Cocozza, Rosa and Di Lorenzo, Emilia and Sibillo, Marilena (2007) The Current Value of the Mathematical Provision: A Financial Risk Prospect. [Pubblicazione in rivista scientifica]


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Item Type: Pubblicazione in rivista scientifica
Title: The Current Value of the Mathematical Provision: A Financial Risk Prospect
Di Lorenzo,
Date: 2007
Number of Pages: 14
Department: Economia aziendale
Official URL:
Journal or Publication Title: Problems and Perspectives in Management
Date: 2007
ISSN: 1727-7051
Volume: 5
Number: 2
Page Range: pp. 127-140
Number of Pages: 14
Uncontrolled Keywords: Risk indicators, life insurance, solvency, financial risk, demographic risk
References: 1. AMERICAN ACADEMY OF ACTUARIES (2003): Comment Letter on Exposure Draft 5 Insurance Contracts. 2. CHAN, K.C., KAROLYI, A.G., LONGSTAFF, F.A. and SANDERS, A.B. (1992): “An Empirical Comparison of Alternative Models of the Short-Term Interest Rate”, The Journal of Finance 47, 1209-1227. 3. COCOZZA, R. (2000): La gestione del rischio di tasso di interesse nelle imprese di assicurazione sulla vita. CEDAM: Padova, I. 4. COCOZZA, R. and DI LORENZO, E. (2001): “Solvency of life insurance companies: methodological issues”. Technical Report 5. COCOZZA, R. and DI LORENZO, E. (2003): “Risk profiles of life insurance business: a combined approach” in Proceedings of the 6th Spanish-Italian Meeting on Financial Mathematics, Dipartimento di Matematica Applicata Bruno de Finetti, Trieste, I, 157-170. 6. COCOZZA, R. and DI LORENZO, E. (2005): “Solvency of life insurance companies: methodological issues”. Journal of Actuarial Practice, forthcoming. 7. COCOZZA, R., DI LORENZO, E. and SIBILLO M. (2004a). “Risk Profiles of Life Insurance Business: quantitative analysis in a managerial perspective” in Atti del convegno Metodi Matematici e Statistici per l’Analisi dei Dati Assicurativi e Finanziari MAF2004 – CUSL, Salerno, I, 81-86. 8. COCOZZA, R., DI LORENZO, E. and SIBILLO M. (2004b). “Methodological problems in solvency assessment of an insurance company”. Investment Management and Financial Innovations, Issue 2, 95-102. 9. COCOZZA, R., DI LORENZO, E. and SIBILLO M. (2004c). “Life insurance risk indicators: a balance sheet approach” in Proceedings of 8th International Congress on Insurance: Mathematics & Economics, Rome, I, 10. COPPOLA, M., DI LORENZO, E. and SIBILLO, M. (2000): “Risk Sources in a Life Annuity Portfolio: Decomposition and Measurement Tools”. Journal of Actuarial Practice, 8, pp. 43-61. 11. COPPOLA, M., DI LORENZO, E. and SIBILLO, M. (2002): “Further Remarks on Risk Sources Measuring in the case of a Life Annuity Portfolio”. Journal of Actuarial Practice, 10, pp. 229-242. 12. COX, J.C., INGERSOL, J.E. and ROSS, S.A. (1985): “A theory of the term structure of the interest rate”. Econometrica 53, pp. 385-407. 13. DEELSTRA, G. and PARKER, G. (1995). ”A Covariance Equivalent Discretisation Of The CIRMode” in Proceedings of the V AFIRColloquium, Rome, I, 732-747. 14. DE FELICE,M. and MORICONI, M. (2004). ”Market based tools for managing the life insurance company”. DFM.pdf 15. DI LORENZO, E. and SIBILLO, M., (2002). ”The Longevity Risk: Measurement and Application Perspectives” in Proc. of the 2nd Conference in Actuarial Science and Finance on Samos, Karlovassi, 16. FEES, E.W. (1990). “Stochastic life contingencies with solvency considerations”. Trans of the Society of Actuaries, XLII, 91-129. 17. HAIRS, C.J., BELSHAM, D.J., BRYSON, N.M., GEORGE, C.M., HARE, D. J.P., SMITH, D.A. and THOMPSON, S. (2001). “Fair valuation of liabilities”. Institute of Actuaries and Faculty of Actuaries, November. 18. IAIS SOLVENCY & ACTUARIAL ISSUES SUBCOMMITTEE (2000). On solvency, solvency assessments and actuarial issues. IAIS, March. 19. IAIS (2002). Glossary of terms. 20. IAIS SOLVENCY & ACTUARIAL ISSUES SUBCOMMITTE (2002). Principles on capital adequacy and solvency. IAIS, January. 21. INTERNATIONAL ACCOUNTING STANDARDS BOARD (2003). Exposure Draft 5 Insurance Contracts. International Accounting Standards Board Committee Foundation, London. 22. MELSA, J.L. and SAGE, A.P. (1973). An Introduction to Probability and Stochastic Processes. Prentice-Hall, New Jersey. 23. PARKER, G. (1997). “Stochastic analysis of the interaction between investment and insurance risks”. North American Actuarial Journal 1 (2), 55-84. 24. VARNDERHOOF I. and ALTMAN, E.I., Ed. (2000). The fair value of Insurance Business. Kluwer Academic Publishers, Boston.
MIUR S.S.D.: Area 13 - Scienze economiche e statistiche > SECS-S/06 - Metodi matematici dell'economia e delle scienze attuariali e finanziarie
Area 13 - Scienze economiche e statistiche > SECS-P/11 - Economia degli intermediari finanziari
Date Deposited: 04 Feb 2011 07:36
Last Modified: 30 Apr 2014 19:43


The paper addresses the question of the calculation of the current value of the mathematical provision and moulds it in a deterministic and stochastic scenario, using a proper term structure of interest rates estimated by means of a Cox-Ingersoll-Ross model. It provides a complete and original year-by-year evaluation model for the business performance, and a closed solution for the current evaluation of the reserve, together with a comprehensive insight into the dynamics of the reserve connected to the selection of a defined term structure of interest rates. Moreover, the calculation of the VaR of the mathematical provision is prospected as risk measure useful to appreciate also the evaluation rate risk. Future research prospects concern the selection of the stochastic process used to describe the dynamics of the interest rates and the possible managerial and regulatory application of a VaR measure. The modelling has been applied, as an exemplification, to a life annuity portfolio but it can be easily replicated for any kind of policy and any kind of portfolios even non homogeneous.

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