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Sensitivity of the joint survival probability for reinsurance schemes
Author(s) -
Roumelioti Eleni E.,
Zazanis Michael A.,
Frangos Nikos E.
Publication year - 2013
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.2922
Subject(s) - mathematics , sensitivity (control systems) , reinsurance , estimator , differentiable function , monte carlo method , malliavin calculus , covariance matrix , covariance , mathematical analysis , statistics , partial differential equation , stochastic partial differential equation , electronic engineering , actuarial science , engineering , business
We model the joint risk process for an insurer and a reinsurer using a diffusion approximation and obtain expressions for the sensitivity of the joint survival probability with respect to parameters of the reinsurance scheme. The approach used leads, more generally, to explicit expressions for the sensitivity of functionals of diffusions inR mwith constant coefficients, whose drift vector and covariance matrix are differentiable functions of a parameter, in a form suitable for efficient Monte Carlo simulation. The functionals examined depend on the values of the diffusion at a finite number of time epochs, and the sensitivities are calculated using the likelihood ratio method. An extension to dynamic reinsurance schemes is also briefly described, and sensitivity estimators are provided using the integration by parts formula of the Malliavin calculus. Copyright © 2013 John Wiley & Sons, Ltd.