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19 pages, 386 KiB

Open AccessArticle

Optimal Investment Strategy for DC Pension Plan with Stochastic Salary and Value at Risk Constraint in Stochastic Volatility Model

by Zilan Liu, Huanying Zhang, Yijun Wang and Ya Huang

Axioms 2024, 13(8), 543; https://doi.org/10.3390/axioms13080543 - 10 Aug 2024

Cited by 1 | Viewed by 1066

Abstract

This paper studies the optimal asset allocation problem of a defined contribution (DC) pension plan with a stochastic salary and value under a constraint within a stochastic volatility model. It is assumed that the financial market contains a risk-free asset and a risky [...] Read more.

This paper studies the optimal asset allocation problem of a defined contribution (DC) pension plan with a stochastic salary and value under a constraint within a stochastic volatility model. It is assumed that the financial market contains a risk-free asset and a risky asset whose price process satisfies the Stein–Stein stochastic volatility model. To comply with regulatory standards and offer a risk management tool, we integrate the dynamic versions of Value-at-Risk (VaR), Conditional Value-at-Risk (CVaR), and worst-case CVaR (wcCVaR) constraints into the DC pension fund management model. The salary is assumed to be stochastic and characterized by geometric Brownian motion. In the dynamic setting, a CVaR/wcCVaR constraint is equivalent to a VaR constraint under a higher confidence level. By using the Lagrange multiplier method and the dynamic programming method to maximize the constant absolute risk aversion (CARA) utility of terminal wealth, we obtain closed-form expressions of optimal investment strategies with and without a VaR constraint. Several numerical examples are provided to illustrate the impact of a dynamic VaR/CVaR/wcCVaR constraint and other parameters on the optimal strategy. Full article

(This article belongs to the Special Issue Stochastic Optimization and Metaheuristic Optimization: Theory and Applications)

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22 pages, 806 KiB

Open AccessFeature PaperArticle

Optimal Investment for Defined-Contribution Pension Plans with the Return of Premium Clause under Partial Information

by Zilan Liu, Huanying Zhang, Yijun Wang and Ya Huang

Mathematics 2024, 12(13), 2130; https://doi.org/10.3390/math12132130 - 7 Jul 2024

Viewed by 1207

Abstract

The optimal investment problem for defined contribution (DC) pension plans with partial information is the subject of this paper. The purpose of the return of premium clauses is to safeguard the rights of DC pension plan participants who pass away during accumulation. We [...] Read more.

The optimal investment problem for defined contribution (DC) pension plans with partial information is the subject of this paper. The purpose of the return of premium clauses is to safeguard the rights of DC pension plan participants who pass away during accumulation. We assume that the market price of risk consists of observable and unobservable factors that follow the Ornstein-Uhlenbeck processes, and the pension fund managers estimate the unobservable component from known information through Bayesian learning. Considering maximizing the expected utility of fund wealth at the terminal time, optimal investment strategies and the corresponding value function are determined using the dynamical programming principle approach and the filtering technique. Additionally, fund managers forsake learning, which results in the presentation of suboptimal strategies and utility losses for comparative analysis. Lastly, numerical analyses are included to demonstrate the impact of model parameters on the optimal strategy. Full article

(This article belongs to the Section E5: Financial Mathematics)

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13 pages, 1672 KiB

Open AccessArticle

Sustaining Retirement during Lockdown: Annuitized Income and Older American’s Financial Well-Being before and during the COVID-19 Pandemic

by Qi Sun and Gary Curnutt

J. Risk Financial Manag. 2023, 16(10), 432; https://doi.org/10.3390/jrfm16100432 - 3 Oct 2023

Cited by 2 | Viewed by 1635

Abstract

The landscape of employer-sponsored retirement plans in the U.S. has changed dramatically during the past few decades as more and more private-sector employers have decided to freeze or terminate traditional pension plans. Defined contribution (DC) plans became the primary choice or the only [...] Read more.

