Skip to main content
SpringerLink
Log in

Valuation of variable long-term care and limited hospitalization coverage benefits and two investment funds

  • Mathematical methods in data science
  • Published:
Soft Computing Aims and scope Submit manuscript

Abstract

Population aging along with rise of medical cost simultaneously increases popularity and uncertainty of healthcare products. To response such challenges, insurance companies try to design/introduce more and more advanced and innovative products. In this direction, this study combines some popular features of newly developed healthcare products and introduces a new long-term care product. More precisely, it improves a variable annuity product by (1) including benefits of: guaranteed lifelong withdrawal option, long-term care coverage and limited hospitalization coverage, and (2) improving the product investment fund from a single fund into two risk-free and risky funds. Theoretical foundation of the product and its fair value has been evaluated, and its practical application has been given through a simulation study.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

Data Availability

We do not use any real data. Therefore, we do not have any data to make statement about its availability.

References

  • Albarran I, Ayuso M, Guillèn M, Monteverde M (2005) A multiple state model for disability using the decomposition of death probabilities and cross-sectional data. Commun Stat Theory Methods 34(9–10):2063–2075

    Article  MathSciNet  MATH  Google Scholar 

  • Asmussen S, Glynn PW (2007) Stochastic Simulation: algorithms and analysis, vol 57. Springer, Cham

    Book  MATH  Google Scholar 

  • Baione F, Levantesi S (2014) A health insurance pricing model based on prevalence rates Application to critical illness insurance. Insur Math Econ 58:174–184

    Article  MathSciNet  MATH  Google Scholar 

  • Bernard GA (2010) Measuring the value of a guaranteed lifetime withdrawal benefit. J Fin Serv Prof 64(2):38–43

    Google Scholar 

  • Boyer MM, Glenzer F (2021) Pensions, annuities, and long-term care insurance: on the impact of risk screening. Geneva Riskd Insur Rev 46(2):133–174

    Article  Google Scholar 

  • Brown J, Warshawsky M (2013) The life care annuity: a new empirical examination of an insurance innovation that addresses problems in the markets for life annuities and long-term care insurance. J Risk Insur 80(3):677–704

    Article  Google Scholar 

  • Chen A, Fuino M, Sehner T, Wagner J (2021) Valuation of long-term care options embedded in life annuities. Ann Actuarial Sci, 1–27

  • Christiansen M, Denuit M, Lucas N, Schmidt JP (2018) Projection models for health expenses. Ann Actuarial Sci 12(1):185–203

    Article  Google Scholar 

  • Cochran JK, Bharti A (2006) A multi-stage stochastic methodology for whole hospital bed planning under peak loading. Int J Ind Syst Eng 1(1–2):8–36

    Google Scholar 

  • D’Amato V, Levantesi S, Menzietti M (2020) De-risking long-term care insurance. Soft Comput 24:8627–8641

    Article  Google Scholar 

  • Di Palo C (2020) Tackling longevity risk by means of financial compensation. Soft Comput 24(12):8583–8597

    Article  Google Scholar 

  • Glasserman P (2004) Monte Carlo methods in financial engineering, vol 53. Springer Science & Business Media, New York

    MATH  Google Scholar 

  • Haberman S, Pitacco E (1998) Actuarial models for disability insurance. CRC Press, Florida

    MATH  Google Scholar 

  • Hsieh MH, Wang JL, Chiu YF, Chen YC (2018) Valuation of variable long-term care annuities with guaranteed lifetime withdrawal benefits: a variance reduction approach. Insur Math Econ 78:246–254

    Article  MathSciNet  MATH  Google Scholar 

  • Holz D, Kling A, Russ J (2012) GMWB for life: an analysis of lifelong withdrawal guarantees. Zeitschrift für die Gesamte Versicherungswissenschaft 101(3):305–325

    Article  Google Scholar 

  • Kirkby JL, Nguyen D (2021) Equity-linked guaranteed minimum death benefits with dollar cost averaging. Insur Math Econ 100:408–428

    Article  MathSciNet  MATH  Google Scholar 

  • Levantesi S, Menzietti M (2012) Managing longevity and disability risks in life annuities with long term care. Insur Math Econ 50(3):391–401

    Article  MathSciNet  MATH  Google Scholar 

  • Liu J, Mukherjee A (2021) Medicaid and long-term care: the effects of penalizing strategic asset transfers. J Risk Insur 88(1):53–77

    Article  Google Scholar 

  • Manton KG, Corder LS, Stallard E (1993) Estimates of change in chronic disability and institutional incidence and prevalence rates in the US elderly population from the 1982, 1984, and 1989 National Long Term Care Survey. J Gerontol 48(4):153–166

