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Search Results (4)

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Keywords = valuation of pension plans

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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 2558
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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24 pages, 563 KB  
Article
On Valuation and Investments of Pension Plans in Discrete Incomplete Markets
by Michail Anthropelos and Evmorfia Blontzou
Risks 2023, 11(6), 103; https://doi.org/10.3390/risks11060103 - 1 Jun 2023
Viewed by 2343
Abstract
We study the valuation of a pension fund’s obligations in a discrete time and space incomplete market model. The market’s incompleteness stems from the non-replicability of the wage process that finances the pension plan through time. The contingent defined-benefit liability of the pension [...] Read more.
We study the valuation of a pension fund’s obligations in a discrete time and space incomplete market model. The market’s incompleteness stems from the non-replicability of the wage process that finances the pension plan through time. The contingent defined-benefit liability of the pension fund is a function of the wages, which can be seen as the payoff of a path-dependent derivative security. We apply the notion of the super-hedging value and propose its difference from the current pension’s fund capital as a measure of distance to liability hedging. The induced closed-form expressions of the values and the related investment strategies provide insightful comparative statistics. Furthermore, we use a utility-based optimization portfolio to point out that in cases of sufficient capital, the application of a subjective investment criterion may result in heavily different strategies than the super-hedging one. This means that the pension fund will be left with some liability risk, although it could have been fully hedged. Finally, we provide conditions under which the effect of a possible early exit leaves the super-hedging valuation unchanged. Full article
(This article belongs to the Special Issue Frontiers in Quantitative Finance and Risk Management)
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17 pages, 2187 KB  
Article
Transforming Private Pensions: An Actuarial Model to Face Long-Term Costs
by J. Iñaki De La Peña, M. Cristina Fernández-Ramos, Asier Garayeta and Iratxe D. Martín
Mathematics 2022, 10(7), 1082; https://doi.org/10.3390/math10071082 - 28 Mar 2022
Cited by 4 | Viewed by 3034
Abstract
A common response in public pension systems to population ageing is to link pensions to observed longevity. This creates an automatic stabiliser that arises from the valuation of a private actuarially funded system. However, no private pension plan mechanism has been articulated to [...] Read more.
A common response in public pension systems to population ageing is to link pensions to observed longevity. This creates an automatic stabiliser that arises from the valuation of a private actuarially funded system. However, no private pension plan mechanism has been articulated to adapt to this ageing in relation to the increased costs it entails. Private pension plans focus on saving for retirement; capital is accumulated to pay for it. However, perceptions of health status change over time and, as retirement age approaches, concerns about long-term care (LTC) increase. Moreover, there is not enough time to plan for it sufficiently in advance. This paper proposes to incorporate a mechanism to add an allowance to the financial pension (retirement, disability, rotation) to cover LTC within a private defined benefit pension plan, in the case of a pensioner becoming dependent. Depending on a pensioner’s health status, both the expected number of payments and their intensity are transformed. For this purpose, a mechanism is defined (through Markov chains) to adapt the amount of LTC support to a beneficiary’s health-related life expectancy. The study’s main contribution is that it establishes a private pension plan model that offers to incorporate dependency aid through this mechanism into the economic pensions without increasing the total cost of the plan. It adapts to life expectancy according to a person’s state (healthy, disabled, dependent). Full article
(This article belongs to the Section E5: Financial Mathematics)
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13 pages, 928 KB  
Article
Mental Time Travel and Retirement Savings
by David Blake and John Pickles
J. Risk Financial Manag. 2021, 14(12), 581; https://doi.org/10.3390/jrfm14120581 - 3 Dec 2021
Cited by 3 | Viewed by 3532
Abstract
We portray the valuation of retirement savings in terms of a mental time travel journey in which a proposed contribution to a pension plan is projected forward to the plan member’s retirement date and this projected value is then discounted back to today, [...] Read more.
We portray the valuation of retirement savings in terms of a mental time travel journey in which a proposed contribution to a pension plan is projected forward to the plan member’s retirement date and this projected value is then discounted back to today, thereby giving a present or personal value. We set this within a broader framework of pension planning, which seeks to smooth consumption over the lifecycle. We explain how two psychological biases—exponential growth bias and present bias—can lead to a difference between the initial value of a pension contribution and its present value, such a difference reflecting an asymmetry between projection and discounting, and how such a difference might lead to inadequate retirement savings and hence to a lower than desired standard of living in retirement. We consider how the two biases might be mitigated. Full article
(This article belongs to the Special Issue Household Finance)
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