The landscape of employer-sponsored retirement plans in the U.S. has changed dramatically during the past few decades as more and more private-sector employers have decided to freeze or terminate traditional pension plans. Defined contribution (DC) plans became the primary choice or the only choice for employees to participate in employer-sponsored retirement plans. In the next ten to twenty years, the income from pension plans will only count for a third of the total retirement income for GenXers when compared to their baby boomer counterparts. It is important for research to provide evidence on how the change in retirement income resources impacts retirees’ retirement security and financial wellness. Using Health and Retirement Study (HRS) data before and during the COVID-19 pandemic, this study examines the association between annuitized income and various measures of older Americans’ financial well-being over time, particularly during the pandemic. This study finds that receiving annuitized income has a statistically significant relationship with reduced subjective financial well-being for both measurements, while only one of the measures of objective well-being, having liquid assets greater than the median household income, has a statistically significant positive relationship with receiving annuitized income. Full article

(This article belongs to the Special Issue Economic Behavior and Risk Management)

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21 pages, 805 KiB

Open AccessArticle

Optimal Choice between Defined Contribution and Cash Balance Pension Schemes: Balancing Interests of Employers and Workers

by Vanessa Hanna and Pierre Devolder

Risks 2023, 11(7), 135; https://doi.org/10.3390/risks11070135 - 21 Jul 2023

Cited by 1 | Viewed by 1504

Abstract

In the context of pension plans, the employer and the worker have distinct interests and face different risks. The worker seeks higher retirement benefits, while the employer aims to minimize the cost of fulfilling his obligations. To address these diverse needs, the defined [...] Read more.

In the context of pension plans, the employer and the worker have distinct interests and face different risks. The worker seeks higher retirement benefits, while the employer aims to minimize the cost of fulfilling his obligations. To address these diverse needs, the defined contribution plan managed with participating life insurance (DC-PL) and the cash balance plan managed with unit-linked insurance (CB-UL) serve as suitable choices. The multi-criteria analysis is conducted using the cumulative prospect theory model to measure the utility of the parties involved toward a mixed product combining these two pension plans. By assigning weights to risk measures and maximizing utilities, the paper employs both additive utility and Nash equilibrium approaches. The results reveal that the CB-UL plan aligns with employers’ interests, offering potential financial gains, while the DC-PL plan attracts workers due to its profit-sharing aspect. Significantly, when equal importance is given to both parties, the CB-UL plan emerges as the prevailing choice. This study contributes to the understanding of pension plan design and decision-making dynamics between employers and workers, providing valuable insights for achieving a balance between retirement benefits and cost management. Full article

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20 pages, 1089 KiB

Open AccessArticle

Optimal Defined Contribution Pension Management with Jump Diffusions and Common Shock Dependence

by Wujun Lv, Linlin Tian and Xiaoyi Zhang

Mathematics 2023, 11(13), 2954; https://doi.org/10.3390/math11132954 - 2 Jul 2023

Cited by 2 | Viewed by 1541

Abstract

This work deals with an optimal asset allocation problem for a defined contribution (DC) pension plan during its accumulation phase. The contribution rate is assumed to be proportional to the individual’s salary. The salary follows a Heston stochastic volatility model with jumps, and [...] Read more.

This work deals with an optimal asset allocation problem for a defined contribution (DC) pension plan during its accumulation phase. The contribution rate is assumed to be proportional to the individual’s salary. The salary follows a Heston stochastic volatility model with jumps, and there exists common shock dependence between the salary and the volatility. Since the time horizon of pension management is quite long, the influence of inflation is considered in the given context. The aim of the pension plan described in this paper is to reduce fluctuations in terminal wealth by investing in the bond and the stock. Through the dynamic programming principle, the Hamilton–Jacobi–Bellman equation is shown. The explicit expression of the investment decision is derived by solving the Hamilton–Jacobi–Bellman equation. In the last part, a numerical analysis is shown to illustrate the impacts of different parameters on the optimal investment policy. Full article

(This article belongs to the Special Issue Modeling, Analysis and Optimization for Mathematical Finance, Economics and Risks)

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15 pages, 325 KiB

Open AccessArticle

Optimal Investment Strategy for DC Pension Plan with Deposit Loan Spread under the CEV Model

by Yang Wang, Xiao Xu and Jizhou Zhang

Axioms 2022, 11(8), 382; https://doi.org/10.3390/axioms11080382 - 4 Aug 2022

Cited by 2 | Viewed by 1893

Abstract

This paper is devoted to determining an optimal investment strategy for a defined-contribution (DC) pension plan with deposit loan spread under the constant elasticity of variance (CEV) model. As far as we know, few studies in the literature have taken loans into account [...] Read more.

