Skip to main content
SpringerLink
Log in

Optimal DC Pension Management Under Inflation Risk With Jump Diffusion Price Index and Cost of Living Process

  • Published:
Methodology and Computing in Applied Probability Aims and scope Submit manuscript

Abstract

This work deals with an optimal benefit distribution and asset allocation problem for a defined contribution (DC) pension plan during its decumulation phase. With the phenomenon of longevity, the time horizon of pension management during this phase might be long, thus the influence of inflation is considered in the context. The inflation index is subjected to a Poisson jump and a Brownian uncertainty. Motivated by the work of Wang et al. (2018), it is assumed that the scheme provides cost of living adjustment, which is extended to a jump diffusion process in this work. The plan aims to reduce fluctuations of benefit and terminal wealth by investing the fund in a financial market consisting of a bank account, an inflation indexed bond and a stock. The dynamics of two risky assets are also given by jump diffusion processes. The closed form decisions are derived by using the dynamic programming approach.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12

Similar content being viewed by others

References

  • Bégin J (2020) Levelling the playing field: A VIX-linked structure for funded pension schemes. Insurance Math Econom 94:58–78

    Article  MathSciNet  Google Scholar 

  • Berstein B, Morales M (2021) The role of a longevity insurance for defined contribution pension systems. Insurance Math Econom 99:233–240

    Article  MathSciNet  Google Scholar 

  • Björk T, Slinko I (2006) Towards a general theory of good-deal bounds. Review of Finance 10:221–260

    Article  Google Scholar 

  • Blake D, Cairns AJG (2021) Longevity risk and capital markets: The 2019–20 update. Insurance Math Econom 99:395–439

    Article  MathSciNet  Google Scholar 

  • Chen DHJ, Beetsma RMWJ, Wijnbergen SJG (2020) Unhedgeable inflation risk within pension schemes. Insurance Math Econom 90:7–24

    Article  MathSciNet  Google Scholar 

  • Chen Z, Li Z, Yan Z, Sun J (2017) Asset allocation under loss aversion and minimum performance constraint in a DC pension plan with inflation risk. Insurance Math Econom 75:137–150

    Article  MathSciNet  Google Scholar 

  • Delong L, Gerrard R, Haberman S (2008) Mean-variance optimization problems for an accumulation phase in a defined benefit plan. Insurance Math Econom 42:107–118

    Article  MathSciNet  Google Scholar 

  • Fleming WH, Soner HM (1993) Controlled Markov Processes and Viscosity Solutions. Springer-Verlag, New York

    MATH  Google Scholar 

  • Han N, Hung M (2012) Optimal asset allocation for DC pension plans under inflation. Insurance Math Econom 51:172–181

    Article  MathSciNet  Google Scholar 

  • Liang X, Bai L, Guo J (2014) Optimal time-consistent portfolio and contribution selection for defined benefit pension schemes under mean-variance criterion. ANZIAM J 56:66–90

    MathSciNet  MATH  Google Scholar 

  • Liang Z, Zhao X (2016) Optimal mean-variance efficiency of a family with life insurance under inflation risk. Insurance Math Econom 71:164–178

    Article  MathSciNet  Google Scholar 

  • Merton RC (1971) Optimal consumption and portfolio rules in a continuous-time model. J Econ Theo 3:373–413

    Article  MathSciNet  Google Scholar 

  • Ngwira B, Gerrard R (2007) Stochastic pension fund control in the presence of Poisson jumps. Insurance Math Econom 40:283–292

    Article  MathSciNet  Google Scholar 

  • Nkeki CI (2018) Optimal pension fund management in a jump Cdiffusion environment: Theoretical and empirical studies. J Comput Appl Math 330:228–252

    Article  MathSciNet  Google Scholar 

  • Pan J, Xiao Q (2017) Optimal dynamic asset-liability management with stochastic interest rates and inflation risks. Chaos, Solitons Fractals 103:460–469

    Article  MathSciNet  Google Scholar 

  • Sun J, Li Z, Zeng Y (2016) Precommitment and equilibrium investment strategies for defined contribution pension plans under a jump-diffusion model. Insurance Math Econom 67:158–172

    Article  MathSciNet  Google Scholar 

  • Tang M, Chen S, Lai GC, Wu T (2018) Asset allocation for a DC pension fund under stochastic interest rates and inflation-protected guarantee. Insurance Math Econom 78:87–104

    Article  MathSciNet  Google Scholar 

  • Wang S, Lu Y, Sanders B (2018) Optimal investment strategies and intergenerational risk sharing for target benefit pension plans. Insurance Math Econom 80:1–14

    Article  MathSciNet  Google Scholar 

  • Yao H, Yang Z, Chen P (2013) Markowitz’s mean-variance defined contribution pension fund management under inflation: A continuous-time model. Insurance Math Econom 53:851–863

    Article  MathSciNet  Google Scholar 

  • Yong X, Zhou XY (1999) Stochastic Controls: Hamiltonian Systems and HJB Equations. Springer-Verlag, New York

    Book  Google Scholar 

  • Zhang A, Ralf K, Ewald C (2007) Optimal management and inflation protection for defined contribution pension plans. Bl DGVFM 28:239–258

    Article  MathSciNet  Google Scholar 

  • Zhang A, Ewald C (2010) Optimal investment for a pension fund under inflation risk. Math Methods Oper Res 71:353–369

    Article  MathSciNet  Google Scholar 

Download references

Funding

This paper was supported by the High School Natural Science Foundation of Hebei Province with NO. QN2021215.

Author information

Authors and Affiliations

  1. School of Economics and Management, Hebei University of Technology, Tianjin, 300401, P.R. China

    Xiaoyi Zhang

Authors
  1. Xiaoyi Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xiaoyi Zhang.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhang, X. Optimal DC Pension Management Under Inflation Risk With Jump Diffusion Price Index and Cost of Living Process. Methodol Comput Appl Probab 24, 1253–1270 (2022). https://doi.org/10.1007/s11009-022-09930-9

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11009-022-09930-9

Keywords

Mathematics Subject Classification

Search

Navigation