Project CEMAPRE internal
|Title||Reinsurance of dependent risks|
|Participants||Maria de Lourdes Centeno, Manuel Guerra, Alexandra Moura (Principal Investigator)|
|Summary||This work focuses on the study of the optimal levels of risk transfer for an insurance company|
intending to reinsure two dependent risks.
While a large quantity of studies can be found in literature regarding optimal reinsurance, only a
few recent works consider dependence. After the pioneering work of Centeno (2005, Dependent risks
and excess of loss insurance), where dependence is considered in the number of claims, several
authors have accounted for dependence between claim numbers. However, regarding this problem of
optimal reinsurance of dependent risks through the claim severity, very little can be found in
literature. In Cai and Wei (2012, Optimal reinsurance with positively dependent risks) the authors
analyze the problem for dependent risks through the claim severities considering the expected value
principle and defining positive dependence through the stochastic ordering. The direct extension of
Cai and Wei result to the case of variance related premiums, was found to be not possible, since one
of the fundamental Lemas was not verified. In many practical cases, the complexity introduced by
dependencies leads to the need for numerical. In Moura (2017, Optimal Reinsurance of Dependent
Risks) a sensitivity analysis of the optimal combination of QS and stop loss treaties for two risks
dependent through a copula structure for several premium principles.
In this work, we intent to further analyze the optimal forms of risk transfer under dependencies of
the underlying risks by means of copula structures. We will further develop numerical procedures to
study the optimal reinsurance problem and its sensitivity to a wide range of factors as well as
possible applications to practical cases. Using this approach, we will explore the possibility of
extending the result in Guerra and Centeno (2010, Optimal reinsurance for variance related premium
calculation principles) to dependent risks.