Proposal for Mathematical and Parallel Computing Modeling as a Decision Support System for Actuarial Sciences
Abstract
:1. Introduction
2. Background
2.1. Actuarial Tables
2.2. Goodness-of-Fit (GoF) Tests
2.3. Chi-Square Adherence Test
- = chi-square test statistics;
- n = maximum age in the actuarial tables;
- = observed frequency of deaths/disability with age i;
- = average death/disability frequency with age i.
3. Methodology
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- Step 1 creating a trusted database;
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- Step 2 define/choose a heuristic to be applied to the data;
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- Step 3 database heuristic adherence test;
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- Step 4 selection of the best model for the study;
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- Step 5 selection of the computational model; and
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- Step 6 analysis of results.
3.1. Creation of SMIB
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- Greater consistency of information based on the maintenance of a unique historical basis;
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- Higher reliability of the database, these being correct and applicable in any situation;
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- Ability to consolidate information, with the possibility of aggregating remunerative installments of various forms;
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- Ability to detail the remuneration structure of the military, with the possibility of explaining the composition of the military remuneration; and
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- Ability to detail payroll by nature of expenses (NE), which provides greater precision in comparisons with the federal government’s integrated financial administration system (FGIFAS).
3.2. Heuristics
3.2.1. The Probabilistic Multidecrements
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- An active military (state 1) can be declared invalid (state 2), marry (state 4), go to reserve (state 9), resign (state 3), or die (state 11);
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- An invalid military (state 2) can return to active (state 1), marry (state 2), or pass away (state 11);
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- If the military member resigns (state 3), he leaves the system and does not generate a pension;
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- A married soldier (state 4) can divorce (state 5), become a widower (state 6), or become a parent (state 8). Once married, the dotted line shows that the military can generate a pension (state 12);
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- A divorced military (state 5) may enter into a new marriage (state 7);
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- A widowed soldier (state 6) may contract a new marriage (state 7);
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- A military who contracted a new marriage (state 7) can become a parent state 8);
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- A military man who became a father (state 8) can generate a pension (state 12) as indicated by the dotted line;
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- A military in the Remunerated Reserve (state 9) can contract marriage (state 4), go to the reserve by age (state 10), or die (state 11);
- ▪
- A military in the reserve by age (state 10) may marry (state 4) or die (state 11); and
- ▪
- Generation of pension (state 12) can be generated by marriage (state 4), by a new marriage (state 7), and by paternity (state 8) once the military passed away (state 12).
3.2.2. The Actuarial Tables
3.2.3. The Mortality Tables
3.2.4. Invalidity Entry Tables
3.2.5. Tables of Invalidity Mortality
3.2.6. Selection of the Model
3.3. Computational Model
3.4. Parallel Computing
3.4.1. Parallel Programming with C #
3.4.2. Asynchro Programming with Async and Await
3.5. The Software Developed
4. Results
4.1. Result of Mortality of Assets, Inactive and Pensioners of the Armed Forces
4.2. Results of Invalidity of Mortality of Armed Forces
4.3. Result of Entry into Disability of the Armed Forces
- ▪
- ALLG-72 for all redemptions between 28% and 39%;
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- USTP-61 for all redemptions between 38% and 48%; and
- ▪
- X17 for all redemptions between 50% and 55%.
