Mathematical and statistical methods in insurance and by Cira Perna, Marilena Sibillo

By Cira Perna, Marilena Sibillo

The interplay among mathematicians and statisticians finds to be an efficient method of the research of assurance and monetary difficulties, particularly in an operative point of view. The Maf2006 convention, held on the collage of Salerno in 2006, had accurately this function and the gathering the following released gathers many of the papers awarded on the convention and successively labored out to this objective. They hide a large choice of matters in coverage and fiscal fields, all handled in mild of the winning cooperation among the 2 quantitative tools.

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The knock-out feature is implied by the fact that this option can be exercised only if the insured is still alive, hence it expires in case of death (“knock-out event”). The additional complication arising in life insurance policies with respect to standard American options is that there is not a fixed date within which the option can be exercised, since its “maturity” is driven by mortality factors. Moreover, the value of the residual contract depends both on mortality and on financial uncertainty and, even if pooling arguments can be ∗ Financial support from Cofinanziamento MIUR on ‘Valutazioni nelle assicurazioni vita e nel settore previdenziale: metodologie attuariali, economiche e finanziarie” is gratefully acknowledged.

T }, with t = T − 1, T − 2, . . , cT (·, ·) measures the distance between a pair of scenarios on the whole time horizon {1, . . , T }. If the minimum is attained at kt∗ , then the scenario i ∗ is deleted and ∗ j ∗ ∈ arg min∗ cT ξ i ξ j , (13) j =i is the aggregating scenario, with i ∗ , j ∗ ∈ D(kt∗ ). The optimal redistribution rule for the probabilities is defined, according to the results in [GKHR03], as follows: k π˜ kτ,τ +1 j∗ , j∗ kτ +1, j ∗ = πkτ, j ∗ k ∗ i + πkτ,τ +1, , i∗ (14) for τ = t, .

IEEE Bologna Power Tech Proceedings (A. Borghetti, C. A. Nucci, M. Paolone eds). (2003) [HR03] Heitsch, H. : Scenario reduction algorithms in stochastic programming. Computational Optimization and Applications, 24, 187–206 (2003) [HRS05] Heitsch, H. and R¨omisch, W. : Stability of multistage stochastic programming. Stochastic programming e-prints, 16 (2005) [HW01] Høyland, K. and Wallace S. : Generating scenario trees for multi-stage decision problems. : Financial Asset-Pricing theory and stochastic programming models for asset/liability management: a synthesis.

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