Optimal retirement income tontines Milevsky, Moshe A.; Salisbury, Thomas S.
Insurance, mathematics & economics,
09/2015, Letnik:
64
Journal Article
Recenzirano
Odprti dostop
Tontines were once a popular type of mortality-linked investment pool. They promised enormous rewards to the last survivors at the expense of those died early. While this design appealed to the ...gambling instinct, it is a suboptimal way to generate retirement income. Indeed, actuarially-fair life annuities making constant payments–where the insurance company is exposed to longevity risk–induce greater lifetime utility. However, tontines do not have to be structured the historical way, i.e. with a constant cash flow shared amongst a shrinking group of survivors. Moreover, insurance companies do not sell actuarially-fair life annuities, in part due to aggregate longevity risk.
We derive the tontine structure that maximizes lifetime utility. Technically speaking we solve the Euler–Lagrange equation and examine its sensitivity to (i) the size of the tontine pool n, and (ii) individual longevity risk aversion γ. We examine how the optimal tontine varies with γ and n, and prove some qualitative theorems about the optimal payout. Interestingly, Lorenzo de Tonti’s original structure is optimal in the limit as longevity risk aversion γ→∞. We define the natural tontine as the function for which the payout declines in exact proportion to the survival probabilities, which we show is near-optimal for all γ and n. We conclude by comparing the utility of optimal tontines to the utility of loaded life annuities under reasonable demographic and economic conditions and find that the life annuity’s advantage over the optimal tontine is minimal.
In sum, this paper’s contribution is to (i) rekindle a discussion about a retirement income product that has been long neglected, and (ii) leverage economic theory as well as tools from mathematical finance to design the next generation of tontine annuities.
Refundable income annuities (IA), such as cash-refund and instalment-refund, differ in material ways from the life-only version beloved by economists. In addition to lifetime income they guarantee ...the annuitant or beneficiary will receive their money back albeit slowly over time. Although we document that refundable IAs now represent the majority of sales in the U.S., they are mostly ignored by insurance and pension economists. Indeed, their pricing, duration, and money's-worth-ratio is complicated by recursivity which will be explained, and we offer a path forward to make refundable IAs tractable.
A key result concerns the market price of cash-refund IAs, when the actuarial present value is grossed-up by an insurance loading. We prove that price is counterintuitively no longer a declining function of age and older buyers might pay more than younger ones. Moreover, there exists a threshold valuation rate below which no price is viable. This may also explain why inflation-adjusted IAs have all but disappeared.
There is growing interest in the design of pension annuities that insure against idiosyncratic longevity risk while pooling and sharing systematic risk. This is partially motivated by the desire to ...reduce capital and reserve requirements while retaining the value of mortality credits; see for example, Piggott et al. (2005) or Donnelly et al. (2014). In this paper, we generalize the natural retirement income tontine introduced by Milevsky and Salisbury (2015) by combining heterogeneous cohorts into one pool. We engineer this scheme by allocating tontine shares at either a premium or a discount to par based on both the age of the investor and the amount they invest. For example, a 55-year old allocating $10,000 to the tontine might be told to pay $200 per share and receive 50 shares, while a 75-year old allocating $8,000 might pay $40 per share and receive 200 shares. They would all be mixed together into the same tontine pool and each tontine share would have equal income rights. The current paper addresses existence and uniqueness issues and discusses the conditions under which this scheme can be constructed equitably — which is distinct from fairly — even though it isn't optimal for any cohort. As such, this also gives us the opportunity to compare and contrast various pooling schemes that have been proposed in the literature and to differentiate between arrangements that are socially equitable, vs. actuarially fair vs. economically optimal.