This paper is devoted to determining an optimal investment strategy for a defined-contribution (DC) pension plan with deposit loan spread under the constant elasticity of variance (CEV) model. As far as we know, few studies in the literature have taken loans into account when using the CEV model in financial market contexts. The contribution of this paper is to study the impact of deposit loan spread on DC pension investment strategy. By considering a risk-free asset, a risky asset driven by CEV model, and a loan in the financial market, we first set up the dynamic equation and the asset market model, which are instrumental in achieving the expected utility of ultimate wealth at retirement. Second, the corresponding Hamilton–Jacobi–Bellman (HJB) equation is derived by means of the dynamic programming principle. The explicit expression for the optimal investment strategy is obtained using the Legendre transform method. Finally, different parameters are selected to simulate the explicit solution, and the financial interpretation of the optimal investment strategy is provided. We find that the deposit loan spread has a great impact on the investment strategy of DC pension plans. Full article

(This article belongs to the Special Issue Financial Mathematics, Stochastic Control, Machine Learning and Related Fields)

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21 pages, 2529 KiB

Open AccessFeature PaperArticle

Optimal Pension Fund Management with Foreign Investment in a Stochastic Environment

by Mei-Ling Tang, Ting-Pin Wu and Ming-Chin Hung

Mathematics 2022, 10(14), 2468; https://doi.org/10.3390/math10142468 - 15 Jul 2022

Cited by 7 | Viewed by 2419

Abstract

To ensure the success of a pension plan under a self-contained defined contribution (DC) retirement plan, the inclusion of foreign assets in a local pension portfolio could be beneficial for risk diversification and the efficient improvement of a fund’s investment performance during its [...] Read more.

To ensure the success of a pension plan under a self-contained defined contribution (DC) retirement plan, the inclusion of foreign assets in a local pension portfolio could be beneficial for risk diversification and the efficient improvement of a fund’s investment performance during its accumulation phase. This study focuses on developing international asset allocation criteria for a DC pension plan; accordingly, we consider risk exposure relative to stochastic interest rates and ex- change rates with minimum guarantees. An arbitrage-free framework, namely, the cross-currency Heath–Jarrow–Morton interest rate model, is introduced in dynamic optimization programming for the DC pension fund. The proposed solution based on the generalized stochastic framework provides tractable and appropriate criteria for the dynamic allocation of a DC pension fund. The constituents of the optimal solution can reflect changes in investment lifecycles and shifts in risk preferences during the accumulation phase of a DC pension plan. Full article

(This article belongs to the Special Issue Pension Mathematics—New Development for the Near Future)

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18 pages, 379 KiB

Open AccessArticle

Optimal Control of Background-Based Uncertain Systems with Applications in DC Pension Plan

by Wei Liu, Wanying Wu, Xiaoyi Tang and Yijun Hu

Entropy 2022, 24(5), 734; https://doi.org/10.3390/e24050734 - 21 May 2022

Cited by 1 | Viewed by 2161

Abstract

In this paper, we propose a new optimal control model for uncertain systems with jump. In the model, the background-state variables are incorporated, where the background-state variables are governed by an uncertain differential equation. Meanwhile, the state variables are governed by another uncertain [...] Read more.