4.4. Processing Time Reduction Results
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
- Logullo, Y.; Bigogno-Costa, V.; Silva, A.C.S.d.; Belderrain, M.C. A Prioritization Approach Based on VFT and AHP for Group Decision Making: A Case Study in the Military Operations. Production 2022, 32. [Google Scholar] [CrossRef]
- Do Nascimento Maêda, S.M.; Basílio, M.P.; Pinheiro, I.; d de Araújo costaa, M.Â.; Moreira, L.; dos Santos, M.; Gomes, C.F.S.; de Almeidaa, I.D.P.; de Araújo Costad, A.P. Investments in Times of Pandemics: An Approach by the SAPEVO-M-NC Method. In Proceedings of the 2nd Conference on Modern Management Based on Big Data, MMBD, Quanzhou, China, 8–11 November 2021; and 3rd Conference on Machine Learning and Intelligent Systems, MLIS, Xiamen, China, 8–11 November 2021. pp. 162–168. [Google Scholar]
- Morais, D.C.; de Almeida, A.T. Group Decision Making on Water Resources Based on Analysis of Individual Rankings. Omega 2012, 40, 42–52. [Google Scholar] [CrossRef]
- Costa, I.P.D.A.; Costa, A.P.D.A.; Sanseverino, A.M.; Gomes, C.F.S.; Santos, M.D. Bibliometric studies on multi-criteria decision analysis (mcda) methods applied in military problems. Pesqui. Oper. 2022, 42. [Google Scholar] [CrossRef]
- Tenorio, F.M.; Santos, M.D.; Gomes, C.F.S.; Araujo, J.D.C.; De Almeida, G.P. THOR 2 Method: An Efficient Instrument in Situations Where There Is Uncertainty or Lack of Data. IEEE Access 2021, 9, 161794–161805. [Google Scholar] [CrossRef]
- Floriano, C.M.; Pereira, V.; Rodrigues, B.E.S. 3MO-AHP: An Inconsistency Reduction Approach through Mono-, Multi- or Many-Objective Quality Measures. Data Technol. Appl. 2022, 56, 645–670. [Google Scholar] [CrossRef]
- Basilio, M.P.; Pereira, V.; Oliveira, M.W.C.D.; Costa Neto, A.F.D. Ranking Policing Strategies as a Function of Criminal Complaints: Application of the PROMETHEE II Method in the Brazilian Context. J. Model. Manag. 2021, 16, 1185–1207. [Google Scholar] [CrossRef]
- Sharma, H.; Sohani, N.; Yadav, A. Comparative Analysis of Ranking the Lean Supply Chain Enablers: An AHP, BWM and Fuzzy SWARA Based Approach. Int. J. Qual. Reliab. Manag. 2022, 39, 2252–2271. [Google Scholar] [CrossRef]
- Rodrigues, L.V.S.; Casado, R.S.G.R.; Carvalho, E.N.d.; Silva, M.M.; Silva, L.C. Using FITradeoff in a Ranking Problem for Supplier Selection under TBL Performance Evaluation: An Application in the Textile Sector. Production 2020, 30. [Google Scholar] [CrossRef] [Green Version]
- dos Santos, F.B.; dos Santos, M. Choice of Armored Vehicles on Wheels for the Brazilian Marine Corps Using PrOPPAGA. Procedia Comput. Sci. 2022, 199, 301–308. [Google Scholar] [CrossRef]
- Costa, I.P.d.A.; Basílio, M.P.; Maêda, S.M.d.N.; Rodrigues, M.V.G.; Moreira, M.Â.L.; Gomes, C.F.S.; dos Santos, M. Algorithm Selection for Machine Learning Classification: An Application of the MELCHIOR Multicriteria Method. Front. Artif. Intell. Appl. 2021, 341, 154–161. [Google Scholar] [CrossRef]
- Moreira, M.Â.L.; Gomes, C.F.S.; Pereira, M.T.; dos Santos, M. SAPEVO-H2 a Multi-Criteria Approach Based on Hierarchical Network: Analysis of Aircraft Systems for Brazilian Navy. In Innovations in Industrial Engineering II; Springer International Publishing: Cham, Switzerland, 2023; pp. 61–74. [Google Scholar]
- Santos, N.; Junior, C.d.S.R.; Moreira, M.Â.L.; Santos, M.; Gomes, C.F.S.; Costa, I.P.d.A. Strategy Analysis for Project Portfolio Evaluation in a Technology Consulting Company by the Hybrid Method THOR. Procedia Comput. Sci. 2022, 199, 134–141. [Google Scholar] [CrossRef]
- Song, Z.; Yan, T.; Ge, Y. Spatial Equilibrium Allocation of Urban Large Public General Hospitals Based on the Welfare Maximization Principle: A Case Study of Nanjing, China. Sustainability 2018, 10, 3024. [Google Scholar] [CrossRef] [Green Version]
- Mellem, P.M.N.; Costa, I.P.A.; Costa, A.P.A.; Moreira, M.Â.L.; Gomes, C.F.S.; dos Santos, M.; Corriça, J.V.P. Prospective Scenarios Applied in Course Portfolio Management: An Approach in Light of the Momentum and ELECTRE-MOr Methods. Procedia Comput. Sci. 2022, 199, 48–55. [Google Scholar] [CrossRef]
