Leader: Emilio Russo (UNICAL); Other collaborator(s): Margherita Borella (UNITO), Rosa Cocozza (UNINA)
- Provide a full map of the financial/insurance instruments which accompany the ageing process. Assess the feasibility of the private arrangements – also learning from international experience.
- Study technical solutions and new financial/insurance instruments in different risk-environments in order to satisfy the demand for protection in old age.
Brief description of the activities and of the intermediate results:
The need for innovative contracts that combine a long-term insurance perspective with a substantial financial content requires careful mathematical modelling.
The research suggests a flexible lattice model for pricing insurance contracts, combining both financial and actuarial factors. This is particularly important in the case of long-term policy benefits linked to the performance of a reference fund invested in financial assets. The proposed discretization technique can also be used to price securitization products based on mortality or longevity risks. In this perspective, the study proposes and evaluates a product aimed at protecting the issuer against possible deviation of the observed mortality compared to a reference value defined ex ante. Moreover, the valuation of equity-linked life insurances policies is provided. In this case, an interesting application considers the discretized processes of interest rate, mortality rate, and equity prices. The presence of a surrender option that allows the policyholder to escape out of the contract early is also introduced.
Moreover, the Reverse Mortgage (RM) contracts have been studied. As well known, these contracts allow elderly homeowners to get a credit line (as a lump sum or as a periodic cash flow for a defined period or the borrower residual life) that will be repaid through the selling of their homes after their deaths. In accordance with regulatory guidelines that direct prudent assessments of future losses to ensure solvency, the estimation of the Conditional Value at Risk of a RM portfolio has been considered. Since the riskiness is affected by nonlinear relationships between risk factors, the Conditional Value at Risk is estimated using a Neural Network algorithm. The main advantage of the proposed model consists in the flexibility of the framework, that is suitable to different geographical contexts and different markets. The study carried out by the research group offers policy advice for all the parties that work to issue and manage these contracts. Then, other relevant information is obtained to reorganize the informative puzzle about RMs; specifically, the sensitivity of the product to the age of the homeowner has been deepened, providing policy indications, that can be matched with subjective situations.
Main policy, industrial and scientific implications
- Indications concerning interesting contracts that combine a long-term insurance perspective with a substantial financial content are provided. Relevant valuations concerning equity-linked life insurances policies are given
- Specific results on Reverse Mortage contracts are obtained; in particular the sensitivity of the product to the age of the homeowner has been explored, thus obtaining interesting information to set and compare even with scenarios more properly individualized.
Brief description of the activities and of the intermediate results:
Spatial inequalities and gender differences are the main drivers of unequal ageing.
1. Preliminary estimates show marked geographical patterns, which may contribute significantly to differences in the access to services for older people, suggesting differential resilience to unexpected shocks.
2. The gender gap in mean retirement income increases across cohorts and with age, but the relative gender gap decreases and survivor’s benefits reduce the gap remarkably, especially late in life: hence it is important to consider the whole “welfare package” within the family.
Brief description of the activities and of the intermediate results:
1. The need for innovative contracts that combine a long-term insurance perspective with a substantial financial content requires careful mathematical modelling. Within this perspective, the research proposes a flexible lattice model for pricing insurance contracts, combining both financial and actuarial factors. This is particularly important in the case of long-term policy benefits linked to the performance of a reference fund invested in financial assets.
2. The demand for innovative policies and technical solutions in relation to the access to healthcare. After government schemes, social health insurance and out-of-pocket payments, private health insurance is an important source of health financing, hence the team looks at Health Insurance Funds (HIF), with the aims of mapping HIFs in Italy, considering their regulation and supervision.
3. The Equity Release Mortgage market's strengths and weaknesses were highlighted through an extensive literature review, looking toward to the development trend of these contracts in the future.
4. The ongoing research deals with a decision problem of a homeowner who is approaching old age and has to evaluate whether to contract a reverse mortgage or not. Elders’ lifetime utility functions were built, considering consumptions, bequest motivations and lifespan uncertainty; then, the maximization problem was solved to find the optimal allocation of the wealth between housing/no housing, consumptions and bequest with and without Reverse Mortgages. Currently, a survey is being carried out on the level of knowledge and opinions in Italy about the Reverse Mortgage contract among the recipients of this financial instrument.
