Reinsurance games with two reinsurers: Tree versus chain

Cao, Jingyi; Li, Dongchen; Young, Virginia R.; Zou, Bin

doi:10.1016/j.ejor.2023.04.005

Cited by 17 publications

(2 citation statements)

References 34 publications

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“…However, instead of a finite or an infinite planning horizon, we assume that the insured's planning horizon τ is random and exogenously given. Several recent papers (see Cao et al, 2022 and followups) on optimal (re)insurance problems also consider a random horizon; in particular, footnote 18 in Cao et al (2023a) discusses in detail the mathematical and economic justifications for the choice of a random horizon. 12 Because we assumed that the insured adopts a homogeneous barrier strategy in reporting, it is natural to assume that the random horizon τ follows a geometric distribution, which is the only memoryless discrete distribution.…”

Section: Insured's Preferencesmentioning

confidence: 99%

“…To be more concrete, the joint effect of (b 1 , d 1 ) and (b 2 , d 2 ) on J i is due to the fact that there is a strictly positive probability that the insured will move from one rate class to another. Consequently, the insured plays against herself in a noncooperative Nash game; please see Remark 3.1 in Cao et al (2023a) for a detailed discussion on this game feature and Björk et al (2014) and ( 2017) for standard references on such a game-theoretical approach.…”

Section: Insured's Preferencesmentioning

confidence: 99%

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Strategic underreporting and optimal deductible insurance

Cao,

Li,

Young

et al. 2024

ASTIN Bull.

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This paper proposes a theoretical insurance model to explain well-documented loss underreporting and to study how strategic underreporting affects insurance demand. We consider a utility-maximizing insured who purchases a deductible insurance contract and follows a barrier strategy to decide whether she should report a loss. The insurer adopts a bonus-malus system with two rate classes, and the insured will move to or stay in the more expensive class if she reports a loss. First, we fix the insurance contract (deductibles) and obtain the equilibrium reporting strategy in semi-closed form. A key result is that the equilibrium barriers in both rate classes are strictly greater than the corresponding deductibles, provided that the insured economically prefers the less expensive rate class, thereby offering a theoretical explanation to underreporting. Second, we study an optimal deductible insurance problem in which the insured strategically underreports losses to maximize her utility. We find that the equilibrium deductibles are strictly positive, suggesting that full insurance, often assumed in related literature, is not optimal. Moreover, in equilibrium, the insured underreports a positive amount of her loss. Finally, we examine how underreporting affects the insurer’s expected profit.

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Section: Insured's Preferencesmentioning

confidence: 99%

Section: Insured's Preferencesmentioning

confidence: 99%