- Costa, I.P.d.A.; Basílio, M.P.; Maêda, S.M.d.N.; Rodrigues, M.V.G.; Moreira, M.Â.L.; Gomes, C.F.S.; Santos, M. Bibliometric Studies on Multi-Criteria Decision Analysis (MCDA) Applied in Personnel Selection. Front. Artif. Intell. Appl. 2021, 341, 119–125. [Google Scholar] [CrossRef]
- Siegenfeld, A.F.; Bar-Yam, Y. An Introduction to Complex Systems Science and Its Applications. Complexity 2020, 2020, 6105872. [Google Scholar] [CrossRef]
- Ahmed, W.; Najmi, A.; Mustafa, Y.; Khan, A. Developing Model to Analyze Factors Affecting Firms’ Agility and Competitive Capability: A Case of a Volatile Market. J. Model. Manag. 2019, 14, 476–491. [Google Scholar] [CrossRef]
- Wu, W. A Revised Grey Relational Analysis Method for Multicriteria Group Decision-Making with Expected Utility Theory for Oil Spill Emergency Management. Math. Probl. Eng. 2021, 2021, 6682332. [Google Scholar] [CrossRef]
- Costa, I.P.d.A.; Moreira, M.Â.L.; Costa, A.P.d.A.; Teixeira, L.F.H.d.S.d.B.; Gomes, C.F.S.; Santos, M.D. Strategic Study for Managing the Portfolio of IT Courses Offered by a Corporate Training Company: An Approach in the Light of the ELECTRE-MOr Multicriteria Hybrid Method. Int. J. Inf. Technol. Decis. Mak. 2021, 21, 351–379. [Google Scholar] [CrossRef]
- Marttunen, M.; Lienert, J.; Belton, V. Structuring Problems for Multi-Criteria Decision Analysis in Practice: A Literature Review of Method Combinations. Eur. J. Oper. Res. 2017, 263, 1–17. [Google Scholar] [CrossRef] [Green Version]
- Moreira, M.Â.L.; Junior, M.A.P.d.C.; Costa, I.P.d.A.; Gomes, C.F.S.; dos Santos, M.; Basilio, M.P.; Pereira, D.A.d.M. Consistency Analysis Algorithm for the Multi-Criteria Methods of SAPEVO Family. Procedia Comput. Sci. 2022, 214, 133–140. [Google Scholar] [CrossRef]
- Doumpos, M.; Zopounidis, C.; Gounopoulos, D.; Platanakis, E.; Zhang, W. Operational Research and Artificial Intelligence Methods in Banking. Eur. J. Oper. Res. 2022, 306, 1–16. [Google Scholar] [CrossRef]
- Silal, S.P. Operational Research: A Multidisciplinary Approach for the Management of Infectious Disease in a Global Context. Eur. J. Oper. Res. 2021, 291, 929–934. [Google Scholar] [CrossRef] [PubMed]
- De Almeida, I.D.P.; de Araújo Costa, I.P.; de Araújo Costa, A.P.; de Pina Corriça, J.V.; Lellis Moreira, M.Â.; Simões Gomes, C.F.; dos Santos, M. A Multicriteria Decision-Making Approach to Classify Military Bases for the Brazilian Navy. Procedia Comput. Sci. 2022, 199, 79–86. [Google Scholar] [CrossRef]
- De Figueiredo, B.H.; dos Santos, M.; Fávero, L.P.L.; Moreira, M.Â.L.; Costa, I.P.d.A. Analysis of Maintenance Activities in Urban Pavement Management Systems Based on Decision Tree Algorithm. Procedia Comput. Sci. 2022, 214, 712–719. [Google Scholar] [CrossRef]
- Pak, T.-Y. Social Protection for Happiness? The Impact of Social Pension Reform on Subjective Well-Being of the Korean Elderly. J. Policy Model. 2020, 42, 349–366. [Google Scholar] [CrossRef]
- Lima, R.C.; Silva, P.F.; Rudzit, G. No Power Vacuum: National Security Neglect and the Defence Sector in Brazil. Def. Stud. 2021, 21, 84–106. [Google Scholar] [CrossRef]
- Maêda, S.M.d.N.; Basílio, M.P.; Costa, I.P.d.A.; Moreira, M.Â.L.; dos Santos, M.; Gomes, C.F.S. The SAPEVO-M-NC Method. Front. Artif. Intell. Appl. 2021, 341, 89–95. [Google Scholar] [CrossRef]
- Jardim, R.; dos Santos, M.; Neto, E.; Muradas, F.M.; Santiago, B.; Moreira, M. Design of a Framework of Military Defense System for Governance of Geoinformation. Procedia Comput. Sci. 2022, 199, 174–181. [Google Scholar] [CrossRef]
- Oxford Analytica. Brazil’s pension reform will await electoral outcome. Expert Brief. 2018. [Google Scholar] [CrossRef]
- Hoffmann, R. Changes in Income Distribution in Brazil. In The Oxford Handbook of the Brazilian Economy; Oxford University Press: New York, NY, USA, 2018; pp. 467–488. [Google Scholar]
