Choosing the Optimal Annuitization Time Post Retirement

In the context of decision making for retirees of a defined contribution pension scheme in the de-cumulation phase, we formulate and solve a problem of finding the optimal time of annuitization for a retiree having the possibility of choosing her own investment and consumption strategy. We formulate the problem as a combined stochastic control and optimal stopping problem. As criterion for the optimization we select a loss function that penalizes both the deviance of the running consumption rate from a desired consumption rate and the deviance of the final wealth at the time of annuitization from a desired target. We find closed form solutions for the problem and show the existence of three possible types of solutions depending on the free parameters of the problem. In numerical applications we find the optimal wealth that triggers annuitization, compare it with the desired target and investigate its dependence on both parameters of the financial market and parameters linked to the risk attitude of the retiree. Simulations of the behaviour of the risky asset seem to show that under typical situations optimal annuitization should occur a few years after retirement.defined contribution pension scheme, de-cumulation phase, stochastic optimal control, optimal annuitization time

Choosing the optimal annuitization time post retirement

In defined contribution pension schemes, the financial risk is borne by the member: contributions are fixed in advance and the benefits provided by the scheme depend on the investment performance experienced during the active membership and on the price of the annuity at retirement, in the case that the benefits are given in the form of an annuity. Therefore, the financial risk can be split into two parts: investment risk, during the accumulation phase, and annuity risk, focused at retirement. In order to limit the annuity risk — which is the risk that high annuity prices (driven by low bond yields) at retirement can lead to a lower than expected pension income — in many schemes the member has the possibility of deferring the annuitization of the accumulated fund. This possibility consists of leaving the fund invested in financial assets as in the accumulation phase, and allows for periodic withdrawals by the pensioner, until annuitization occurs (if ever). In UK this option is named “income drawdown option”, in US the periodic withdrawals are called ”phased withdrawals”. The current actuarial literature about the financial risk in defined contribution pension schemes is quite rich. Papers dealing with the financial risk in DC schemes in the accumulation phase are

The role of acupuncture in treating perimenopausal insomnia : an overview and quality assessment of systematic reviews and meta-analyses

Objective: To summarize and critically assess the reliability of the methodological quality and outcome measures from systematic reviews (SRs)/meta-analyses (MAs) and provide an overall verdict about the therapeutic value of acupuncture for perimenopausal insomnia (PMI). Methods: We conducted a comprehensive literature search for SRs/MAs of seven major data-bases (English and Chinese). For each included review, the methodological quality was appraised according to the Assessing the Methodological Quality of Systematic Reviews 2 (AMSTAR-2), the evidence quality was classified on the basis of the Grading of Recommendations, Assessment, Development and Evaluation (GRADE), and reporting quality was evaluated complying with Preferred Reporting Items for Systematic Reviews and Meta-Analyses 2009 (PRISMA-2009). Veritas plots were used to quantify the quality of included SRs/MAs. Results: Nine SRs/MAs were deemed eligible for the present overview. Considering the assessment of results from the AMSTAR-2 checklist, the methodological quality of one SR/ MA was considered low, and the remaining eight were critically low. Major methodological deficiencies were concentrated on item 2 (the lack of protocol and/or registration informa-tion), item 7 (the lack of a list of excluded studies), and item 10 (the lack of reports on funding sources for individual studies included in the SRs/MAs). For the GRADE system, of the 25 outcomes, only three (12%) were rated as moderate-quality, while the remaining 22 were rated between low-and very low-quality. The PRISMA-2009 statement indicated three major reporting quality limitations in most SRs/MAs, namely: 1) only search terms without specific retrieval strategy; 2) incomplete descriptions for study characteristics, particularly the specific dosage and frequency of interventions in treatment/control groups; and 3) inadequate investigation and explanation of the source of high heterogeneity among original randomized control trials included. According to Veritas plots, quality rank scores of included SRs/MAs ranged from 3.3 to 8.3, with an average score of 6.4 ± 1.7. Conclusion: Acupuncture appears to be beneficial for PMI management, but the quality of evidence is weakened by the unsatisfactory quality of both SRs/MAs and original trials included. © 2021 Zhao et al

Less is more: increasing retirement gains by using an upside terminal wealth constraint

We solve a portfolio selection problem of an investor with a deterministic savings plan who aims to have a target wealth value at retirement. The investor is an expected power utility-maximizer. The target wealth value is the maximum wealth that the investor can have at retirement. By constraining the investor to have no more than the target wealth at retirement, we find that the lower quantiles of the terminal wealth distribution increase, so the risk of poor financial outcomes is reduced. The drawback of the optimal strategy is that the possibility of gains above the target wealth are eliminated

Optimal investment choices post-retirement in a defined contribution pension scheme