Abstract Background Falls are common in a range of clinical cohorts, where routine risk assessment often comprises subjective visual observation only. Typically, observational assessment involves ...evaluation of an individual’s gait during scripted walking protocols within a lab to identify deficits that potentially increase fall risk, but subtle deficits may not be (readily) observable. Therefore, objective approaches (e.g., inertial measurement units, IMUs) are useful for quantifying high resolution gait characteristics, enabling more informed fall risk assessment by capturing subtle deficits. However, IMU-based gait instrumentation alone is limited, failing to consider participant behaviour and details within the environment (e.g., obstacles). Video-based eye-tracking glasses may provide additional insight to fall risk, clarifying how people traverse environments based on head and eye movements. Recording head and eye movements can provide insights into how the allocation of visual attention to environmental stimuli influences successful navigation around obstacles. Yet, manual review of video data to evaluate head and eye movements is time-consuming and subjective. An automated approach is needed but none currently exists. This paper proposes a deep learning-based object detection algorithm ( VARFA ) to instrument vision and video data during walks, complementing instrumented gait. Method The approach automatically labels video data captured in a gait lab to assess visual attention and details of the environment. The proposed algorithm uses a YoloV8 model trained on with a novel lab-based dataset. Results VARFA achieved excellent evaluation metrics (0.93 mAP50), identifying, and localizing static objects (e.g., obstacles in the walking path) with an average accuracy of 93%. Similarly, a U-NET based track/path segmentation model achieved good metrics (IoU 0.82), suggesting that the predicted tracks (i.e., walking paths) align closely with the actual track, with an overlap of 82%. Notably, both models achieved these metrics while processing at real-time speeds, demonstrating efficiency and effectiveness for pragmatic applications. Conclusion The instrumented approach improves the efficiency and accuracy of fall risk assessment by evaluating the visual allocation of attention (i.e., information about when and where a person is attending) during navigation, improving the breadth of instrumentation in this area. Use of VARFA to instrument vision could be used to better inform fall risk assessment by providing behaviour and context data to complement instrumented e.g., IMU data during gait tasks. That may have notable (e.g., personalized) rehabilitation implications across a wide range of clinical cohorts where poor gait and increased fall risk are common.
Background: Abusive head trauma (AHT) is currently the accepted terminology that encompasses previously used terms such as non-accidental injury (NAI) or non-accidental head injury (NAHI) and shaken ...baby syndrome (SBS). It is AHT and its ocular manifestations that ophthalmologists are vital in identifying and reporting. Objectives: To investigate whether there is a change in the incidence or severity of AHT pre- and during COVID-19 lockdown. Participants and Settings: AHT cases reported between March-June 2019 and March-June 2020. Data will be collected from *** *** NHS Foundation Trust. Methods: A retrospective comparative study. Main Outcome Measures: Comparison of total number of children reported to child protection services pre- and during lockdown. Severity of reported cases. Ophthalmic involvement. Results: Of the pre-lockdown safeguarding referrals, 5/61 (8.19%) had confirmed AHT, and 4/40 (10%) of the during lockdown group were confirmed AHT. The absence of teachers was evident, as in the pre-lockdown group 40% (2) of referrals originated from schools compared to none during the lockdown period. Ophthalmic involvement was not present in any of the pre-lockdown cases and only 50% (2) of the during lockdown cases, with the appropriate proforma only used in one of these cases. Unfortunately, no further statistical testing was meaningful in light of the small sample size. Conclusions: The loss of the early warning detection mechanism provided by schools and health visitors may have contributed to both the change in presentation and severity of cases during the lockdown. There is also a need for ophthalmology and paediatrics to collaborate to ensure AHT cases are thoroughly investigated and documented. Keywords: child abuse, abusive head trauma, retinal haemorrhage, COVID-19, non-accidental injury
We consider connectivity properties and asymptotic slopes for certain random directed graphs on ℤ2 in which the set of points
$\mathcal{C}_o$
that the origin connects to is always infinite. We obtain ...conditions under which the complement of
$\mathcal{C}_o$
has no infinite connected component. Applying these results to one of the most interesting such models leads to an improved lower bound for the critical occupation probability for oriented site percolation on the triangular lattice in two dimensions.
