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

2019 ◽  
Vol 360 ◽  
pp. 55-61 ◽  
Author(s):  
Walter Mudzimbabwe
Keyword(s):  
Numerical Solution ◽  
Diffusion Model ◽  
Pension Plan ◽  
Optimal Investment ◽  
Jump Diffusion ◽  
Investment Strategy ◽  
Optimal Investment Strategy ◽  
Jump Diffusion Model

scholarly journals The Role of Inflation-indexed Bond in Optimal Management of Defined Contribution Pension Plan During the Decumulation Phrase

2018 ◽  
Author(s):  
Xiaoyi Zhang ◽  
Junyi Guo
Keyword(s):  
Pension Plan ◽  
Optimal Investment ◽  
Investment Strategy ◽  
Programming Approach ◽  
Defined Contribution ◽  
Inflation Risk ◽  
Dynamic Programming Approach ◽  
Optimal Investment Strategy ◽  
Defined Contribution Pension Plan ◽  
Hamilton Jacobi Bellman

In this paper we investigate the optimal investment strategy for a defined contribution (DC) pension plan during the decumulation phrase which is risk-averse and pays close attention to inflation risk. The plan aims to maximize the expected constant relative risk aversion (CRRA) utility from the terminal wealth by investing the wealth in a financial market consisting of an inflation-indexed bond, an ordinary zero coupon bond and a risk-free asset. We derive the optimal investment strategy in closed-form using the dynamic programming approach by solving the corresponding Hamilton-Jacobi-Bellman (HJB) equation. Our theoretical and numerical results reveal that under some rational assumptions, an inflation-indexed bond do has significant advantage to hedge inflation risk.

scholarly journals Alpha-robust mean-variance investment strategy for DC pension plan with uncertainty about jump-diffusion risk

2020 ◽  
Author(s):  
Danping Li ◽  
Junna BI ◽  
Mengcong Hu
Keyword(s):  
Ambiguity Aversion ◽  
Pension Plan ◽  
Optimal Investment ◽  
Jump Diffusion ◽  
Investment Strategy ◽  
Investment Strategies ◽  
Value Functions ◽  
Defined Contribution ◽  
Optimal Investment Problem ◽  
Mean Variance

This paper considers an alpha-robust optimal investment problem for a defined contribution (DC) pension plan with uncertainty about jump and diffusion risks in a mean-variance framework. Our model allows the pension manager to have different levels of ambiguity aversion, rather than only consider the extremely ambiguity-averse attitude. Moreover, in the DC pension plan, contributions are supposed to be a predetermined amount of money as premiums and the pension funds are allowed to be invested in a financial market which consists of a risk-free asset, and a risky asset satisfying a jump-diffusion process. Notice that a part of pension members could die during the accumulation phase, and their premiums should be withdrawn. Thus, we consider the return of premiums clauses by an actuarial method and assume that the surviving members will share the difference between the return and the accumulation equally. Taking account of the pension fund size and the volatility of the accumulation, a mean-variance criterion as the investment objective for the DC plan can be formulated. By applying a game theoretic framework, the equilibrium investment strategies and the corresponding equilibrium value functions can be obtained explicitly. Economic interpretations are given in the numerical simulation, which is presented to illustrate our results.

RISK MANAGEMENT OF FINANCIAL CRISES: AN OPTIMAL INVESTMENT STRATEGY WITH MULTIVARIATE JUMP-DIFFUSION MODELS

2017 ◽  
Vol 47 (2) ◽  
pp. 501-525 ◽  
Author(s):  
Chou-Wen Wang ◽  
Hong-Chih Huang
Keyword(s):  
Risk Management ◽  
Financial Crisis ◽  
Asset Allocation ◽  
Optimal Investment ◽  
Jump Diffusion ◽  
Investment Strategy ◽  
Dependence Structure ◽  
Allocation Strategy ◽  
Investment Performance ◽  
Optimal Investment Strategy

AbstractThis paper provides an optimal asset allocation strategy to enhance risk management performance in the face of a financial crisis; this strategy entails constructing a good asset model – a multivariate jump-diffusion (MJD) model which includes idiosyncratic and systematic jumps simultaneously – and choosing suitable asset allocations and objective functions for fund management. This study also provides the dependence structure for the MJD model. The empirical implementation demonstrates that the proposed MJD model provides more detailed information about the financial crisis, allowing fund managers to determine an appropriate asset allocation strategy that enhances investment performance during the crisis.

scholarly journals Optimal Investment Strategy for DC Pension Plan with Stochastic Income and Inflation Risk under the Ornstein–Uhlenbeck Model

Mathematics ◽  
2021 ◽  
Vol 9 (15) ◽  
pp. 1756
Author(s):  
Yang Wang ◽  
Xiao Xu ◽  
Jizhou Zhang
Keyword(s):  
Control Method ◽  
Closed Form Solution ◽  
Pension Plan ◽  
Optimal Investment ◽  
Investment Strategy ◽  
Risky Asset ◽  
Legendre Transform ◽  
Defined Contribution ◽  
Inflation Risk ◽  
Optimal Investment Strategy

This paper is concerned with the optimal investment strategy for a defined contribution (DC) pension plan. We assumed that the financial market consists of a risk-free asset and a risky asset, where the risky asset is subject to the Ornstein–Uhlenbeck (O-U) process, and stochastic income and inflation risk were also considered in the model. We firstly derived the Hamilton–Jacobi–Bellman (HJB) equation through the stochastic control method. Secondly, under the logarithmic utility function, the closed-form solution of optimal asset allocation was obtained by using the Legendre transform method. Finally, we give several numerical examples and a financial analysis.

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