Main policy, industrial and scientific implications
- The proposed discretization technique can also be used to price securitization products based on mortality or longevity risks. In this perspective, the study proposes and evaluates a product aimed at protecting the issuer against possible deviation of the observed mortality compared to a reference value defined ex ante. Moreover, the valuation of equity-linked life insurances policies is provided. In this case, an interesting application considers the discretized processes of interest rate, mortality rate, and equity prices. The presence of a surrender option that allows the policyholder to escape out of the contract early is also introduced.
- Findings encourage pursuing this research direction to improve the understandability and scalability of these innovative financial tools. In addition, formulas have been given to quantify all of the major risks that impact ERMs. These formulas are simple to understand and apply, and are helpful for establishing profitable risk control strategies. Moreover, the volatility of RM contracts in Italian cities has been investigated from the lenders’ point of view. Several key parameters were used to develop this analysis: aging indicators (life expectancy at birth, fertility rate); living indicators (income and poverty of older people, old-age dependency ratio, house price pattern, house ownership, perception of home housing solutions).
Brief description of the activities and of the intermediate results:
Technical solutions and new financial/insurance instruments in different risk-environments were explored, in order to satisfy the demand for protection in old age; models that depict the combined trend of mortality, financial markets and macroeconomic quantities were provided. Moreover, the research dealt with a decision problem of a homeowner who is approaching old age and has to evaluate whether to contract a reverse mortgage or not. Elders’ lifetime utility functions were built, considering consumptions, bequest motivations and lifespan uncertainty; then, the maximization problem was solved to find the optimal allocation of the wealth between housing/no housing, consumptions and bequest with and without Reverse Mortgages.
A survey was carried out on the level of knowledge and opinions in Italy about the Reverse Mortgage contract among the recipients of this financial instrument. 1) indicator of economic hope, considering the economic resources to rely on for old age (by a sampling of 904 potential Italian RM subscribers) considering the economic resources to rely on for old age. 2) Net Positivity Score (NPS) (measure of people’s propensity to recommend a certain product/service or social initiative) (by a sampling of 904 potential Italian RM subscribers). 3) Risk indicators of RM capturing the impact of different geographical areas. 4) Testing pricing methods for equilty-linked insurance contracts.
Main policy, industrial and scientific implications
- Explain the skepticism experienced by seniors in purchasing RM.
- Importance of financial and demographic literature.
- Focus on a specific group of individuals with extremely low incomes and no other resources, already retired, exacerbated by other debts, and/or more engaged in family support.
- Customize products that fit the specific financial situations of different regions.
Dissemination Events:
- XLVII Annual Meeting of the Italian Association for Mathematics Applied to Social and Economic Sciences University of Milano-Bicocca, September 20-21-22, 2023
- 26th International Congress on Insurance: Mathematics and Economics, 04 - 07 July 2023,
Heriot-Watt University, Edinburgh, p.14
- the 26th International Congress on Insurance: Mathematics and Economics, 04 - 07 July 2023,
Heriot-Watt University, Edinburgh
- the 20th Conference of the Applied Stochastic Models and Data Analysis International Society ASMDA2023 and Demographics2023 Workshop, 6-9 June 2023, Heraklion, Crete, Greece.
- AHL-Napoli 2023: Scaling-up digital solutions for active and healthy living: implementing across scientific disciplines, industrial sectors and scenarios, University of Naples Federico II, 13-15 November 2023
- International Conference on Scientific Computing, Modeling and Simulation (ICSCMS-23), 29th November 2023, London, UK
- International Conference “Mathematical and Statistical Methods for Actuarial Sciences and Finance. MAF 2024”. University of Le Havre Normandie, Le Havre Cedex, April 4-6, 2024
- The 1st SWUFE-Sapienza International Finance Workshop,
- AGE-It General Meeting. Age-It announced the Call for Papers for the General Meeting, organized by Spoke 6, which took place in Venice at the Ca’ Foscari University from May 20th to May 22nd at San Giobbe Economic Campus – Cannaregio 873 – 30121 Venice. During the meeting, parallel sessions were hold dedicated to the research conducted by members of the Age-It community. Each session focused on a broad theme with contributions from various disciplines. Every session emphasized the implications of the research for practice and policies in the biomedical, demographic, social, and economic fields, and/or on technological innovation. The General Meeting was an important dissemination event that reached and engaged more than 400 participants. The main results presented and discussed at the Age-It general meeting, received significant attention by the research community and are expected to influence both practice and policies for an active and healthy ageing.
