The Optimisation of Insurance Contracts on the Viatical Market
We focus on ensuring the financial requirements of a person that has life insurance and needs money because of suffering from a terminal illness that requires costly diagnosis and treatment. On the secondary market of life insurance (the viatical market), companies offer purchase of rights to benefits after the death of the insured. The paper aims to analyse the problem of optimising the life settlement for the insured. We determine the amount of the nominal value of the benefit which the insured intends to sell in such a way so that the number of benefits and premiums maximise the average amount of funds available to the insured. We use various approaches of the insured to risk to find an optimal solution, which also allows taking into consideration the different kinds of human behaviour in risky conditions. The obtained theoretical results are illustrated with examples demonstrating the possibility of their application in practice. (original abstract)
-  BHUYAN V.B., Life Markets: Trading Mortality and Longevity Risk with Life Settlements and Linked Securities, Wiley, New York 2009.
-  BOWERS N.L., GERBER H.U., HICHMANN J.C., JONES D.A., NESBITT C.J., Actuarial Mathematics, Illinois Society of Actuaries, Itasca 1986.
-  DENNEBERG D., Lectures on Non-Additive Measure and Integral, Kluwer, Boston 1994.
-  DĘBICKA J., HEILPERN S., Investor's expected profit from viatical settlements, International Scientific Conference Applications of Mathematics in Economics, Szklarska Poręba, Poland, 30 August-3 September 2017, Conference Proceedings, Wydawnictwo Uniwersytetu Wrocławskiego, Wrocław 2017, 105-116, available at http://www.amse.ue.wroc.pl/papers/2017/Debicka_Heilpern.pdf
-  DĘBICKA J., ZMYŚLONA B., Construction of multistate life tables for critical illness insurance. Influence of age and sex on the incidence of health inequalities, Silesian Statistical Review, 2016, 14 (20), 41-59.
-  DĘBICKA J., ZMYŚLONA B., Modelling of lung cancer survival data for critical illness insurances, Stat. Meth. Appl., 2019, 28 (4), 723-747.
-  GATZERT N., The secondary market for life insurance in the United Kingdom, Germany, and the United States: comparison and overview, Risk Manage. Ins. Rev., 2010, 13 (2), 279-301.
-  HABERMAN S., PITACCO E., Actuarial Models for Disability Insurance, Chapman and Hall/CRC, 1999.
-  HEILPERN S., A rank-dependent generalization of zero utility principle, Ins. Math. Econ., 2004, 33, 67-73.
-  HEY J.D., Intermediate Microeconomics. People are different, McGraw-Hill, London 2004.
-  Life Tables of Poland 2008, available at www.stat.gov.pl/en/topics/population/life-expectancy/
-  KAHNEMAN D., TVERSKY A., Prospect theory. An analysis of decision under risk, Econometrica, 1997, 47, 313-327.
-  KAŁUSZKA M., KRZESZOWIEC M., Pricing insurance contracts under cumulative prospect theory, Ins. Math. Econ., 2012, 50, 159-166.
-  NARDON M., PIANCA P., Behavioral premium principles, Dec. Econ. Fin., 2019, 42 (1), 229-257.
-  NEERAJ S., Cashing Out Life Insurance. An Analysis of the Viatical Settlements Market, Santa Monica, California, RAND Corporation, RGSD-175, 2003. As of April 15, 2013: http://www.rand.org/pubs/rgs_dissertations/RGSD175
-  VON NEUMAN J., MORGENSTERN O., Theory of Games and Economic Behavior, Princeton University Press, Princeton 1944.
-  QUIGGIN J., A theory of anticipated utility, J. Econ. Beh. Org., 1982, 3, 323-343.
-  SAMUELSON P.A., A note on measurement of utility, Rev. Econ. Stud., 1937, 4 (2), 155-161.
-  SLOAN F.A., NORTON E.C., Adverse selection, bequests, crowding out, and private demand for insurance: evidence from the long-term care insurance market, J. Risk Uncert., 1997, 15, 201-219.
-  TVERSKY A., KAHNEMAN D., Advances in prospect theory: cumulative representation of uncertainty, J. Risk Uncert., 1992, 5, 297-323.