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21 pages, 660 KB  
Article
Heterogeneous Effects of Income on Physical and Mental Health of the Elderly: A Regression Discontinuity Design Based on China’s New Rural Pension Scheme
by Tao Ju and Mengmeng Pan
Int. J. Environ. Res. Public Health 2025, 22(11), 1709; https://doi.org/10.3390/ijerph22111709 - 13 Nov 2025
Viewed by 886
Abstract
Aging has been a social phenomenon unprecedented in history, which poses greater challenges on ensuring the health of the growing old population. We aim to estimate the effects of pension income on the physical and mental health of the elderly and further explore [...] Read more.
Aging has been a social phenomenon unprecedented in history, which poses greater challenges on ensuring the health of the growing old population. We aim to estimate the effects of pension income on the physical and mental health of the elderly and further explore the complementary effects of external community medical environments with external pension income. We develop a Regression Discontinuity Design using an exogenous shock to the income—China’s New Rural Pension Scheme (NRPS), the world’s largest existing pension scheme. We find that public pension policy provides financial support to the elderly but also increases the loss of their perceived controllability. Specifically, empirical results indicate that pension income plays a positive effect on physical health and a negative effect on mental health. The positive effect only exists when communities have better medical environments, while the negative relationship is not affected by the external medical environment. Our findings reveal that internal pension income and external medical environment are therefore complementary factors to achieve better physical health of the elderly, while passive dependence on pension income may reduce mental health by heightening older people’s negative perceptions of losing controllability of their lives. Money is not omnipotent in both the physical and mental health of the elderly. Full article
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13 pages, 450 KB  
Article
South Africa’s Two-Pot Retirement Savings Model Under Labor Market Uncertainty
by Tichaona Chikore and Farai Nyabadza
Economies 2025, 13(11), 318; https://doi.org/10.3390/economies13110318 - 7 Nov 2025
Viewed by 682
Abstract
This study addresses the critical challenge of designing retirement savings systems that effectively balance liquidity needs and long-term accumulation in contexts characterized by high unemployment and labor market instability, with a focus on South Africa. Traditional pension schemes often assume uninterrupted careers and [...] Read more.
This study addresses the critical challenge of designing retirement savings systems that effectively balance liquidity needs and long-term accumulation in contexts characterized by high unemployment and labor market instability, with a focus on South Africa. Traditional pension schemes often assume uninterrupted careers and stable incomes, assumptions frequently violated in low- and middle-income countries, leading to inadequate retirement security and consumption volatility during working life. Motivated by this gap, we develop a stochastic two-pot retirement savings model that explicitly integrates labor market uncertainty using a Markov chain-based Monte Carlo simulation. The model allocates annual contributions between an accessible savings pot and a locked retirement pot, with individuals optimizing consumption and withdrawal decisions to maximize expected lifetime utility under Constant Relative Risk Aversion (CRRA) preferences. Our findings, derived from calibration to South African labor data, reveal that high unemployment and career uncertainty significantly increase the welfare-maximizing preference for liquidity. This result challenges conventional policies prescribing fixed contribution allocations, such as the one-third/two-thirds split in the new two-pot system, and underscores the importance of flexible retirement savings designs. We conclude that tailoring pension design to labor market realities can enhance both retirement security and welfare in volatile economies. Full article
(This article belongs to the Section Labour and Education)
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38 pages, 1461 KB  
Article
Mixed ABMs for NDC Pension Schemes in the Presence of Demographic and Economic Uncertainty
by Jacopo Giacomelli and Massimiliano Menzietti
Mathematics 2025, 13(21), 3454; https://doi.org/10.3390/math13213454 - 29 Oct 2025
Viewed by 562
Abstract
The crisis of pension systems based on pay-as-you-go (PAYG) financing has led to the introduction in some countries, including Italy, of so-called notional defined contribution (NDC) pension accounts. These systems mimic the functioning of defined contribution systems in benefit calculations while remaining based [...] Read more.
