TY - JOUR

T1 - A Risk-Theory Model to Assess the Capital Requirement for Mortality and Longevity Risk

AU - Savelli, Nino

AU - Clemente, Gian Paolo

PY - 2014

Y1 - 2014

N2 - There is considerable uncertainty regarding the future development of life expectancy that leads to significant change in many fields of the insurance market. Pricing annuity products and mortality-linked securities seem primary goals of actuarial literature. At the same
time, the valuation of non-hedgeable liabilities (as technical provisions for contracts where risk is not entirely borne by the policyholders) and the estimation of capital requirement appear very important issues in Solvency II framework. In this context, we propose a model
based on Risk Theory in order to evaluate the capital requirement for mortality and longevity
risk. We assume a life portfolio characterized by traditional and with-profit products
divided in several homogeneous generations of contracts. Each cohort includes equal contracts that differ only by the insured sum with the aim to consider the eff ect of variability
coefficient. Some assumptions allow to obtain closed formulae for the exact characteristics of demographic profit distribution regardless of contract types (i.e either with survival or
death benefits). Furthermore Monte-Carlo methods provide the simulated distribution of
mortality and longevity profit for each generation. Some case studies show the moments and the capital requirements for diff erent life portfolios. Finally, further research will regard both the aggregation effect between several generations and a valuation of liabilities consistent to
Solvency II context.

AB - There is considerable uncertainty regarding the future development of life expectancy that leads to significant change in many fields of the insurance market. Pricing annuity products and mortality-linked securities seem primary goals of actuarial literature. At the same
time, the valuation of non-hedgeable liabilities (as technical provisions for contracts where risk is not entirely borne by the policyholders) and the estimation of capital requirement appear very important issues in Solvency II framework. In this context, we propose a model
based on Risk Theory in order to evaluate the capital requirement for mortality and longevity
risk. We assume a life portfolio characterized by traditional and with-profit products
divided in several homogeneous generations of contracts. Each cohort includes equal contracts that differ only by the insured sum with the aim to consider the eff ect of variability
coefficient. Some assumptions allow to obtain closed formulae for the exact characteristics of demographic profit distribution regardless of contract types (i.e either with survival or
death benefits). Furthermore Monte-Carlo methods provide the simulated distribution of
mortality and longevity profit for each generation. Some case studies show the moments and the capital requirements for diff erent life portfolios. Finally, further research will regard both the aggregation effect between several generations and a valuation of liabilities consistent to
Solvency II context.

KW - Homans formula

KW - capital requirement,

KW - mortality and longevity risk,

KW - profit distribution,

KW - Homans formula

KW - capital requirement,

KW - mortality and longevity risk,

KW - profit distribution,

UR - http://hdl.handle.net/10807/54529

U2 - 10.1080/09720502.2013.849943

DO - 10.1080/09720502.2013.849943

M3 - Article

VL - 16

SP - 397

EP - 429

JO - Journal of Interdisciplinary Mathematics

JF - Journal of Interdisciplinary Mathematics

SN - 0972-0502

ER -