TY - JOUR
T1 - Minimization of risks in defined benefit pension plan with time-inconsistent preferences
AU - Zhao, Qian
AU - Wang, Rongming
AU - Wei, Jiaqin
PY - 2016/3/1
Y1 - 2016/3/1
N2 - In this paper, we investigate the defined benefit pension plan, where the object of the manager is to minimise the contribution rate risk and the solvency risk by considering a quadratic performance criterion. To incorporate some well-documented behavioural features of human beings, we consider the situation where the discounting is non-exponential. It leads to a time-inconsistent control problem in the sense that the Bellman optimality principle does no longer hold. In our model, we assume that the benefit outgo is constant, and the pension fund can be invested in a risk-free asset and a risky asset whose return follows a geometric Brownian motion. We characterise the time-consistent strategies and value function in terms of the solution of a system of integral equations. The existence and uniqueness of the solution is verified, and the approximation of the solution is obtained. Some numerical results of the equilibrium contribution rate and equilibrium investment policy are presented for three types of discount functions.
AB - In this paper, we investigate the defined benefit pension plan, where the object of the manager is to minimise the contribution rate risk and the solvency risk by considering a quadratic performance criterion. To incorporate some well-documented behavioural features of human beings, we consider the situation where the discounting is non-exponential. It leads to a time-inconsistent control problem in the sense that the Bellman optimality principle does no longer hold. In our model, we assume that the benefit outgo is constant, and the pension fund can be invested in a risk-free asset and a risky asset whose return follows a geometric Brownian motion. We characterise the time-consistent strategies and value function in terms of the solution of a system of integral equations. The existence and uniqueness of the solution is verified, and the approximation of the solution is obtained. Some numerical results of the equilibrium contribution rate and equilibrium investment policy are presented for three types of discount functions.
KW - defined benefit pension fund
KW - non-exponential discounting
KW - time inconsistence
KW - equilibrium strategies
UR - http://www.scopus.com/inward/record.url?scp=84949254615&partnerID=8YFLogxK
UR - https://ulrichsweb.serialssolutions.com/title/1507260411961/152903
U2 - 10.1002/asmb.2148
DO - 10.1002/asmb.2148
M3 - Article
AN - SCOPUS:84949254615
SN - 1524-1904
VL - 32
SP - 243
EP - 258
JO - Applied Stochastic Models in Business and Industry
JF - Applied Stochastic Models in Business and Industry
IS - 2
ER -