- Lobato, L.d.V.C.; Costa, A.M.; Rizzotto, M.L.F. Pension Reform: The Fatal Blow to Brazilian Social Security. Saúde Debate 2019, 43, 5–14. [Google Scholar] [CrossRef] [Green Version]
- Costanzi, R.N.; Ansiliero, G.; Da Silva Bichara, J. Survivors’ Pensions and Their Impact on the Brazilian Labour Market. Int. Soc. Secur. Rev. 2017, 70, 19–48. [Google Scholar] [CrossRef]
- Wang, L. Fertility and Unemployment in a Social Security System. Econ. Lett. 2015, 133, 19–23. [Google Scholar] [CrossRef]
- Lægreid, P.; Rykkja, L.H. Societal Security and Crisis Management; Governance Capacity and Legitimacy; Springer: Berlin/Heidelberg, Germany, 2019. [Google Scholar]
- Rejda, G.E. Social Insurance and Economic Security; Routledge: London, UK, 2015; ISBN 1315700735. [Google Scholar]
- Brockett, P.L.; Zhang, Y. Actuarial (Mathematical) Modeling of Mortality and Survival Curves. In Handbook of the Mathematics of the Arts and Sciences; Springer: Cham, Switzerland, 2021. [Google Scholar] [CrossRef]
- Santos, M.D.; Gomes, C.F.S.; Martins, E.R.; Costa, I.P.D.A.; Santos, R.C.E.D. Processing Time Reduction of Actuarial Calculus of the Armed Forces: An Application of Parallel Computing. In Proceedings of the IJCIEOM 2020—International Joint Conference on Industrial Engineering and Operations Management, Rio de Janeiro, Brazil, 8–11 July 2020. [Google Scholar]
- Zuanazzi, P.T.; Fochezatto, A.; Júnior, M.V.W. Social Security Reform and Personal Saving: Evidence from Brazil. Int. J. Econ. Financ. 2018, 10. [Google Scholar] [CrossRef] [Green Version]
- Nascimento, I.F.d.; Albuquerque, P.H.M. Fair and Balance Rate for Benefits Not Scheduled in Defined Contribution Plans. Rev. Contab. Finanças 2021, 32, 560–576. [Google Scholar] [CrossRef]
- Cuevas, M.A.; Karpowicz, M.I.; Mulas-Granados, M.C.; Soto, M. Fiscal Challenges of Population Aging in Brazil; International Monetary Fund: Washington, DC USA, 2017; ISBN 1475595557. [Google Scholar]
- Aragão, R.; Linsi, L. Many Shades of Wrong: What Governments Do When They Manipulate Statistics. Rev. Int. Political Econ. 2020, 29, 88–113. [Google Scholar] [CrossRef]
- Roncada, A.L.C. Reforming Old-Age Pension Systems in Developing Countries: Lessons from Latin America. Braz. J. Political Econ. 2022, 20, 124–145. [Google Scholar] [CrossRef]
- De La Peña, J.I.; Fernández-Ramos, M.C.; Garayeta, A.; Martín, I.D. Transforming Private Pensions: An Actuarial Model to Face Long-Term Costs. Mathematics 2022, 10, 1082. [Google Scholar] [CrossRef]
- Godínez-Olivares, H.; Boado-Penas, M.d.C.; Pantelous, A.A. How to Finance Pensions: Optimal Strategies for Pay-as-you-go Pension Systems. J. Forecast. 2016, 35, 13–33. [Google Scholar] [CrossRef]
- Hassani, H.; Unger, S.; Beneki, C. Big Data and Actuarial Science. Big Data Cogn. Comput. 2020, 4, 40. [Google Scholar] [CrossRef]
- Teixeira, L.F.H.d.S.d.B. Análise Dos Testes de Aderência Em Tábuas Atuariais: Uma Contribuição Para o Sistema de Proteção Social Dos Militares Das Forças Armadas, Dissertação (Mestrado em Engenharia de Produção)—Escola de Engenharia; Universidade Federal Fluminense: Niterói, RJ, Brazil, 2020. [Google Scholar]
- Castro, M.C.d. Entradas e Saídas No Sistema Previdenciário Brasileiro: Uma Aplicação de Tábuas de Mortalidade; Universidade Federal de Minas Gerais: Minas Gerais, Brazil, 1997. [Google Scholar]
- Vaupel, J.W.; Villavicencio, F.; Bergeron-Boucher, M.-P. Demographic Perspectives on the Rise of Longevity. Proc. Natl. Acad. Sci. USA 2021, 118, e2019536118. [Google Scholar] [CrossRef]
- Queiroz, B.L.; Gonzaga, M.R.; Vasconcelos, A.; Lopes, B.T.; Abreu, D.M.X. Comparative Analysis of Completeness of Death Registration, Adult Mortality and Life Expectancy at Birth in Brazil at the Subnational Level. Popul. Health Metr. 2020, 18, 11. [Google Scholar] [CrossRef] [PubMed]