In this paper, we propose a new optimal control model for uncertain systems with jump. In the model, the background-state variables are incorporated, where the background-state variables are governed by an uncertain differential equation. Meanwhile, the state variables are governed by another uncertain differential equation with jump, in which both the background-state variables and the control variables are involved. Under the optimistic value criterion, using uncertain dynamic programming method, we establish the principle and the equation of optimality. As an application, the optimal investment strategy and optimal payment rate for DC pension plans are given, where the corresponding background-state variables represent the salary process. This application in DC pension plans illustrates the effectiveness of the proposed model. Full article

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21 pages, 1865 KiB

Open AccessArticle

Good Practice Principles in Modelling Defined Contribution Pension Plans

by Kevin Dowd and David Blake

J. Risk Financial Manag. 2022, 15(3), 108; https://doi.org/10.3390/jrfm15030108 - 26 Feb 2022

Cited by 3 | Viewed by 3102

Abstract

We establish 16 good practice principles for modelling defined contribution pension plans. These principles cover the following issues: model specification and calibration; modelling quantifiable uncertainty; modelling member choices; modelling member characteristics, such as occupation and gender; modelling plan charges; modelling longevity risk; modelling [...] Read more.

We establish 16 good practice principles for modelling defined contribution pension plans. These principles cover the following issues: model specification and calibration; modelling quantifiable uncertainty; modelling member choices; modelling member characteristics, such as occupation and gender; modelling plan charges; modelling longevity risk; modelling the post-retirement period; integrating the pre- and post-retirement periods; modelling additional sources of income, such as the state pension and equity release; modelling extraneous factors, such as unemployment risk, activity rates, taxes and welfare entitlements; scenario analysis and stress testing; periodic updating of the model and changing assumptions; and overall fitness for purpose. Full article

(This article belongs to the Special Issue Macroeconomic Modelling)

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15 pages, 305 KiB

Open AccessArticle

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

by Yang Wang, Xiao Xu and Jizhou Zhang

Mathematics 2021, 9(15), 1756; https://doi.org/10.3390/math9151756 - 26 Jul 2021

Cited by 9 | Viewed by 2772

Abstract

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 [...] Read more.

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. Full article

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27 pages, 603 KiB

Open AccessArticle

Defined Contribution Pension Plans: Who Has Seen the Risk?

by Peter A. Forsyth and Kenneth R. Vetzal

J. Risk Financial Manag. 2019, 12(2), 70; https://doi.org/10.3390/jrfm12020070 - 24 Apr 2019

Cited by 5 | Viewed by 5228

Abstract

The trend towards eliminating defined benefit (DB) pension plans in favour of defined contribution (DC) plans implies that increasing numbers of pension plan participants will bear the risk that final realized portfolio values may be insufficient to fund desired retirement cash flows. We [...] Read more.

The trend towards eliminating defined benefit (DB) pension plans in favour of defined contribution (DC) plans implies that increasing numbers of pension plan participants will bear the risk that final realized portfolio values may be insufficient to fund desired retirement cash flows. We compare the outcomes of various asset allocation strategies for a typical DC plan investor. The strategies considered include constant proportion, linear glide path, and optimal dynamic (multi-period) time consistent quadratic shortfall approaches. The last of these is based on a double exponential jump diffusion model. We determine the parameters of the model using monthly US data over a 90-year sample period. We carry out tests in a synthetic market which is based on the same jump diffusion model and also using bootstrap resampling of historical data. The probability that portfolio values at retirement will be insufficient to provide adequate retirement incomes is relatively high, unless DC investors adopt optimal allocation strategies and raise typical contribution rates. This suggests there is a looming crisis in DC plans, which requires educating DC plan holders in terms of realistic expectations, required contributions, and optimal asset allocation strategies. Full article

(This article belongs to the Special Issue Computational Finance)

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16 pages, 322 KiB

Open AccessArticle

Stochastic Game Theoretic Formulation for a Multi-Period DC Pension Plan with State-Dependent Risk Aversion

by Liyuan Wang and Zhiping Chen

Mathematics 2019, 7(1), 108; https://doi.org/10.3390/math7010108 - 21 Jan 2019

Cited by 7 | Viewed by 3408

Abstract

When facing a multi-period defined contribution (DC) pension plan investment problem during the accumulation phase, the risk aversion attitude of a mean-variance investor may depend on state variables. In this paper, we propose a state-dependent risk aversion model which is a linear function [...] Read more.

