Importance The solvency and financial stability of an insurance company depends on the quality of estimates of insurance reserves. In long-term personal insurance, the insurer should take into account possible investment income when creating insurance reserves. Therefore, it is important to study as many factors as possible, which have an impact on potential income from investing insurance reserve funds. Objectives The main objective of this paper is to develop an actuarial model for long-term personal insurance reserve that would reflect the influence of significant factors and enable to estimate the dependence of the insurance reserve on real rate of return. Methods To build the model, I propose to use actuarial finite-state models and the Thiele differential equation. Herewith, a set of models is defined by specific conditions of long-term personal insurance contracts. Results The proposed model of long-term personal insurance reserve enables to take into account the influence of significant factors like arising cash flows and investment income on the insurance reserve. In addition, the model allows recalculating the reserve at any time until the contract expires. Moreover, the model is sensible to the specifics of various types of long-term personal insurance contracts and a particular insurance product within each type. Conclusions and Relevance The results obtained on the basis of these theoretical models may be useful when dealing with practical problems, including the application of flexible rate of return for investing the insurance funds.
Abdyusheva S., Spivak S. Obratnye zadachi dlya markovskikh modelei [Inverse problems for the Markov models]. Aktuarii = Actuary, 2007, no. 1, pp. 41–46.
Baskakov V.N., Andreeva O.N., Baskakova M.E., Kartashov G.D., Krylova E.K. Strakhovanie ot neschastnykh sluchaev na proizvodstve: aktuarnye osnovy [Occupational injury insurance: the actuarial foundation]. Moscow, Academia Publ., 2001, 192 p.
Bowers N., Gerber H., Jones D., Nesbitt J., Hickman J. Aktuarnaya matematika [Actuarial Mathematics]. Moscow, Yanus-K Publ., 2001, 656 p.
Kudryavtsev A.A. Demograficheskie osnovy strakhovaniya zhizni. Kurs lektsii [Demographic fundamentals of life insurance. A course of lectures]. St. Petersburg, Institut strakhovaniya Publ., 1998, 237 p.
Kudryavtsev A.A. Metodologiya aktuarnogo analiza [The methodology of actuarial analysis]. St. Petersburg, SPbSU Publ., 2009, 204 p.
Faizova A.A. Modelirovanie rezerva po strakhovaniyu zhizni s uchetom stsenariev razvitiya protsentnoi stavki [Modeling the life insurance reserve subject to interest rate development scenarios]. Nauchnye trudy Vol'nogo ekonomicheskogo obshchestva Rossii = Scientific Works of the Free Economic Society of Russia, 2013, vol. 172, pp. 437–449.
Amsler M.H.Les chaines de Markov des assurances vie, invalidité et maladie. Transactions of the 18th International Congress of Actuaries. München, 1968, vol. 5, pp. 731–746.
Bernoulli D.Essai d’une nouvelle analyse de la mortalité causée par la petite vérole, et des avantages de l'inoculation pour la prévenir. Histoire et mémoires de l'Académie Royale des Sciences, 1960, pp. 1–45.
Christiansen M. Multistate Models in Health Insurance. AStA Advances in Statistical Analysis, 2012, vol. 96, no. 2, pp. 155–186.
Du Pasquier L.G.Mathematische Theorie der Invaliditätversicherung. Mitteilungen der Vereinigung schweizerischer Versicherungsmathematiker, 1912, vol. 7, pp. 1–7.
Du Pasquier L.G.Mathematische Theorie der Invaliditätversicherung. Mitteilungen der Vereinigung schweizerischer Versicherungsmathematiker, 1913, vol. 8, pp. 1–153.
Haberman S., Pitacco E. Actuarial Models for Disability Insurance. London, Chapman & Hall, 1999, 280 p.
Haberman S., Sibbett T.A. History of Actuarial Science. London, William Pickering, 1995, 391 p.
Hamilton-Jones J.Actuarial aspects of long-term sickness insurance. Journal of the Institute of Actuaries, 1972, no. 98, pp. 17–67.
Hoem J.M. Markov chain models in life insurance. Blätter der Deutschen Gesellschaft für Versicherungsmathematik, 1969, vol. 9, pp. 91–107.
Møller T., Steffenson M.Market-Valuation Methods in Life and Pension Insurance. New York, Cambridge University Press, 2007, 279 p.
Pitacco E. Multistate models for long-term care insurance and related indexing problems. Applied Stochastic Models in Business and Industry, 1999, no. 15, pp. 429–441.
Ramlau-Hansen H.Distribution of Surplus in Life Insurance. ASTIN Bulletin, 1991, vol. 21, pp. 57–71.
Wolthuis H.Life insurance mathematics (The Markovian model). Brussels, Caire Education Series, 1993, 288 p.
