Markowitz’s mean–variance defined contribution pension fund management under inflation: A continuous-time model

Yao, Haixiang; Yang, Zhou; Chen, Ping

doi:10.1016/j.insmatheco.2013.10.002

Cited by 53 publications

(43 citation statements)

References 18 publications

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“…It is usually assumed that a price index, which is used to proxy an inflation rate, is modeled by a stochastic process. Here, as in Munk et al [15] and Yao et al [38], it is supposed that the evolution of the nominal price index of a consumption good in an economy over time is governed by the following geometric Brownian motion with stochastic drift:…”

Section: Price Indexmentioning

confidence: 99%

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Optimal Investment-Reinsurance Policy with Stochastic Interest and Inflation Rates

Zhang

Zheng²

2019

Mathematical Problems in Engineering

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The aim of this paper is to study a classic problem in actuarial mathematics, namely, an optimal reinsurance-investment problem, in the presence of stochastic interest and inflation rates. This is of relevance since insurers make investment and risk management decisions over a relatively long horizon where uncertainty about interest rate and inflation rate may have significant impacts on these decisions. We consider the situation where three investment opportunities, namely, a savings account, a share, and a bond, are available to an insurer in a security market. In the meantime, the insurer transfers part of its insurance risk through acquiring a proportional reinsurance. The investment and reinsurance decisions are made so as to maximize an expected power utility on terminal wealth. An explicit solution to the problem is derived for each of the two well-known stochastic interest rate models, namely, the Ho–Lee model and the Vasicek model, using standard techniques in stochastic optimal control theory. Numerical examples are presented to illustrate the impacts of the two different stochastic interest rate modeling assumptions on optimal decision making of the insurer.

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Section: Price Indexmentioning

confidence: 99%

“…To simplify our discussion, it is assumed that σ 0 (t), α(t), β(t), and σ 0 (t) are deterministic and continuous functions of time t ∈ [0, T]. However, we adopt here a time-dependent OU process rather than the one in Munk et al [15] and Yao et al [38].…”

Section: Price Indexmentioning

confidence: 99%

Optimal Investment-Reinsurance Policy with Stochastic Interest and Inflation Rates

Zhang

Zheng²

2019

Mathematical Problems in Engineering

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“…Also, a DC pension plan is a function of the contribution that the pension member paid during his or her working life, in which only the contributions are fixed, and therefore the benefits depend solely on the returns of the fund's portfolio, so it is meaningful to protect inflation risk in such kind of pension scheme. Yao et al [8] solve a mean-variance problem by 2 of 12 considering the real wealth process including the influence of inflation. Okoro and Nkeki [9] examine the optimal variational Merton portfolios with inflation protection strategy.…”

Section: Introductionmentioning

confidence: 99%

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

Zhang¹,

Guo²

2018

Preprint

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Abstract: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.

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“…Guan and Liang (2014) considered the risks of interest and volatility of stock together and obtained the explicit solution to maximize the CRRA utility of terminal wealth over an annuity guarantee. Recently, Yao et al (2013), Han and Hung (2012) solved problem of DC plan with inflation risk under CRRA utility maximization and mean-variance criterion, respectively. Yao et al (2014) studied risks of mortality and contribution.…”

Section: Introductionmentioning

confidence: 99%

Optimal management of DC pension plan under loss aversion and Value-at-Risk constraints

Guan

Liang

2016

Insurance: Mathematics and Economics

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Markowitz’s mean–variance defined contribution pension fund management under inflation: A continuous-time model

Cited by 53 publications

References 18 publications

Optimal Investment-Reinsurance Policy with Stochastic Interest and Inflation Rates

Optimal Investment-Reinsurance Policy with Stochastic Interest and Inflation Rates

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

Optimal management of DC pension plan under loss aversion and Value-at-Risk constraints

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