Liability valuation on several bases
Projected benefit cash flows are discounted on funding, accounting, guarantee and buyout bases, so the board sees how the same promises look under each purpose and which assumptions drive the differences.
GRA · Institutional Funds Nexus
Spatial financeWhere capital meets hazard, exposure and transition
Actuarial mathematics for pension funds
Actuarial mathematics turns a promise to pay into a number a board can manage: the present value of benefits, the contributions needed to fund them and their sensitivity to rates, inflation and survival. For institutional funds it is the measure of the liability side, and every assumption it rests on is a judgement that must be stated.
01ناوەڕۆک
Actuarial mathematics for pension funds in five parts.
02بەکارهێنان
What actuarial mathematics does here.
Actuarial mathematics applies probability, statistics and financial theory to measure and price contingent risks, particularly in insurance and pensions. It determines reserves and premiums for uncertain future obligations. In capital markets and investment and society and human development, actuarial methods determine whether risks can be insured and at what cost. They help assess accumulation of correlated losses across portfolios and regions. The canonical description is on the STEM Commons.
Mortality and longevity projection
Base tables are adjusted to scheme experience and combined with improvement models, and the liability is revalued under alternative improvement paths to show longevity sensitivity.
Funding plan and recovery path
Contributions, expected returns and benefit outgo are projected forward to show how a deficit is closed over the recovery period, and how the path changes under stressed returns or a weaker sponsor.
03چاودێری
Tail fit.
The screen a team would use to follow this method: its measures, states and decisions. Names are examples and values are illustrative.
Tail fit
Institutional funds · Actuarial mathematics for pension · Run R-7350
Shape parameter uncertainGRA · Institutional Funds Nexus
Return level curve
Method card
- ڕێگا
- Actuarial mathematics
- ڕێباز
- peaks over threshold
- Threshold
- 98th percentile
- ناونیشان
- مۆدێلکراو
Parameters
generalised Pareto fit
| Shape ξ | 0.29 | −0.04 | 0.47 | heavy tail if above zero |
| Scale σ | 3.0 | 1.1 | 5.1 | units of the variable |
| Exceedances | 68 | declustered |
04داتا
What the method consumes.
Datasets and records used by actuarial mathematics on this platform, with the role each plays and the label its values carry. Sources are listed in the source register.
| داتا | ڕۆڵ | ناونیشان |
|---|---|---|
| Scheme membership and benefit data | Projected benefit cash flows | REPORTED |
| National and actuarial mortality tables | Base mortality and improvement | ئامارە بڵاوکراوەکان |
| Government bond and swap curves | Discount rates and inflation expectations | چاودێریکراو |
| Scheme mortality experience studies | Adjustment of tables to the membership | مەزەندەکراو |
| Disclosed actuarial assumptions | Comparison across funds | DECLARED |
05Loss model
Loss exceedance, average annual loss and probable maximum loss.
The loss a portfolio in the footprint can expect per year and at the 1 in 100 and 1 in 250 levels that insurers and lenders price, from the same three blocks every catastrophe model uses. Teaching model with stated illustrative values, not a prediction.
کۆنترۆڵەکان
- Typical annual hazard intensity (location)
- 1.00 intensity index
- بڵاوبوونەوەی لێکەوتە توندەکان (پێوەر)
- 0.80 intensity index
- توندییەک کە تێیدا نیوەی بەها لەدەست دەچێت
- 4.00 intensity index
- بڵاوبوونەوەی لاوازی
- 0.55
- بەشی بەها لە شوێنپێی مەترسیدەردا
