: This work was supported by the 111 Project (B14019); the National Natural Science Foundation of China (11601157, 11571113, 11601320, 11971301); and the Natural Sciences and Engineering Research Council of Canada (RGPIN-2016-05677)

In this paper we investigate the management of a defined benefit pension plan under a model with random coefficients. The objective of the pension sponsor is to minimize the solvency risk, contribution risk and the expected terminal value of the unfunded actuarial liability. By measuring the solvency risk in terms of the variance of the terminal unfunded actuarial liability, we formulate the problem as a mean-variance problem with an additional running cost. With the help of a system of backward stochastic differential equations, we derive a time-consistent equilibrium strategy towards investment and contribution rate. The obtained equilibrium strategy turns out to be a good candidate for a stable contribution plan. When the interest rate is given by the Vasicek model and all other coefficients are deterministic, we obtain closed-form solutions of the equilibrium strategy and efficient frontier.

Citation: Qian Zhao, Yang Shen, Jiaqin Wei. Mean-variance investment and contribution decisions for defined benefit pension plans in a stochastic framework. Journal of Industrial & Management Optimization, doi: 10.3934/jimo.2020015
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##### References:
The variance and total expected contribution versus $\rho$
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