Optimal DC pension management under inflation risk with jump diffusion price index and cost of living process. (English) Zbl 1489.91228
Summary: 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 S. Wang et al. [Insur. Math. Econ. 80, 1–14 (2018; Zbl 1402.91218)], 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.
MSC:
| 91G05 | Actuarial mathematics |
| 91G10 | Portfolio theory |
| 49N90 | Applications of optimal control and differential games |
| 90C39 | Dynamic programming |
Keywords:
DC pension plan; inflation; Poisson process; stochastic optimal control; dynamic programming approach; HJB equationCitations:
Zbl 1402.91218References:
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