The adoption of digital technologies in healthcare, accelerated by the COVID-19 pandemic, requires a well-prepared workforce capable of implementing those technologies. Here, we examine the role and ...impact of digital fellowships in facilitating digital transformation in healthcare systems. Digital fellowships are structured educational programmes designed to equip healthcare professionals with advanced digital skills. Focusing on UK-based initiatives like the Topol Digital Fellowship and the Fellowship in Clinical AI, we explore their efforts to prepare healthcare leaders for digital and AI adoption. Each fellowship programme provides participants with hands-on experience in digital healthcare projects and fosters interdisciplinary collaboration and post-fellowship support. We discuss how these fellowships contribute to staff retention by diversifying professional experiences and opportunities. We call for increased collaborations between universities, industry, and professional bodies to integrate lessons from digital fellowships into relevant curricula, acknowledging that digital fellowships are just one piece of the puzzle in bridging the digital skills gap in the healthcare workforce.
BackgroundAn article published by Sidpra J et al, in ADC in July 2020 reported an increase of approximately 1500% in the incidence of abusive head trauma (AHT) in children, understandably shocking ...paediatricians nationally.ObjectivesWe wanted to see the impact of lockdown on referrals made to our hospital (University Hospital of North Tees, Stockton, UK) for children suspected to have non-accidental injuries (NAI) or AHT.MethodsWe audited the records of children referred with suspected NAI during the first lockdown period (23rd of March to 4th of July 2020) and compared it with the preceding year (23rd of March to 4th of July 2019)As children under two are more likely to suffer AHT, these cases were identified by two auditors and then a single auditor reviewed these case records in detail.ResultsTotal of thirty-one children in 2019 & twenty-five in 2020 were referred for Child Protection Medical Assessments. Eleven children - six in 2019 and five in 2020 - were less than two years old. Of these, four were girls and seven boys. Five children were less than three months oldNine children were referred with suspicious bruising, one was the sibling of an index child with NAI and for one, an allegation was made of rough handling.Two children with skull fractures and one with a rib fracture (on follow up scan) were identified on radiological investigations. Hematological investigations and ophthalmic findings were unremarkable for all the children.All children were seen within 24 hours of a referral being made. In all cases, an interim report was provided on the same day and a final report within seven working days. All children were investigated as per RCPCH guidelines.Seven out of eleven children referred for NAI assessment were concluded to have probable non-accidental injuries – three in 2019, and four in 2020.Our neighbouring hospital received five and four referrals for suspected NAI in children under 2 years old in the same period of time in 2019 and 2020 respectively. One of these children in 2020 had retinal haemorrhages associated with AHT and a skull fracture.ConclusionsOur audit of children referred for NAI medical assessment does not suggest any significant difference between numbers in 2019 and 2020. This is in contrast with what colleagues from UCL, London have reported, and surprising given the high levels of socioeconomic deprivation in our area, which is usually associated with a higher incidence of child abuse.In order to understand national trends, we recommend other areas of the United Kingdom to review their data to establish whether this pandemic and associated lockdowns are impacting children in Teesside differently.
Financial valuation OF GMWBs: We develop a variety of methods for assessing the cost and value of a very popular ‘rider’ available to North American investors on variable annuity (VA) policies called ...a Guaranteed Minimum Withdrawal Benefit (GMWB). The GMWB promises to return the entire initial investment, albeit spread over an extended period of time, regardless of subsequent market performance. First, we take a
static approach that assumes individuals behave passively and holds the product to maturity. We show how the product can be decomposed into a Quanto Asian Put plus a generic term-certain annuity. At the other extreme of consumer behavior, the
dynamic approach leads to an optimal stopping problem akin to pricing an American put option, albeit complicated by the non-traditional payment structure. Our main result is that the No Arbitrage hedging cost of a GMWB ranges from 73 to 160 basis points of assets. In contrast, most products in the market only charge 30–45 basis points. Although we suggest a number of behavioral reasons for the apparent under-pricing of this feature in a typically overpriced VA market, we conclude by arguing that current pricing is not sustainable and that GMWB fees will eventually have to increase or product design will have to change in order to avoid blatant arbitrage opportunities.
PDF
