A simple numerical solution for an optimal investment strategy for a DC pension plan in a jump diffusion model

Abstract In this paper, we study an optimal investment strategy for a fund manager of a DC pension who wants to maximise the expected exponential utility of the terminal wealth in a market where the stock is a jump diffusion process. Using stochastic control theory, we derive a Hamilton–Jacobi–Bellman equation. Since the market is not complete, the optimal strategy cannot be found in closed as is done in most literature on DC pension plans. We characterise the optimal strategy as a solution of an integro-ordinary differential equation which can easily be solved by a simple numerical method. We investigate the impact of different jump parameters through numerical experiments using a familiar distribution of jumps.

[1]  Michael Ludkovski,et al.  EUROPEAN OPTION PRICING WITH LIQUIDITY SHOCKS , 2013 .

[2]  L. C. G. Rogers,et al.  Pathwise Stochastic Optimal Control , 2007, SIAM J. Control. Optim..

[3]  W. Fleming,et al.  Controlled Markov processes and viscosity solutions , 1992 .

[4]  Guohui Guan,et al.  Optimal management of DC pension plan in a stochastic interest rate and stochastic volatility framework , 2014 .

[5]  Sid Browne,et al.  Optimal Investment Policies for a Firm With a Random Risk Process: Exponential Utility and Minimizing the Probability of Ruin , 1995, Math. Oper. Res..

[6]  F. Menoncin,et al.  Portfolio Optimisation with Jumps: Illustration with a Pension Accumulation Scheme , 2012 .

[7]  Wenyuan Li,et al.  Dual control Monte-Carlo method for tight bounds of value function in regime switching utility maximization , 2017, Eur. J. Oper. Res..

[8]  Ling Zhang,et al.  Nash equilibrium strategies for a defined contribution pension management , 2015 .

[9]  Lin He,et al.  Optimal investment strategy for the DC plan with the return of premiums clauses in a mean–variance framework , 2013 .

[10]  Hailiang Yang,et al.  Optimal investment for insurer with jump-diffusion risk process , 2005 .

[11]  Elena Vigna.  On efficiency of mean–variance based portfolio selection in defined contribution pension schemes , 2014 .

[12]  Carlos Vázquez,et al.  Pricing pension plans under jump-diffusion models for the salary , 2014, Comput. Math. Appl..

[13]  Jian-wei Gao.  Stochastic optimal control of DC pension funds , 2008 .

[14]  Xiang Lin,et al.  Optimal investment and reinsurance in a jump diffusion risk model , 2010 .

[15]  Steven Kou,et al.  A Jump Diffusion Model for Option Pricing , 2001, Manag. Sci..

[16]  N. Han,et al.  Optimal asset allocation for DC pension plans under inflation , 2012 .

[17]  Salvatore Federico,et al.  Pension funds with a minimum guarantee: a stochastic control approach , 2008, Finance Stochastics.

[18]  Zhongfei Li,et al.  Precommitment and equilibrium investment strategies for defined contribution pension plans under a jump–diffusion model , 2016 .

[19]  Zhenjie Ren,et al.  A Dual Algorithm for Stochastic Control Problems: Applications to Uncertain Volatility Models and CVA , 2015, SIAM J. Financial Math..

[20]  G. Deelstra,et al.  Optimal investment strategies in the presence of a minimum guarantee , 2003 .

[21]  Dynamic Portfolio Choice with Stochastic Wage and Life Insurance , 2012 .

[22]  C. Nkeki.  Optimal pension fund management in a jumpdiffusion environment , 2018 .

[23]  Hui Wang,et al.  First passage times of a jump diffusion process , 2003, Advances in Applied Probability.

[24]  Guohui Guan,et al.  Mean–variance efficiency of DC pension plan under stochastic interest rate and mean-reverting returns , 2015 .