The crisis of pension systems based on pay-as-you-go (PAYG) financing has led to the introduction in some countries, including Italy, of so-called notional defined contribution (NDC) pension accounts. These systems mimic the functioning of defined contribution systems in benefit calculations while remaining based on PAYG financing. Despite many appealing features, NDC accounts cannot automatically guarantee a system’s financial sustainability in the presence of demographic or economic fluctuations. The literature proposes automatic balance mechanisms (ABMs) of the notional rate applied to notional accounts and an indexation rate applied to pensions. ABMs may be based on two indicators: the liquidity ratio or the solvency ratio. Such ABMs may strengthen a system’s financial sustainability but may produce significant fluctuations in the adjusted notional rate, thereby undermining the social adequacy of the system. In this work, we introduce a mixed ABM based on both the liquidity ratio and solvency ratio and identify the optimal combination that guarantees financial sustainability of the system and, at the same time, maximizes the return paid to the participants at fixed levels of confidence. The numerical results show the advantages of a mixed mechanism over those based on a single indicator. Indeed, although the results depend on the system’s initial conditions and the different ABM configurations tested (16 in total), some common patterns emerge across the solutions. A solvency ratio-based ABM maximizes social utility, while a liquidity ratio-based one ensures financial stability. Although not optimal for either criterion, the ABM that mixes the liquidity ratio and solvency ratio in proportions ranging from 60–40% to 50–50% emerges from our numerical simulations as the best compromise to achieve these two objectives jointly. Full article
(This article belongs to the Special Issue Modern Trends in Mathematics, Probability and Statistics for Finance)
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27 pages, 2158 KB  
Article
Threshold Effects of PM2.5 on Pension Contributions: A Fuzzy Regression Discontinuity Design and Machine Learning Approach
by Bingxia Wang, Zailan Siri and Mohd Azmi Haron
Sustainability 2025, 17(19), 8620; https://doi.org/10.3390/su17198620 - 25 Sep 2025
Cited by 1 | Viewed by 625
Abstract
Air pollution risk significantly impacts social and economic systems. Given the critical role of the pension system in socioeconomic stability, it is crucial to explore the impact of air pollution on pension contributions. Utilizing panel data from eight Chinese provinces between 2014 and [...] Read more.
Air pollution risk significantly impacts social and economic systems. Given the critical role of the pension system in socioeconomic stability, it is crucial to explore the impact of air pollution on pension contributions. Utilizing panel data from eight Chinese provinces between 2014 and 2024, this study quantifies the impact of Particulate Matter (PM2.5) on pension contributions and explores its nonlinear and lagged effects through a fuzzy regression discontinuity design (FRDD) coupled with double machine learning (DML) techniques. Through the application of the FRDD, we found that pension contributions are significantly reduced when the PM2.5 concentration exceeds the standard annual threshold of 35 µg/m3, and the effects differ between the Urban Employees Basic Pension Insurance (UEBPI) and the Urban and Rural Residents’ Pension Scheme (URRPS). Further, the DML approach validated these findings and suggested that a complex hysteresis response mechanism exists in relation to air pollution. Additionally, it indicated that when PM2.5 concentrations do not exceed the threshold, this similarly has a negative effect on pension contributions. These findings emphasize the need for policymakers and pension fund managers to integrate environmental considerations into pension sustainability strategies to increase resilience to ongoing environmental risks. Full article
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32 pages, 1601 KB  
Article
Assessing Vertical Equity in Defined Benefit Pension Plans: An Application to Switzerland
by Tanja Kirn and Gijs Dekkers
Risks 2025, 13(5), 89; https://doi.org/10.3390/risks13050089 - 8 May 2025
Viewed by 1407
Abstract
This paper establishes a theoretical link between actuarial neutrality and the Oaxaca–Blinder decomposition to empirically assess vertical equity in public defined-benefit schemes. We demonstrate how this approach can be generalized to non-linear functions, point systems, and notional accounts. We use an aligned dynamic [...] Read more.