- 33rd European Conference on Operational Research, 30th June-3rd July 2024, Technical University of Denmark (DTU), Copenhagen, Denmark
- Scandinavian Actuarial Conference 2024, University of Copenhagen, Denmark – August 14-16, 2024
- XLVIII Annual Conference of the Association for Mathematics Applied to Social and Economic Sciences (AMASES). Ischia, September 5-6-7, 2024.
Scientific Outputs:
- Domenico De Giovanni; Marco Pirra; Fabio Viviano, Joint mortality models based on linear hypercubes, Working paper 2023
- - Apicella G., E. Di Lorenzo, G. Magni, M. Sibillo: Longevity comparison by gender: exploring the future through an evidence-based approach, 2023
- Apicella G., E. Di Lorenzo, G. Piscopo, M. Sibillo: The Functional Clustering of the Mortality Gender Gap: A Multi- country Analysis, 2023
- G. Apicella, E. De Giorgi, E. Di Lorenzo and M. Sibillo: The Gender Longevity Gap: improving economic decisions through demographic literacy. https://papers.ssrn.com/sol3/papers.cfm?abstract_id=4331841#Swiss Finance Institute Research Paper No. 23-02
- E. Di Lorenzo, F. Rania, M. Sibillo, A. Trotta: Meeting the challenges of longevity: lifetime income from real estate. In: Corazza, M., Gannon, F., Legros, F., Pizzi, C., Touzé, V. (eds) Mathematical and Statistical Methods for Actuarial Sciences and Finance. MAF 2024. Springer, Cham. https://doi.org/10.1007/978-3-031-64273-9_21, ISBN 978-3-031-64272-2, pp. 124-129.
- G. Apicella, E. Di Lorenzo, G. Magni, M. Sibillo: The cost of retirement income provision: some quantitative insights in life insurance. . In: Corazza, M., Gannon, F., Legros, F., Pizzi, C., Touzé, V. (eds) Mathematical and Statistical Methods for Actuarial Sciences and Finance. MAF 2024. Springer, Cham. https://doi.org/10.1007/978-3-031-64273-9_1, ISBN 978-3-031-64272-2, pp. 1-6.
- E. Di Lorenzo, G. Piscopo, M. Sibillo, A. Trotta: Looking toward the future: well-ageing solutions from the equity release mortgage. Encyclopedia of Monetary Policy, Financial Markets and Banking, Editor: Nicholas Apergis, Elsevier, 2024, ISBN 9780443157851, https://doi.org/10.1016/B978-0-44-313776-1.00267-1.
- G. Apicella, E. De Giorgi, E. Di Lorenzo and M. Sibillo: Financial and Demographic Literacy: Monetizing the Gender Mortality Gap. Applied Stochastic Models in Business and Industry, Applied Stochastic Models in Business and Industry, DOI: 10.1002/asmb.2876, 2024, pp. 1-23 https://onlinelibrary.wiley.com/doi/10.1002/asmb.2876
- R. Blundell, M. Borella, J. Commault, and M. Nardi (2023) Old Age Risks, Consumption, and Insurance. NBER Working Paper No. 2734
- Rosa Casillo, Permessi e agevolazioni per i lavoratori caregivers familiari (art. 3, comma 1, lett. B, d.lgs. n. 105/2022) in Fili, Garofalo, Tiraboschi, Trojsi, Trasparenza e attività di cura nei contratti di lavoro. Commentario ai decreti legislativo n. 105 e n. 105 del 2022, Adapt Labour Studies e-Book series n. 96, Adapt University Press, 2023, Tomo II, pp. 568- 576, ISBN 979-12-80922-15-1.
