Document Type : Original Research Paper

Authors

• Navideh Modarresi
• Parsa Yahyavi

Department of Mathematics, Faculty of Statistics, Mathematics and Computer Science, Allameh Tabataba'i University, Tehran, Iran

Abstract

BACKGROUND AND OBJECTIVES: Companies and institutes in industrial and developed countries have changed their pension plans from defined benefit (DB) plans to defined contribution (DC) ones. By this approach, they have transferred the risk of forming and managing a portfolio to buy suitable life insurance at the time of retirement to the employees of these centers.  In line with these changes, the aim of this paper is to present an optimal investment portfolio to buy a favorable life insurance at the time of retirement.
METHODS: In this paper, with the aim of determining an optimal investment portfolio during the accumulation phase in an efficient market, the Martingale method and a target-based mean-variance approach are applied to solve the stochastic optimal control problem.
FINDINGS: By the presented method, we explicitly acquire optimal investment strategy during the accumulation phase by the time of retirement. An optimal investment strategy is an optimal investment portfolio where available assets in financial markets are included. Financial markets consist of risky assets, riskless assets and cash where the price of risky assets follows the geometric Brownian motion model. The investor’s contributions to the pension plan also follow geometric Brownian motion with two factors and the interest rate has Vasicek model. Finally, using the historical data of the financial market of Iran, we calibrate the parameters of the introduced models and construct the corresponding optimal portfolio. For investment strategies with low, mild, and high risk tendencies, we simulate the construction and change in the value of the optimal investment portfolio for each year of the accumulation phase.
CONCLUSION: Based on the simulations conducted, the high risk strategy, with a small percentage of assets allocated to investment in risky assets, eliminates opportunities for profit through risk-taking, which may result in an undesirable accumulated fund. On the other hand, low risk startegies, with a high percentage of assets allocated to investment in risky assets, increases bankruptcy and failing probability to reach a minimum level of accumulated capital. Therefore, according to these results, a mild risk- strategy, which simultaneously emphasizes opportunities for risk-taking and greater guarantee about the minimum accumulated capital, can meet the needs of a wide range of investors.  
 

Keywords

• Defined contribution pension plan
• Geometric Brownian motion with two Factors
• Martingale method
• Stochastic optimal control
• Vasicek model

Main Subjects

• Financial / Applied Mathematics