Search Results (20)

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

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 paper investigates a dynamic liability-driven investment policy for defined-benefit (DB) plans by incorporating the loss aversion of a sponsor, who is assumed to be more sensitive to underfunding than overfunding. Through the lens of prospect theory, we first set up a loss-aversion utility function for a sponsor whose utility depends on the funding ratio in each period, obtained from stochastic processes of pension assets and liabilities. We then construct a multi-horizon dynamic control optimization problem to find the optimal investment strategy that maximizes the expected utility of the plan sponsor. A genetic algorithm is employed to provide a numerical solution for our nonlinear dynamic optimization problem. Our results suggest that the overall paths of the optimal equity allocation decline as the age of a plan participant reaches retirement. We also find that the equity portion of the portfolio increases when a sponsor is less loss-averse or the contribution rate is lower. Full article

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

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

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 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

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

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

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

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

In the past 30 years, as sponsors of defined benefit (DB) pension plans were facing more severe underfunding challenges, pension de-risking strategies have become prevalent for firms with DB plans to reduce pension-related risks. However, it remains unclear how pension de-risking activities affect firms’ performance, partially due to the lack of de-risking data. In this study, we develop a multi-phase methodology to build a de-risking database for the purpose of investigating impacts of firms’ pension risk transfer activities. We extract company filings between 1993 and 2018 from the SEC EDGAR database to identify different “de-risking” strategies that US-based companies have used. A combination of text mining, machine learning, and natural language processing methods is applied to the textual data for automated identification and classification of de-risking strategies. The contribution of this study is three-fold: (1) the design of a multi-phase methodology that identifies and extracts hidden information from a large amount of textual data; (2) the development of a comprehensive database for pension de-risking activities of US-based companies; and (3) valuable insights to companies with DB plans, pensioners, and practitioners in pension de-risking markets through empirical analysis. Full article

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

The central issue of this paper is analysis and resulting proposals to help unsophisticated pension participants achieve pension portfolios that match their level of risk aversion when there is a large amount of unexplained heterogeneity in risk aversion. Target date funds are commonly used as the default investment in defined contribution plans in the U.S., UK and other countries. These funds recognize that individuals usually should hold less risky investment portfolios as their expected retirement date approaches because their ability to bear financial market risk declines as the time horizon decreases. However, these funds do not account for differences in risk aversion among people with the same target date. Empirical studies find large amounts of unexplained heterogeneity in risk aversion. Target date funds cannot deal with this issue simply by sorting people into demographic groupings, other than age, that are known to affect risk aversion, such as gender. Financial education can help people do a better job of managing financial market risk in their pension portfolios, but we argue that it is unreasonable to expect millions of pension participants to attain advanced levels of financial literacy. This paper considers three innovations in target date funds that can help individual pension participants do a better job of managing financial market risk. The analysis can be applied to other situations where defaults are used for investing pension participants’ portfolios. The paper suggests new lines of research relating to individual differences in risk aversion. Full article

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