Optimal Insurance Under the Insurer's VaR Constraint

Optimal Insurance Indemnity and Reinsurance Strategy for Health Insurance

“…e authors in [1][2][3] established the optimal insurance framework under static setting and showed that the deductible insurance is optimal in the sense of maximizing the expected concave utility function of an insurer's wealth. Since then, various models on optimal insurance design have been formulated and studied extensively, for instance, modeks of Smith [4], Spence and Zeckhauser [5], Raviv [6], Gollier and Schlesinger [7], Young [8], Wang et al [9], Promislow and Young [10], Moore and Young [11], Lee [12], Zhou and Wu [13], and references therein. More recently, Zhou et al [14] developed an optimal insurance in the presence of insurer's loss limit and proved that the optimal insurance is an inferior (normal) good for the insured with a DARA (IARA) utility function.…”

A unifying approach to risk-measure-based optimal reinsurance problems with practical constraints

“…As far as (3) is concerned, Cummins & Mahul (2004) were among the first to revisit Arrow's classical optimal reinsurance model by imposing a deterministic upper bound on each allowable ceded loss function. Subsequently, in a series of published papers initiated in Zhou & Wu (2008) and followed up in Wu (2009) andZhou et al (2010), 1 risk constraints in the form of expected tail loss or VaR were imposed on the reinsurer's net risk exposure. Such reinsurer's risk constraints take into account not only the financial goals of the insurer but also the level of risk tolerance of the reinsurer.…”