In defined contribution pension schemes, the financial risk is borne by the member. Financial risk occurs both during the accumulation phase (investment risk) and at retirement, when the annuity is bought (annuity risk). The annuity risk faced by the member can be reduced through the “income drawdown option”: the retiree is allowed to choose when to convert the final capital into pension within a certain period of time after retirement. In some countries, there is a limiting age when annuitization becomes compulsory (in UK this age is 75). In the interim, the member can withdraw periodic amounts of money to provide for daily life, within certain limits imposed by the scheme’s rules (or by law). In this paper, we investigate the income drawdown option and define a stochastic optimal control problem, looking for optimal investment strategies to be adopted after retirement, when allowing for periodic fixed withdrawals from the fund. The risk attitude of the member is also considered, by changing a parameter in the disutility function chosen. We find that there is a natural target level of the fund, interpretable as a safety level, which can never be exceeded when optimal control is used. Numerical examples are presented in order to analyse various indices — relevant to the pensioner — when the optimal investment allocation is adopted. These indices include, for example, the risk of outliving the assets before annuitization occurs (risk of ruin), the average time of ruin, the probability of reaching a certain pension target (that is greater than or equal to the pension that the member could buy immediately on retirement), the final outcome that can be reached (distribution of annuity that can be bought at limit age), and how the risk attitude of the member affects the key performance measures mentioned above

Mean-variance optimization problems for an accumulation phase in a defined benefit plan

In this paper we deal with contribution rate and asset allocation strategies in a pre-retirement accumulation phase. We consider a single cohort of workers and investigate a retirement plan of a defined benefit type in which an accumulated fund is converted into a life annuity. Due to the random evolution of a mortality intensity, the future price of an annuity, and as a result, the liability of the fund, is uncertain. A manager has control over a contribution rate and an investment strategy and is concerned with covering the random claim. We consider two mean–variance optimization problems, which are quadratic control problems with an additional constraint on the expected value of the terminal surplus of the fund. This functional objectives can be related to the well-established financial theory of claim hedging. The financial market consists of a risk-free asset with a constant force of interest and a risky asset whose price is driven by a Lévy noise, whereas the evolution of a mortality intensity is described by a stochastic differential equation driven by a Brownian motion. Techniques from the stochastic control theory are applied in order to find optimal strategies

The Management of Decumulation Risks in a Defined Contribution Pension Plan

The aim of the paper is to lay the theoretical foundations for the construction of a flexible tool that can be used by pensioners to find optimal investment and consumption choices in the distribution phase of a defined contribution pension plan. The investment/consumption plan is adopted until the time of compulsory annuitization, taking into account the possibility of earlier death. The effect of the bequest motive and the desire to buy a higher annuity than the one purchasable at retirement are included in the objective function. The mathematical tools provided by dynamic programming techniques are applied to find closed-form solutions: numerical examples are also presented. In the model, the tradeoff between the different desires of the individual regarding consumption and final annuity can be dealt with by choosing appropriate weights for these factors in the setting of the problem. Conclusions are twofold. First, we find that there is a natural time-varying target for the size of the fund, which acts as a sort of safety level for the needs of the pensioner. Second, the personal preferences of the pensioner can be translated into optimal choices, which in turn affect the distribution of the consumption path and of the final annuity

Tail Dependence Measure for Examining Financial Extreme Co-movements

Modeling and forecasting extreme co-movements in financial market is important for conducting stress test in risk management. Asymptotic independence and asymptotic dependence behave drastically different in modeling such co-movements. For example, the impact of extreme events is usually overestimated whenever asymptotic dependence is wrongly assumed. On the other hand, the impact is seriously underestimated whenever the data is misspecified as asymptotic independent. Therefore, distinguishing between asymptotic independence/dependence scenarios is very informative for any decision-making and especially in risk management. We investigate the properties of the limiting conditional Kendall’s tau which can be used to detect the presence of asymptotic independence/dependence. We also propose nonparametric estimation for this new measure and derive its asymptotic limit. A simulation study shows good performances of the new measure and its combination with the coefficient of tail dependence proposed by Ledford and Tawn (1996, 1997). Finally, applications to financial and insurance data are provided

Moral Disengagement and Risk Prototypes in the Context of Adolescent Cyberbullying: Findings From Two Countries

Cyberbullying is associated with a wide range of mental health difficulties and behavioral problems in adolescents and research is needed to better understand psychological correlates of this behavior. The present study used a novel model that incorporated Social Cognitive Theory and the prototype/willingness model to identify the correlates of behavioral willingness to engage in cyberbullying in two countries. Adolescent students were randomly selected from secondary schools in Italy (n = 1710) and Greece (n = 355), and completed anonymous measures of moral disengagement, descriptive norms, risk prototype evaluations and behavioral willingness to engage in cyberbullying. Hierarchical linear regression analyses showed that willingness to engage in cyberbullying was associated with moral disengagement, prototype evaluations and descriptive social norms in Italy, and with gender, moral disengagement and descriptive social norms in Greece. Regression-based multiple mediation modeling further showed that the association between moral disengagement and cyberbullying willingness was mediated by prototype evaluations in Italy and by descriptive norms in Greece. The implications of our findings are discussed in the context of self-regulating cyberbullying perpetration in adolescents and informing school-based policies and interventions to prevent cyberbullying behavior

PENGUIn multi‐instrument observations of dayside high‐latitude injections during the 23 March 2007 substorm

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/94875/1/jgra19563.pd