- Zied Chaieb, Domenico De Giovanni & Djibril Gueye (10 Oct 2023): Two hybrid models for dependent death times of couple: a common shock approach, Scandinavian Actuarial Journal, DOI: 10.1080/03461238.2023.2264555
- Devolder, E. Russo, Alessandro Staino: A flexible lattice model for fair policy valuations under multiple risk factors. Astin Bulletin (2024)
- Claudio Daminato, Mario Padula: The Life-Cycle Effects of Pension Reforms: A Structural Approach, Journal of the European Economic Association, 2023; jvad049, https://doi.org/10.1093/jeea/jvad049
- R. Casillo: La tutela in età di vecchiaia per i lavoratori non subordinati. In corso di stampa Collana di Diritto della sicurezza sociale
- Debon, S. Haberman, G. Piscopo: Multipopulation mortality analysis: bringing out the unobservable with latent clastering. Quality and Quantity, August 2023
- G. Apicella, E. Di Lorenzo, G. Piscopo, M. Sibillo: Lee-Carter model: Assessing the potential to capture gender-related mortality dynamics. Decisions in Economics and Finance (2023) https://doi.org/10.1007/s10203-023-00417
- E. Di Lorenzo, G. Piscopo, M. Sibillo: Addressing the economic and demographic complexity via a neural network approach: risk measures for reverse mortgages. Computational Management Science 21, 11 (2024) https://doi.org/10.1007/s10287-023-00491-x
- E. Di Lorenzo, G. Piscopo, M. Sibillo: Reverse Mortgage: some remarks on the interplay between contract benefit and borrower’s age. Working paper (2023)
- E. Di Lorenzo, G. Piscopo, M. Sibillo: Multi country investigation of the Healthy Life Expectancy. Abstract. AHL-Napoli 2023: Scaling-up digital solutions for active and healthy living: implementing across scientific disciplines, industrial sectors and scenarios, University of Naples Federico II, 13-15 November 2023 (2023)
- Z. Chaieb, D. De Giovanni, D. Gueye (10 Oct 2023): Two hybrid models for dependent death times of couple: a common shock approach, Scandinavian Actuarial Journal, DOI: 10.1080/03461238.2023.2264555 https://doi.org/10.1080/03461238.2023.2264555
- R. Blundell, M. Borella, J. Commault, and M. Nardi (2023) Old Age Risks, Consumption, and Insurance. NBER Working Paper No. 27348
- Rosa Casillo: Invecchiamento e lavoro. Federalismi, ISSN 1826-3534
Numero 19, 2024, pp. 21-53
- Rosa Casillo: L’universalità della tutela di pensione per i lavoratori autonomi. Dottrina Previdenza - il Lavoro nella Giurisprudenza 7/2024, pp. 653-660
- Awareness, understanding and attitudes toward Reverse Mortgage in Italy." A survey addressed to Italian homeowners aged over 60. b) Working papers: 1) Russo, E., Leccadito, A., Staino, A. (2024). “On binomial discretizations of correlated skew Brownian motions: Applications to option pricing”. Submitted to International Review of Financial Analysis. Elsevier Inc., US. ISSN: 10575219.
- Costabile, M., Massabò, I., Mamon, R., Russo, E., Staino, A., Zhao, Y. (2024). “Pricing a guaranteed annuity option under a stochastic correlation setting”. Submitted to Journal of Mathematical Analysis and Applications. Academic Press Inc., US. ISSN: 0022247X, 10960813.
- Russo, E., Leccadito, A., Staino, A. (2024). “Skew Brownian motion discretization: A lattice approach for financial and actuarial applications”. Submitted to Financial Innovation. SpingerOpen, Germany. ISSN: 21994730.
- Costabile, M., Massabò, I., Mamon, R., Russo, E., Staino, A., Zhao, Y. (2024). “A lattice-based approach for life insurance pricing in a stochastic correlation framework”. Submitted to Mathematics and Computers in Simulation. Elsevier B.V., Netherlands. ISSN: 03784754.
- Costabile, M., Massabò, I., Russo, E., Staino, A. (2024). “A lattice-based algorithm for pricing derivatives in a fractional Brownian motion framework”. Submitted to Annals of Finance. Springer-Verlag GmbH, Germany. ISSN: 1614-2446, 1614-2454.