When facing a multi-period defined contribution (DC) pension plan investment problem during the accumulation phase, the risk aversion attitude of a mean-variance investor may depend on state variables. In this paper, we propose a state-dependent risk aversion model which is a linear function of the current wealth level after contribution. This risk aversion model is reasonable from both the dimensional analysis and the economic point of view. Moreover, we incorporate the wage income factor into our model. In the field of dynamic investment analysis, most studies have irrational situations in their models because of the lack of the positiveness for the wealth process. In view of it, we further improve the work of Wang and Chen by completely eliminating the irrationality of the model. Due to the time-inconsistency of the resulting stochastic control problem, we derive the explicit expressions of the equilibrium control and the corresponding equilibrium value function by adopting the game theoretic framework developed in Björk and Murgoci. Further, two special cases are discussed. Finally, using a more realistic risk aversion coefficient, we provide a series of empirical tests based on the real data from the American market and compare our results with the relevant results in the literature. Full article

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16 pages, 409 KiB

Open AccessArticle

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

by Xiaoyi Zhang and Junyi Guo

Risks 2018, 6(2), 24; https://doi.org/10.3390/risks6020024 - 22 Mar 2018

Cited by 4 | Viewed by 4014

Abstract

This paper investigates the optimal investment strategy for a defined contribution (DC) pension plan during the decumulation phase 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 [...] Read more.

This paper investigates the optimal investment strategy for a defined contribution (DC) pension plan during the decumulation phase 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 real wealth by investing the fund 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 related Hamilton-Jacobi-Bellman (HJB) equation. The results reveal that, with any level of the parameters, an inflation-indexed bond has significant advantage to hedge inflation risk. Full article

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14 pages, 481 KiB

Open AccessFeature PaperArticle

Minimum Protection in DC Funding Pension Plans and Margrabe Options

by Pierre Devolder and Sébastien De Valeriola

Risks 2017, 5(1), 5; https://doi.org/10.3390/risks5010005 - 18 Jan 2017

Cited by 5 | Viewed by 5292

Abstract

The regulation on the Belgian occupational pension schemes has been recently changed. The new law allows for employers to choose between two different types of guarantees to offer to their affiliates. In this paper, we address the question arising naturally: which of the [...] Read more.

The regulation on the Belgian occupational pension schemes has been recently changed. The new law allows for employers to choose between two different types of guarantees to offer to their affiliates. In this paper, we address the question arising naturally: which of the two guarantees is the best one? In order to answer that question, we set up a stochastic model and use financial pricing tools to compare the methods. More specifically, we link the pension liabilities to a portfolio of financial assets and compute the price of exchange options through the Margrabe formula. Full article

(This article belongs to the Special Issue Actuarial and Financial Risks in Life Insurance, Pensions and Household Finance)

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26 pages, 330 KiB

Open AccessArticle

Portability, Salary and Asset Price Risk: A Continuous-Time Expected Utility Comparison of DB and DC Pension Plans

by An Chen and Filip Uzelac

Risks 2015, 3(1), 77-102; https://doi.org/10.3390/risks3010077 - 13 Mar 2015

Cited by 3 | Viewed by 6027

Abstract

This paper compares two different types of private retirement plans from the perspective of a representative beneficiary: a defined benefit (DB) and a defined contribution (DC) plan. While salary risk is the main common risk factor in DB and DC pension plans, one [...] Read more.

This paper compares two different types of private retirement plans from the perspective of a representative beneficiary: a defined benefit (DB) and a defined contribution (DC) plan. While salary risk is the main common risk factor in DB and DC pension plans, one of the key differences is that DB plans carry portability risks, whereas DC plans bear asset price risk. We model these tradeoffs explicitly in this paper and compare these two plans in a utility-based framework. Our numerical analysis focuses on answering the question of when the beneficiary is indifferent between the DB and DC plan. Most of our results confirm the findings in the existing literature, among which, e.g., portability losses considerably reduce the relative attractiveness of the DB plan. However, we also find that the attractiveness of the DB plan can decrease in the level of risk aversion, which is inconsistent with the existing literature. Full article

(This article belongs to the Special Issue Life Insurance and Pensions)

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