This paper establishes a theoretical link between actuarial neutrality and the Oaxaca–Blinder decomposition to empirically assess vertical equity in public defined-benefit schemes. We demonstrate how this approach can be generalized to non-linear functions, point systems, and notional accounts. We use an aligned dynamic microsimulation model to apply this method to the first pillar of the Swiss pension system and highlight the following three key effects: (1) the impact of the accrual rate on vertical equity; (2) the assessment of actuarial neutrality through the comparison of migrants with the non-migrant population; and (3) vertical equity across marital statuses. Our findings indicate that changing societal trends, such as increased migration, female labor participation, and the rise in non-marital unions, may alter the extent of vertical equity. This has significant implications for actuarial risk management, as a higher degree of vertical equity is associated with increased pension expenses, thereby raising the financial sustainability risk of the pension system. Future research should explore these dynamics to ensure that pension systems remain both equitable and financially sustainable in the face of evolving societal trends. Full article
(This article belongs to the Special Issue Risk Analysis in Insurance and Pensions)
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22 pages, 3690 KB  
Article
The Influence of Factors in Consumer Sustainable Auto-Enrolment Pensions
by Beata Świecka, Patrycja Kowalczyk-Rólczyńska, Sylwia Pieńkowska-Kamieniecka, Jakub Śledziowski and Paweł Terefenko
Sustainability 2025, 17(3), 1340; https://doi.org/10.3390/su17031340 - 6 Feb 2025
Cited by 2 | Viewed by 3125
Abstract
As pension benefits from statutory public schemes become less generous, and many countries face pension-savings crises, the willingness to participate in supplementary retirement saving instruments becomes crucial for sustainable financial well-being. The main objective of this article is to present how trust and [...] Read more.
As pension benefits from statutory public schemes become less generous, and many countries face pension-savings crises, the willingness to participate in supplementary retirement saving instruments becomes crucial for sustainable financial well-being. The main objective of this article is to present how trust and financial literacy influence the choice of sustainable auto-enrolment pension scheme as a private and supplementary pension savings. The study highlighted factors influencing participation in auto-enrollment and private supplementary pension savings. The study focuses mainly on financial literacy and trust. We used the CAWI method with 857 interviews in Poland—the first country in Central and Eastern Europe to introduce an auto-enrolment pension system. Our study uses multivariable data-mining tools, and several regression models were applied. We used Logistic Regression (LR), Multivariate Linear Regression (MLR), and Factor Analysis of Mixed Data (FAMD) to support the LR analysis. We propose four regression models. Our findings present that: 1. The lower the consumer’s knowledge level, the more their decisions are based on trust. 2. Trust in the state, rather than trust in financial institutions, plays a crucial role for people with low financial literacy, which is a critical factor in choosing the auto-enrolment option for pension savings. 3. Men had higher odds of auto-enrolment pension saving than women. 4. Employees of economic universities and academics had higher odds of participating in capital pension plans than those of general universities and non-academics. Our findings can signal to governments and policymakers about factors influencing the choice of auto-enrolment supplementary retirement savings. These findings strengthen the role of sustainable economic education. Full article
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36 pages, 11596 KB  
Article
A Policy Proposal to Strengthen the Income Redistribution Function of the National Pension Scheme in South Korea: An Analysis of South Korea’s 5th National Pension Comprehensive Plan (Draft)
by Jeonyong Park
Economies 2024, 12(10), 275; https://doi.org/10.3390/economies12100275 - 9 Oct 2024
Viewed by 10052
Abstract
In this study, we elucidate the income redistribution effects of the proposal to incorporate the Bend Points mechanism of the U.S. OASDI into the Korean National Pension Scheme (BP-KNPS Proposal) through a micro-simulation analysis using individual data from the Korean Labor and Income [...] Read more.
