2023/09/05 by Hui Mi, Mi, Hui, Zuo Quan Xu +3
Business, Management and Accounting · Economics, Econometrics and Finance · Social Sciences · #FOS: Economics and business #FOS: Mathematics #Financial Literacy, Pension, Retirement Analysis #Insurance, Mortality, Demography, Risk Management #Mathematical Finance (q-fin.MF) #Optimization and Control (math.OC) #Portfolio Management (q-fin.PM) #Probability (math.PR) #Risk Management (q-fin.RM) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2309.01936
openalex publication_date 2023/09/05 · openalex created_date 2023/09/09 · openalex updated_date 2026/07/28
This paper investigates an optimal investment problem under the tail Value at Risk (tail VaR, also known as expected shortfall, conditional VaR, average VaR) and portfolio insurance constraints confronted by a defined-contribution pension member. The member's aim is to maximize the expected utility from the terminal wealth exceeding the minimum guarantee by investing his wealth in a cash bond, an inflation-linked bond and a stock. Due to the presence of the tail VaR constraint, the problem cannot be tackled by standard control tools. We apply the Lagrange method along with quantile optimization techniques to solve the problem. Through delicate analysis, the optimal investment output in closed-form and optimal investment strategy are derived. A numerical analysis is also provided to show how the constraints impact the optimal investment output and strategy.