- 40%
- ستانداردی پاراستن (ماوەی گەڕانەوە)
- 50 ساڵ
خوێندنەوەکان
- تێکڕای زیانی ساڵانە
- 0.51% of value
- زیان لە 1 لە 100 ساڵدا
- 24.5% of value
- زیان لە 1 لە 250 ساڵدا
- 28.4% of value
- توندی لە 1 لە 100 ساڵدا
- 4.68 intensity index
ژمارە، ڕێگا و سەرچاوەکان
| ماوەی گەڕانەوە (ساڵ) | Intensity (intensity index) | زیان (% ی بەها) |
|---|---|---|
| 1 | 0.09 | 0.00 |
| 2 | 1.27 | 0.00 |
| 4 | 1.91 | 0.00 |
| 7 | 2.47 | 0.00 |
| 13 | 3.00 | 0.00 |
| 24 | 3.51 | 0.00 |
| 44 | 4.02 | 0.00 |
| 82 | 4.53 | 23.55 |
| 154 | 5.03 | 26.44 |
| 287 | 5.53 | 28.87 |
| 536 | 6.03 | 30.88 |
| 1,000 | 6.53 | 32.53 |
ڕێگاکان
- مەترسیدەری بەهای زۆرداری Gumbel Gumbel (1958)، Statistics of Extremes، Columbia University Press
- ناسکیی لۆگنۆرماڵ (لاوازی) FEMA (2003)، HAZUS-MH Technical Manual
- چەمکی ئەگەری تێپەڕبوون و تێکڕای زیانی ساڵانە Grossi و Kunreuther (2005)، Catastrophe Modeling، Springer
- کاریگەری بەربەست Di Baldassarre و ئەوانی دیکە (2013)، Socio-hydrology، HESS 17
- پەنجەی نادڵنیایی (مۆنتی کارلۆی پارامیتەر) Spiegelhalter, Pearson و Short (2011)، Visualising uncertainty about the future، Science 333
- هەستیاریی یەک-یەک (تۆرناد) Saltelli و ئەوانی دیکە (2008)، Global Sensitivity Analysis: The Primer، Wiley
داتا
The model runs on the teaching values set by the controls. To calibrate it for a place, read it against these admitted layers and series, which this page’s map can draw:
- ڕووبارەکان Natural Earth
- بەرینی شارەکان Natural Earth
- شارەکان Natural Earth
- بوومەلەرزەکانی M4.5+، هەفتەی ڕابردوو (USGS) U.S. Geological Survey · register usgs.earthquake.summary-feeds
- ڕێژەی باران، نیو کاتژمێری ڕابردوو (IMERG) NASA GPM IMERG Early · register nasa.gibs.context-live-layers
- پێشبینی ڕۆیشتنی ڕووبار، 30 ڕۆژ لەگەڵ مەودا (GloFAS لە ڕێگەی Open-Meteo) Open-Meteo.com (CC BY 4.0), Copernicus GloFAS · register open-meteo.public-pages
- بەرینی دروستکراو و نیشتەجێبوون، 2010 (HBASE، Landsat) CIESIN/Columbia, NASA SEDAC HBASE · register sedac.context-urban-layers
لە ناو شەش کۆڵەکەکەدا، بە سەرپەرشتیی Nexus Consortium
- تاقیکردنەوەکان Labs
- تێدا دروستکراوە Institutional Funds Nexus in Foundry
- تاقیکراوەتەوە لە Institutional Funds Nexus in Universe
- کۆدکراوە لە دارایی، بیمە و ئابووری لە Standards
- بڵاوکراوەتەوە لە Institutional Funds Nexus in Reports
- فێرکراو لە کۆلێژی دارایی و ئابووری لە Academy
06پشتڕاستکردنەوە
How results are checked.
Assumptions are tested through experience studies and actual-versus-expected analysis. Independent actuarial review checks methods and results.
| بپشکنە | How it is done |
|---|---|
| Actual versus expected analysis | Deaths, retirements and withdrawals are compared with what the assumptions implied, and persistent gaps prompt a change of assumption |
| Analysis of surplus | The change in funding between valuations is decomposed into returns, rates, experience and assumption changes, and the residual is reported |
| Sensitivity reporting | Liabilities are restated under shifts in discount rate, inflation and longevity so each assumption’s weight is visible |
| Independent actuarial review | Methods and assumptions are reviewed by an actuary not involved in the valuation, under professional standards |
Historical experience may not reflect emerging or correlated risks. Long-tail liabilities are sensitive to assumptions about future trends.
07Exposure, loss and capital
What actuarial mathematics for pension funds means for exposure, loss and capital.
The exposure, loss, scenario and capital views a risk officer, supervisor or ministry of finance would ask for, with the frameworks they report against. Structures follow supervisory and actuarial practice. Values are illustrative: never prices, ratings or advice.