In this study, we elucidate the income redistribution effects of the proposal to incorporate the Bend Points mechanism of the U.S. OASDI into the Korean National Pension Scheme (BP-KNPS Proposal) through a micro-simulation analysis using individual data from the Korean Labor and Income Panel Study (KLIPS). In addition to examining the effects of introducing the BP-KNPS Proposal into the current National Pension Scheme (NPS), we also consider the impact of this scheme being combined with the 5th National Pension Comprehensive Plan (Draft), announced by Korea’s Ministry of Health and Welfare on 30 October 2023. When the BP-KNPS Proposal is introduced into the current NPS, the Mean Log Deviation (MLD) of the net transfer amount (lifetime pension benefits minus lifetime pension contributions) for regular employees decreases from 0.2022863 to 0.1929960. Similarly, the MLD for self-employed and irregular workers decreases from 0.2046127 to 0.1721433, indicating a reduction in income inequality. Furthermore, when the BP-KNPS Proposal is combined with the 5th National Pension Comprehensive Plan (Draft), the effects are mixed. The proposals to increase the pension contribution rate and adjust the rate increase speed via generation lead to a reduction in income inequality compared to the current NPS when combined with the BP-KNPS Proposal. However, the proposals to raise the pensionable age result in increased income inequality, similar to the outcomes under the current system. This finding suggests that the triple burden identified by literature review—the reduction in benefits due to disparities in contribution periods and life expectancy, and the raised pensionable age—has a greater impact on low-income participants than the inequality-reducing effects of the BP-KNPS Proposal. Full article
(This article belongs to the Section International, Regional, and Transportation Economics)
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12 pages, 948 KB  
Article
Fair and Sustainable Pension System: Market Equilibrium Using Implied Options
by Ishay Wolf and Lorena Caridad López del Río
Risks 2024, 12(8), 127; https://doi.org/10.3390/risks12080127 - 8 Aug 2024
Cited by 2 | Viewed by 2146
Abstract
This study contributes to the discussion about a fair and balanced pension system with a collectively funded pension scheme or social security and a defined contribution pillar. With an invigorated risk approach using financial option positions, it considers the variance of socioeconomic interests [...] Read more.
This study contributes to the discussion about a fair and balanced pension system with a collectively funded pension scheme or social security and a defined contribution pillar. With an invigorated risk approach using financial option positions, it considers the variance of socioeconomic interests of different society-earning cohorts. By that, it enables the assumption of un-uniformity in interests about the fair and sustainable pension design. Specifically, we claim that the alternative cost of hedging the ideal position to the counterparty position studies the implied risks and returns that participants are willing to absorb and hence may lead to a fair compromise when there are different interests. The novelty of the introduced method is mainly based on the variety of participants’ risks and not on the utility function. Accordingly, we spare the discussion about the right shape of the utility function and the proper calibrations. Full article
(This article belongs to the Special Issue Risks Journal: A Decade of Advancing Knowledge and Shaping the Future)
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11 pages, 1168 KB  
Article
Sustaining Algeria’s Retirement System in the Population Aging Context: Could a Contribution Cap Strategy Work?
by Farid Flici and Inmaculada Dominguez-Fabian
Risks 2024, 12(6), 96; https://doi.org/10.3390/risks12060096 - 14 Jun 2024
Viewed by 8581
Abstract
Previous research predicts an increasing financial deficit in Algeria’s PAYG retirement system, mainly due to rapid population aging, and parametric adjustments will be insufficient to alleviate this imbalance. Mitigating the effects of population aging will necessitate further intervention. In this work, we analyze [...] Read more.