- Queiroz, B.L.; Ferreira, M.L.A. The Evolution of Labor Force Participation and the Expected Length of Retirement in Brazil. J. Econ. Ageing 2021, 18, 100304. [Google Scholar] [CrossRef]
- Santos, M.D. Proposta de Modelagem Atuarial Aplicada Ao Setor Militar Considerando Influências Econômicas e Biométricas, Tese de Doutorado Apresentada no Programa de Pós-Graduação em Engenharia de Produção da Universidade Federal Fluminense; RIUFF: Niterói, Brazil, 2018. [Google Scholar]
- Krit, M.; Gaudoin, O.; Remy, E. Goodness-of-Fit Tests for the Weibull and Extreme Value Distributions: A Review and Comparative Study. Commun. Stat. Simul. Comput. 2021, 50, 1888–1911. [Google Scholar] [CrossRef]
- Chu, J.; Dickin, O.; Nadarajah, S. A Review of Goodness of Fit Tests for Pareto Distributions. J. Comput. Appl. Math. 2019, 361, 13–41. [Google Scholar] [CrossRef]
- D’Agostino, R.B.; Stephens, M.A. Goodness-of-Fit-Techniques; CRC Press: Boca Raton, FL, USA, 1986; Volume 68, ISBN 0824774876. [Google Scholar]
- Lospinoso, J.; Snijders, T.A.B. Goodness of Fit for Stochastic Actor-Oriented Models. Methodol. Innov. 2019, 12, 2059799119884282. [Google Scholar] [CrossRef] [Green Version]
- Assis, J.P.d.; Souza, R.P.d.; Dias Santos, C.T.d. Glossary of Statistics. In Proceedings of the EdUFERSA; Vanderbilt University School of Medicine: Nashville, TN, USA, 2019; p. 901. [Google Scholar]
- Pho, K.-H. Goodness of Fit Test for a Zero-Inflated Bernoulli Regression Model. Commun. Stat. -Simul. Comput. 2022, 1–16. [Google Scholar] [CrossRef]
- Lohse, B.; Mitchell, D.C. Valid and Reliable Measure of Adherence to Satter Division of Responsibility in Feeding. J. Nutr. Educ. Behav. 2021, 53, 211–222. [Google Scholar] [CrossRef]
- Meseguer, J. How Does Mortality Among Disability-Program Beneficiaries Compare with That of the General Population? A Summary of Actuarial Estimates. Soc. Sec. Bull. 2021, 81, 19. [Google Scholar]
- Haberman, S.; Pitacco, E. Actuarial Models for Disability Insurance; Routledge: London, UK, 2018; ISBN 1351469045. [Google Scholar]
- García-Díaz, V.; Espada, J.P.; Crespo, R.G.; G-Bustelo, B.C.P.; Lovelle, J.M.C. An Approach to Improve the Accuracy of Probabilistic Classifiers for Decision Support Systems in Sentiment Analysis. Appl. Soft Comput. 2018, 67, 822–833. [Google Scholar] [CrossRef]
- Turhan, N.S. Karl Pearson’s Chi-Square Tests. Educ. Res. Rev. 2020, 16, 575–580. [Google Scholar]
- Müller, M. Item Fit Statistics for Rasch Analysis: Can We Trust Them? J. Stat. Distrib. Appl. 2020, 7, 5. [Google Scholar] [CrossRef]
- Rokicki, B.; Ostaszewski, K. Actuarial Credibility Approach in Adjusting Initial Cost Estimates of Transport Infrastructure Projects. Sustainability 2022, 14, 13371. [Google Scholar] [CrossRef]
- Kenkel, K.M. Contributor Profile: Brazil. In Providing for Peacekeeping; PUC-Rio: Rio de Janeiro, Brazil, 2017. [Google Scholar]
- Herodotou, H.; Chen, Y.; Lu, J. A Survey on Automatic Parameter Tuning for Big Data Processing Systems. ACM Comput. Surv. 2021, 53, 1–37. [Google Scholar] [CrossRef]
- Bertsekas, D.; Tsitsiklis, J. Parallel and Distributed Computation: Numerical Methods; Athena Scientific: Athena, Greece, 2015; ISBN 1886529159. [Google Scholar]
- Arató, M.; Bozsó, D.; Elek, P.; Zempléni, A. Forecasting and Simulating Mortality Tables. Math. Comput. Model. 2009, 49, 805–813. [Google Scholar] [CrossRef]
- Dowd, K.; Cairns, A.J.G.; Blake, D.; Coughlan, G.D.; Epstein, D.; Khalaf-Allah, M. Evaluating the Goodness of Fit of Stochastic Mortality Models. Insur. Math. Econ. 2010, 47, 255–265. [Google Scholar] [CrossRef]
- Ochalek, J.; Wang, H.; Gu, Y.; Lomas, J.; Cutler, H.; Jin, C. Informing a Cost-Effectiveness Threshold for Health Technology Assessment in China: A Marginal Productivity Approach. Pharmacoeconomics 2020, 38, 1319–1331. [Google Scholar] [CrossRef] [PubMed]
- Brasil Medida Provisória No 2.215-10, de 31 de Agosto de 2001; 2001. Available online: https://www.planalto.gov.br/ccivil_03/mpv/2215-10.htm (accessed on 23 February 2023).