Exposure and loss at return periods
How losses from actuarial mathematics for pension funds grow with severity, gross and net of reinsurance, against capital.
| Return period | Annual probability | Gross loss | Net loss | Net, capital = 100 |
|---|---|---|---|---|
| 1 in 10 | 0.10 | 14 | 10 | 10 |
| 1 in 50 | 0.02 | 33 | 21 | 21 |
| 1 in 100 | 0.01 | 46 | 27 | 27 |
| 1 in 250 | 0.004 | 68 | 39 | 39 |
| تێکڕای زیانی ساڵانە | 3.1 | 2.2 | 2.2 |
NGFS climate scenarios · Network for Greening the Financial SystemIFRS S2 Climate-related Disclosures · ISSBTCFD recommendations · Financial Stability Board TCFDPrinciples for the effective management of climate-related financial risks · Basel Committee on Banking Supervision
08Connections
Topics that rely on this method.
09Stewardship
Who maintains the method.
مەترسی ئەکچوەری و بڕی stewards actuarial mathematics for the Consortium and reviews how it is applied across platforms.
10پەیوەست
ئەو شوێنانەی ئەم لاپەڕەیە لە ناو کۆنسۆرتیۆم بۆیان دەبات.
11پرسیارەکان
پرسیار و وەڵام.
What are the limits of actuarial mathematics in this field?
Historical experience may not reflect emerging or correlated risks. Long-tail liabilities are sensitive to assumptions about future trends.
How are results checked?
Assumptions are tested through experience studies and actual-versus-expected analysis. Independent actuarial review checks methods and results.
Are the values on this page real?
The data names, roles and checks are real descriptions of practice. The canvas shows a design of the method’s use, not a run; no result is reported here.
Where else is this method applied?
ئەو canonical method page lists every platform that applies it.
Reportsبەشداربە
لەم لاپەڕەیەوە بەڵگە پێشکەش بکە.
Reports is the Consortium’s quarterly publication. What you know about this subject can become evidence, a case or a correction in the next edition, credited to you and published under CC BY 4.0 where it is your own work.
Global Risks AllianceInstitutional Funds Nexusئامادەیی دارایی و بیمەسیناریۆ و تاقیکردنەوەی گوشار
- ئیمەیڵGateway GW-GRAلەم لاپەڕەیەوە بینێرەبەڵگە، ڕاستکردنەوە، بابەت، ڕێگا، پێداچوونەوە، وەرگێڕان یان تێکردنی پڕۆفایل. بە نیشانەی ئەم لاپەڕەیە دەگات، بۆ ئەوەی دەستکاریکەری خاوەنەکەی وەریبگرێت.
- Zenodoتەکیەی کراوەدایبنێ و بیدە بە کۆمەڵگاتۆماری خۆت لە Zenodo بە ORCID iD ی خۆت بڵاو بکەرەوە، پاشان لەوێ بیدە بە کۆمەڵگای Reports. سەرپەرشتیارەکان پێداچوونەوەی بۆ دەکەن؛ DOI هەر هی تۆیە.
- ReportsGlobal Risks Allianceهەموو ڕێگاکانی بەشداری ببینەجۆرەکانی بەشداری، هەریەکە چۆن پێداچوونەوەی بۆ دەکرێت، چ ناوبردنێک وەردەگریت، مۆڵەتەکە و ئەوەی هەرگیز وەرناگیرێت.
هەرگیز داتای کەسی، وردەکاریی هەستیاری ژێرخان یان هیچ شتێک مەنێرە کە مافی بڵاوکردنەوەت نییە. بەشدارییەک پێش بەکارهێنان پێداچوونەوەی بۆ دەکرێت؛ ناردنی ماف نابەخشێت بە نووسەرایەتی یان بەڕێوەبردنی ڕاگەیاندن، و پاڵپشتی دارایی هەرگیز دۆزینەوەیەک ناکڕێت.
Institutional Funds Nexus
Bring an exposure or capital question to the Alliance.
زانیاری و پرسیار ئەمڕۆ کراوەن. پرسیارێک ژمارەی ئاماژەی پێدەدرێت و هەنگاوی دواتر دیاری دەکات؛ داواکاری، پارەدان، تەرخانکردنی کۆمپیوتەر و تۆمارکردن تەنیا کاتێک دەکرێنەوە کە تیم، مەرج و توانای پێداچوونەوەیان هەبێت.
یاسایی
بەڵگەنامە یاساییەکان.
نەخشە، داتا و وێنەکانی ئەم ماڵپەڕە بۆ ناوەڕۆک و زانیاریی گشتی پیشان دراون. ئامۆژگاری، پێشبینی یان ئاگادارکردنەوە نین؛ سنوورەکانی زانیارییەکە لە ڕەتکردنەوەی بەرپرسیارێتی و ئاگاداریی داتادا دەستنیشان کراون.