Previous research predicts an increasing financial deficit in Algeria’s PAYG retirement system, mainly due to rapid population aging, and parametric adjustments will be insufficient to alleviate this imbalance. Mitigating the effects of population aging will necessitate further intervention. In this work, we analyze how capping contributed salaries can help to mitigate the effects of population aging on the retirement system. Under generous Pay-As-You-Go schemes, promised pension payouts far exceed contributions. Thus, restricting contributions is expected to reduce the burden of future benefits by accepting lower contributions today, while directing public subsidies to low-income individuals. We simulate the future evolution of the financial balance of Algeria’s retirement system under various contributable salary caps versus various scenarios of environmental evolution and potential parametric reform actions. The results demonstrated that a 40% cap, along with major parametric reforms and an ideal environment, would help achieve a cumulatively balanced system in the long run. Full article
(This article belongs to the Special Issue Life Insurance and Pensions: Latest Advances and Prospects)
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16 pages, 876 KB  
Review
Supporting Ageing Populations in Developing Countries: A Comparative Analysis of Pension Schemes and Policy Insights
by Tual Sawn Khai, Jacob Oppong Nkansah, Abdul Wali Khan and Muhammad Asaduzzaman
Challenges 2024, 15(2), 27; https://doi.org/10.3390/challe15020027 - 23 May 2024
Cited by 3 | Viewed by 5509
Abstract
The rapid growth of the elderly population is a major global demographic and social issue. Unfortunately, there is a shortage of pension plans and social security programmes for this population in developing countries, which has severe consequences for their quality of life and [...] Read more.
The rapid growth of the elderly population is a major global demographic and social issue. Unfortunately, there is a shortage of pension plans and social security programmes for this population in developing countries, which has severe consequences for their quality of life and well-being. In this article, we aim to better understand the pension systems in developing country contexts such as Ghana, Pakistan, and Myanmar by reviewing official government materials (for example, pension reports) and the published literature to suggest relevant policy recommendations. We observed several policy implementation gaps and inequities in pension schemes for older people, specifically for informal and private sector workers. Considering the size of formal versus informal economies and the level of development index of each country, we suggest a wide variety of options for pension policies, financing, designing cash benefits, and pension payments to cover all older citizens. This article addresses the unmet needs of the elderly and their wider economic sustainability to ensure social justice and resource utilisation. Governments in developing countries should embrace and establish unique, inclusive, and friendly policies encompassing the informal sector to warrant older adults’ functional and social well-being with dignity and honour. Full article
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17 pages, 494 KB  
Article
Two-Population Mortality Forecasting: An Approach Based on Model Averaging
by Luca De Mori, Pietro Millossovich, Rui Zhu and Steven Haberman
Risks 2024, 12(4), 60; https://doi.org/10.3390/risks12040060 - 27 Mar 2024
Cited by 1 | Viewed by 2634
Abstract
The analysis of residual life expectancy evolution at retirement age holds great importance for life insurers and pension schemes. Over the last 30 years, numerous models for forecasting mortality have been introduced, and those that allow us to predict the mortality of two [...] Read more.
The analysis of residual life expectancy evolution at retirement age holds great importance for life insurers and pension schemes. Over the last 30 years, numerous models for forecasting mortality have been introduced, and those that allow us to predict the mortality of two or more related populations simultaneously are particularly important. Indeed, these models, in addition to improving the forecasting accuracy overall, enable evaluation of the basis risk in index-based longevity risk transfer deals. This paper implements and compares several model-averaging approaches in a two-population context. These approaches generate predictions for life expectancy and the Gini index by averaging the forecasts obtained using a set of two-population models. In order to evaluate the eventual gain of model-averaging approaches for mortality forecasting, we quantitatively compare their performance to that of the individual two-population models using a large sample of different countries and periods. The results show that, overall, model-averaging approaches are superior both in terms of mean absolute forecasting error and interval forecast accuracy. Full article
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17 pages, 469 KB  
Article
The Role of Longevity-Indexed Bond in Risk Management of Aggregated Defined Benefit Pension Scheme
by Xiaoyi Zhang, Yanan Li and Junyi Guo
Risks 2024, 12(3), 49; https://doi.org/10.3390/risks12030049 - 6 Mar 2024
Cited by 2 | Viewed by 2694
Abstract
Defined benefit (DB) pension plans are a primary type of pension schemes with the sponsor assuming most of the risks. Longevity-indexed bonds have been used to hedge or transfer risks in pension plans. Our objective is to study an aggregated DB pension plan’s [...] Read more.