    Article  Google Scholar 

  • Migon HS, Moura FA (2005) Hierarchical bayesian collective risk model: an application to health insurance. Insur Math Econ 36(2):119–135

    Article  MathSciNet  MATH  Google Scholar 

  • Moenig T (2021) Variable annuities: market incompleteness and policyholder behavior. Insur Math Econ 99:63–78

    Article  MathSciNet  MATH  Google Scholar 

  • Murtaugh CM, Spillman BC, Warshawsky MJ (2001) In sickness and in health: An annuity approach to financing long-term care and retirement income. J Risk Insur 68(2):225–253

    Article  Google Scholar 

  • Oksendal B (2013) Stochastic differential equations: an introduction with applications. Springer Science & Business Media, Norway

    MATH  Google Scholar 

  • Orji IMJ, Akanbi O, Wei S (2015) Cost modelling in healthcare systems: a case of radiology department of a teaching hospital. Int J Ind Syst Eng 19(1):50–74

    Google Scholar 

  • Piscopo G (2009) The fair price of guaranteed lifelong withdrawal benefit option in variable annuity. Probl Perspect Manag 7(4):79–83

    Google Scholar 

  • Piscopo G, Haberman S (2011) The valuation of guaranteed lifelong withdrawal benefit options in variable annuity contracts and the impact of mortality risk. North Am Actuarial J 15(1):59–76

    Article  MathSciNet  Google Scholar 

  • Pitacco E (2014) Health insurance: basic actuarial models. Springer Science & Business Media, Switzerland

  • Pitacco E. (2013). From Benefits to Guarantees: Looking at Life Insurance Products in a New Framework. Available at SSRN: https://ssrn.com/abstract=2200310 or https://doi.org/10.2139/ssrn.2200310

  • Pitacco E (1995) Actuarial models for pricing disability benefits: towards a unifying approach. Insur Math Econ 16(1):39–62

    Article  MathSciNet  MATH  Google Scholar 

  • Piontkowski J (2019) Forecasting health expenses using a functional data model. Ann Actuarial Sci 14:72–82

    Article  Google Scholar 

  • Pritchard DJ (2006) Modeling disability in long-term care insurance. North Am Actuarial J 10(4):48–75

    Article  MathSciNet  MATH  Google Scholar 

  • R Development Core Team (2011). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. ISBN 3-900051-07-0. http://www.R-project.org/

  • Rosenberg MA, Farrell PM (2008) Predictive modeling of costs for a chronic disease with acute high-cost episodes. North Am Actuarial J 12(1):1–19

    Article  MathSciNet  Google Scholar 

  • Shreve SE (2004) Stochastic calculus for finance II: continuous-time models, vol 11. Springer, New York

    Book  MATH  Google Scholar 

  • Tessera A (2007) Probabilistic models for medical insurance claims. Appl Stoch Models Bus Ind 23(4):307–317

    Article  MathSciNet  MATH  Google Scholar 

  • Webb DC (2009) Asymmetric information, long term care insurance, and annuities: the case for bundled contracts. J Risk Insur 76(1):53–85

    Article  Google Scholar 

  • Weng SJ, Wu T, Mackulak GT, Verdivi WA (2012) A multi-tool integrated methodology for distributed resource allocation in healthcare. Int J Ind Syst Eng 11(4):428–452

    Google Scholar 

  • Yang SY, Wang CW, Huang HC (2016) The valuation of lifetime health insurance policies with limited coverage. J Risk Insur 83(3):777–800

    Article  Google Scholar 

Download references

Acknowledgements

We would like to thank referees whose helpful comments led to substantial improvements in this paper. This work was supported by the Iran National Science Foundation (INSF) Grant No. 98022900.

Funding

There is no financial support for the study. Authors declare that they have no conflict of interest.

Author information

Authors and Affiliations

  1. Department of Actuarial Science, Faculty of Mathematical Sciences, Shahid Beheshti University, Evin, 1983969411, Tehran, Iran

    Sara S. Moosavi & Amir T. Payandeh Najafabadi

Authors
  1. Sara S. Moosavi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Amir T. Payandeh Najafabadi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Amir T. Payandeh Najafabadi.

Ethics declarations

Compliance with Ethical Standards

This study does not contain any studies with human participants or animals performed by any of the authors.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Moosavi, S.S., Najafabadi, A.T.P. Valuation of variable long-term care and limited hospitalization coverage benefits and two investment funds. Soft Comput 26, 3227–3235 (2022). https://doi.org/10.1007/s00500-022-06817-2

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00500-022-06817-2

Keywords

Search

Navigation