Contributed Session 3:  Modeling, Math Biology and Math Finance
Inter-temporal Defined Contribution Pension Management
Ho Man Tai
Dublin City University
Ireland
  Co-Author(s):    Paolo Guasoni, Bohan Li, Ho Man Tai, Tak Kwong Wong, Sheung Chi Phillip Yam
  Abstract:
 

The objective of this article is to resolve the pension management problem with constant contribution from fund holders in the perspective of the manager who aims to maximize the expectation of generic running and terminal utilities of the management fees collected. Research on the existing literature largely neglects the impacts of inter-temporal reward for the manager. With the aim of the Dynamic Programming Principle, the problem is associated with a singular, fully non-linear HJB equation. We develop a direct mathematical primal analysis to establish the unique existence of its classical solution by transforming the problem into a non-canonical variational inequality problem and then solving it in a trailer Sobolev space. In addition, an efficient numerical scheme has been introduced to compute the optimal trading strategy and the value function numerically.