- Goldschmidt, R.; Passos, E.; Bezerra, E. Data Mining; Elsevier Brasil: Rio de Janeiro, Brazil, 2015; ISBN 8535278230. [Google Scholar]
- Dolatabad, F.R.; Hashemi, F.; Yektatalab, S.; Ayaz, M.; Zare, N.; Mansouri, P. Fatemeh Rahimi et al. Effect of Orem Self-Care Program on Self-Efficacy of Burn Patients Referred to Ghotb-Al-Din-E-Shirazi Burn Center, Shiraz, Iran. Int. J. Med. Investig. 2021, 10, 135–146. [Google Scholar]
- Sutton, W. On the Method Used by Milne in the Construction of the Carlisle Table of Mortality. J. Inst. Actuar. 1883, 24, 110–129. [Google Scholar] [CrossRef]
- Hughes, J. International Public Sector Accounting Standards. In Handbook of Governmental Accounting; Routledge: New York, NY, USA, 2008; pp. 513–540. [Google Scholar]
- Friedler, L.M.; Newton, L.; Bowers, H.U., Jr.; Gerber, J.C.; Hickman, D.A.; Jones, C.J. NesbittActuarial Mathematics. Am. Math. Mon. 1986, 93, 489–491. [Google Scholar] [CrossRef]
- Storto, C.L.; Gončiaruk, A.G. Efficiency vs. Effectiveness: A Benchmarking Study on European Healthcare Systems. Econ. Sociol. 2017, 10, 102–115. [Google Scholar] [CrossRef] [Green Version]
- Wahlberg, A.; Rose, N. The Governmentalization of Living: Calculating Global Health. Econ. Soc. 2015, 44, 60–90. [Google Scholar] [CrossRef] [Green Version]
- Mennicken, A.; Espeland, W.N. What’s New with Numbers? Sociological Approaches to the Study of Quantification. Annu. Rev. Sociol. 2019, 45, 223–245. [Google Scholar] [CrossRef] [Green Version]
- Beechey, S.N. Social Security Tomorrow. In Social Security and the Politics of Deservingness; Springer: Berlin/Heidelberg, Germany, 2016; pp. 99–112. [Google Scholar]
- Nigri, A.; Levantesi, S.; Marino, M.; Scognamiglio, S.; Perla, F. A Deep Learning Integrated Lee–Carter Model. Risks 2019, 7, 33. [Google Scholar] [CrossRef] [Green Version]
- Russolillo, M. Assessing Actuarial Projections Accuracy: Traditional vs. Experimental Strategy. Open J. Stat. 2017, 7, 608–620. [Google Scholar] [CrossRef] [Green Version]
- Ortega, A. Tablas de Mortalidad; 1987. Available online: https://repositorio.cepal.org/handle/11362/8977 (accessed on 23 February 2023).
