Mathematical and Statistical Methods for Actuarial Sciences and Finance

284 F. Quittard-Pinon and R. Randrianarivony the stochastic process modelling the instantaneous risk-free rate. The discount fac ...

Fair costs of guaranteed minimum death benefit contracts 285 2.3 Main Equations Under a chosen risk-neutral measureQ, the GMDB o ...

286 F. Quittard-Pinon and R. Randrianarivony price processSis supposed to behaveaccording to the following SDEunder the chosen e ...

Fair costs of guaranteed minimum death benefit contracts 287 A lengthy calculation shows that the characteristic exponentφT(u)of ...

288 F. Quittard-Pinon and R. Randrianarivony where(a,x)= ∫∞ x e−tta−^1 dtis the upper incomplete gamma function whereamust be p ...

Fair costs of guaranteed minimum death benefit contracts 289 4.1 Impact of jumps and interest rates The GMDB contract expiry is ...

290 F. Quittard-Pinon and R. Randrianarivony Ta b le 2 .Jumps impact, female policyholder;r=6%,g=5 %, 200 % cap Purchase age No- ...

Fair costs of guaranteed minimum death benefit contracts 291 Ta b le 3 .Stochastic interest rates impact, male policyholder;g=5 ...

292 F. Quittard-Pinon and R. Randrianarivony 30 35 40 45 50 55 60 65 70 75 0 20 40 60 80 100 120 Mortality impact −− USA Age (ye ...

Fair costs of guaranteed minimum death benefit contracts 293 References Ballotta, L., Haberman, S.: The fair valuation problem ...

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Solvency evaluation of the guaranty fund at a large financial cooperative Jean Roy Abstract.This paper reports on a consulting p ...

296 J. Roy eventually select the methods to be applied. The two polar approaches in terms of ag- gregation of data were implemen ...

Solvency evaluation of the guaranty fund at a large financial cooperative 297 was reviewed: the three studies of the Federal Dep ...

298 J. Roy Ta b le 1 .Characterisation of the two approaches selected for implementation Aggregated Disaggregated Aggregation of ...

Solvency evaluation of the guaranty fund at a large financial cooperative 299 to the historical data. With these distributions o ...

300 J. Roy 5 The disaggregated approach Under the disaggregated approach, the income statement of each credit union is simu- lat ...

Solvency evaluation of the guaranty fund at a large financial cooperative 301 two policies for premiums were simulated: the curr ...

302 J. Roy Ta b le 5 .Summary of solvency estimates under the two approaches Approach Probability of Probability of Implied S&am ...

Solvency evaluation of the guaranty fund at a large financial cooperative 303 8 Conclusions This study faced the challenge of es ...