Defined benefit (DB) pension plans are a primary type of pension schemes with the sponsor assuming most of the risks. Longevity-indexed bonds have been used to hedge or transfer risks in pension plans. Our objective is to study an aggregated DB pension plan’s optimal risk management problem focusing on minimizing the solvency risk over a finite time horizon and to investigate the investment strategies in a market, comprising a longevity-indexed bond and a risk-free asset, under stochastic nominal interest rates. Using the dynamic programming technique in the stochastic control problem, we obtain the closed-form optimal investment strategy by solving the corresponding Hamilton–Jacobi–Bellman (HJB) equation. In addition, a comparative analysis implicates that longevity-indexed bonds significantly reduce solvency risk compared to zero-coupon bonds, offering a strategic advantage in pension fund management. Besides the closed-form solution and the comparative study, another novelty of this study is the extension of actuarial liability (AL) and normal cost (NC) definitions, and we introduce the risk neutral valuation of liabilities in DB pension scheme with the consideration of mortality rate. Full article
(This article belongs to the Special Issue Optimal Investment and Risk Management)
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16 pages, 571 KB  
Article
Assessing Delayed Retirement Policies Linked to Dynamic Life Expectancy with Stochastic Dynamic Mortality
by Lei He, Tianquan Zhong and Zhenqi Wang
Mathematics 2023, 11(24), 4929; https://doi.org/10.3390/math11244929 - 12 Dec 2023
Cited by 2 | Viewed by 1913
Abstract
The question of how to effectively alleviate the financial pressure on pension insurance due to the increase in life expectancy has become an important issue in the reform of China’s social security system. This paper introduced two life expectancy-related delayed retirement schemes, namely [...] Read more.
The question of how to effectively alleviate the financial pressure on pension insurance due to the increase in life expectancy has become an important issue in the reform of China’s social security system. This paper introduced two life expectancy-related delayed retirement schemes, namely the fixed expected retirement residual life and the fixed life burden ratio. We modeled the financial balance of the employee pension fund and the pension wealth of employees with a dynamic retirement age according to pension policy. Using the population mortality data, the dynamic retirement age under the two schemes was estimated under the stochastic mortality model. Following this, the impact of the two delayed retirement schemes was quantitatively assessed from the perspectives of the financial sustainability of the pension fund and the pension wealth of employees using insurance actuarial methods. This study found that the two life expectancy-related delayed retirement schemes have obvious effects on reducing the gap between the income and expenditure of the pension fund and increasing the pension wealth of employees. Moreover, it found that the fixed expected retirement residual life program contributes more than the fixed life burden ratio program to improve the financial sustainability of the pension fund and the pension wealth benefits of employees. Full article
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21 pages, 805 KB  
Article
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 1810
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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16 pages, 899 KB  
Article
A Guaranteed-Return Structured Product as an Investment Risk-Hedging Instrument in Pension Savings Plans
by Zvika Afik, Elroi Hadad and Rami Yosef
Risks 2023, 11(6), 107; https://doi.org/10.3390/risks11060107 - 5 Jun 2023
Cited by 2 | Viewed by 4204
Abstract
This study proposes a structured product (SP) for hedging defined contribution pension fund members against capital market risk. Using Monte Carlo simulations on three different guaranteed returns to test the investment strategy of the SP against a balanced investment portfolio, we measure their [...] Read more.
This study proposes a structured product (SP) for hedging defined contribution pension fund members against capital market risk. Using Monte Carlo simulations on three different guaranteed returns to test the investment strategy of the SP against a balanced investment portfolio, we measure their performance across a wide variety of capital market returns and risk scenarios. The results show that the SP guarantees a minimal return on the pension savings portfolio and offers a higher portfolio return at a lower investment risk, compared with the balanced investment portfolio. We conclude that the SP may become popular among pension fund members, potentially leading to improved risk management, greater competition, and investment strategy innovations for defined contribution pension schemes. Full article
(This article belongs to the Special Issue Frontiers in Quantitative Finance and Risk Management)
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