- Spreeuw, J.; Owadally, I.; Kashif, M. Projecting Mortality Rates Using a Markov Chain. Mathematics 2022, 10, 1162. [Google Scholar] [CrossRef]
- Li, Z.; Shao, A.W.; Sherris, M. The Impact of Systematic Trend and Uncertainty on Mortality and Disability in a Multistate Latent Factor Model for Transition Rates. North Am. Actuar. J. 2017, 21, 594–610. [Google Scholar] [CrossRef]
- Lozano, I.A.; Alonso-González, P.J.; Núñez-Velázquez, J.J. Estimation of Life Expectancy for Dependent Population in a Multi-State Context. Int. J. Environ. Res. Public Health 2021, 18, 11162. [Google Scholar] [CrossRef]
- Planchet, F.; Debonneuil, É.; Péju, M. Proposal to Extend Access to Loans for Serious Illnesses Using Open Data. Risks 2022, 10, 51. [Google Scholar] [CrossRef]
- Domínguez-Fabián, I.; del Olmo-García, F.; Miguel, H.-S.; Antonio, J. Reinventing Social Security: Towards a Two-Step Mixed Pension System. In Economic Challenges of Pension Systems; Springer: Berlin/Heidelberg, Germany, 2020; pp. 441–472. [Google Scholar]
- Almasi, G.S.; Gottlieb, A. Highly Parallel Computing; Benjamin-Cummings Publishing Co.: New York, NY, USA, 1994; ISBN 0805304436. [Google Scholar]
- Fávero, L.P.; Belfiore, P.; Santos, H.P.; dos Santos, M.; de Araújo Costa, I.P.; Junior, W.T. Classification Performance Evaluation from Multilevel Logistic and Support Vector Machine Algorithms through Simulated Data in Python. Procedia Comput. Sci. 2022, 214, 511–519. [Google Scholar] [CrossRef]
- Junior, C.d.S.R.; Moreira, M.Â.L.; Costa, I.P.d.A.; Gomes, C.F.S.; dos Santos, M.; Silva, F.C.A.; Pereira, R.C.A.; Basilio, M.P.; Pereira, D.A.d.M. Parallel Processing Proposal by Clustering Integration of Low-Cost Microcomputers. Procedia Comput. Sci. 2022, 214, 100–107. [Google Scholar] [CrossRef]
- Junior, C.d.S.R.; Moreira, M.Â.L.; Costa, I.P.d.A.; Gomes, C.F.S.; dos Santos, M.; Silva, F.C.A.; Pereira, R.C.A.; Basilio, M.P.; Pereira, D.A.d.M. IoT Technology Proposal for Multi-Adaptative Sensing Integrated into Data Science and Analytics Scenarios. Procedia Comput. Sci. 2022, 214, 108–116. [Google Scholar] [CrossRef]
- Cader, J.M.A.; Cader, A.J.M.A.; Gamaarachchi, H.; Ragel, R.G. Optimisation of Plagiarism Detection Using Vector Space Model on CUDA Architecture. Int. J. Innov. Comput. Appl. 2022, 13, 232–244. [Google Scholar] [CrossRef]
- Hossain, M.A.; Assiri, B. Facial Expression Recognition Based on Active Region of Interest Using Deep Learning and Parallelism. PeerJ Comput. Sci. 2022, 8, e894. [Google Scholar] [CrossRef] [PubMed]
- López, A.; Jurado, J.M.; Ogayar, C.J.; Feito, F.R. An Optimized Approach for Generating Dense Thermal Point Clouds from UAV-Imagery. ISPRS J. Photogramm. Remote Sens. 2021, 182, 78–95. [Google Scholar] [CrossRef]
- Morishima, S. Scalable Anomaly Detection in Blockchain Using Graphics Processing Unit. Comput. Electr. Eng. 2021, 92, 107087. [Google Scholar] [CrossRef]
- Zhang, Y. Bayesian Analysis of Big Data in Insurance Predictive Modeling Using Distributed Computing. ASTIN Bull. J. IAA 2017, 47, 943–961. [Google Scholar] [CrossRef]
- Hwang, K.; Dongarra, J.; Fox, G.C. Distributed and Cloud Computing: From Parallel Processing to the Internet of Things; Morgan Kaufmann: Burlington, MA, USA, 2013; ISBN 0128002042. [Google Scholar]
- Kirk, D.B.W.; Mei, W.; Wu, H. Programming Massively Parallel Processors; Morgan Kauffman: Burlington, MA, USA, 2010. [Google Scholar]
- Golov, N.; Rönnbäck, L. Big Data Normalization for Massively Parallel Processing Databases. Comput. Stand. Interfaces 2017, 54, 86–93. [Google Scholar] [CrossRef]
- Laili, Y.; Zhang, L.; Li, Y. Parallel Transfer Evolution Algorithm. Appl. Soft Comput. 2019, 75, 686–701. [Google Scholar] [CrossRef] [Green Version]
CS0-41 | CSO-58 | CSO-80 | AT-49 | AT-50 | AT-55 |
---|---|---|---|---|---|
AT-71 | American Experience | GAM-1971 | SGB-51 | SGB-71 | SGB-75 |
IAPC | Hunter Semitropical | Rentiers Français | Grupal Americana | USTP-61 | GKM-70 |
GKM-80 | ALLG-72 | X-17 | CSG-60 | Prudential 1950 | GAM 1994 Male |
RP-2000-1992 Base-Male Aggregate | AT-2000 | AT-2000 F | AT-83 | AT-83 male | UP-84 |
UP94Men | UP94Woman | UP-94 MT-M-ANB | GRM-80 | GRF-80 | GRM-95 |
GRF-95 | BR-EMSsb-v.2010-m | BR-EMSsb-v.2010-f | BR-EMSmt-v.2010-m | BR-EMSmt-v.2010-f | BR-EMSsb-v.2015-m |
BR-EMSsb-2015-f | BR-EMSmt-2015-m | BR-EMSmt-2015-f | CSO2001MALE | CSO2001FEMALE | IBGE-2011-M |
IGBE-2011-F | IBGE-2011 | IBGE-2012-M | IBGE-2012-F | IBGE-2012 | - |
Invalidity and Mortality Tables for Invalids Used | |||||
---|---|---|---|---|---|
IAPB-57 Weak | IAPB-57 Strong | Zimmermann | Zimmermann (Ferr. Germans) | Zimmermann (Empre. Write.) | Grupal Americana |
Álvaro Comings | TASA-1927 | Prudential (Ferr. Retired.) | IBA (Railways) | Muller | Hunter’s |
IAPB-57 (AJUST/ITAU) | Winklevoss | Bentzien | IAPC | IAPB-57 | ALLG72 |
USTP61 | Rentiers Français | X17 | - | - | - |
Invalidity and Mortality Tables for Invalids Used | |||||
---|---|---|---|---|---|
IAPB-57 Weak | IAPB-57 Strong | Zimmermann | Zimmermann (Ferr. Germans) | Zimmermann (Empre. Write.) | Grupal Americana |
Álvaro Comings | TASA-1927 | Prudential (Ferr. Retired.) | IBA (Railways) | Muller | Hunter’s |
IAPB-57 (AJUST/ITAU) | Winklevoss | Bentzien | IAPC | IAPB-57 | ALLG72 |
USTP61 | Rentiers Français | X17 | - | - | - |
Process | Previous Version [Approximate] HH:MM:SS | Refactored Version [Approximate] HH:MM:SS | Time Reduction (%) |
---|---|---|---|
Importing databases. | 04:00:00 | 00:08:00 | 96.7% |
Actuarial calculation of present value. | 23:00:00 | 00:07:00 | 99.5% |
Actuarial projection with a term of 75 years. | 16:00:00 | 00:05:00 | 99.5% |
Total Time | 43:00:00 | 00:20:00 | 99.2% |
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Santos, M.d.; Gomes, C.F.S.; Pereira Júnior, E.L.; Moreira, M.Â.L.; Costa, I.P.d.A.; Fávero, L.P. Proposal for Mathematical and Parallel Computing Modeling as a Decision Support System for Actuarial Sciences. Axioms 2023, 12, 251. https://doi.org/10.3390/axioms12030251
Santos Md, Gomes CFS, Pereira Júnior EL, Moreira MÂL, Costa IPdA, Fávero LP. Proposal for Mathematical and Parallel Computing Modeling as a Decision Support System for Actuarial Sciences. Axioms. 2023; 12(3):251. https://doi.org/10.3390/axioms12030251
Chicago/Turabian StyleSantos, Marcos dos, Carlos Francisco Simões Gomes, Enderson Luiz Pereira Júnior, Miguel Ângelo Lellis Moreira, Igor Pinheiro de Araújo Costa, and Luiz Paulo Fávero. 2023. "Proposal for Mathematical and Parallel Computing Modeling as a Decision Support System for Actuarial Sciences" Axioms 12, no. 3: 251. https://doi.org/10.3390/axioms12030251
APA StyleSantos, M. d., Gomes, C. F. S., Pereira Júnior, E. L., Moreira, M. Â. L., Costa, I. P. d. A., & Fávero, L. P. (2023). Proposal for Mathematical and Parallel Computing Modeling as a Decision Support System for Actuarial Sciences. Axioms, 12(3), 251. https://doi.org/10.3390/axioms12030251