Reducing risk by merging counter-monotonic risks

Cheung, Ka Chun; Dhaene, Jan; Lo, Ambrose; Tang, Qihe

doi:10.1016/j.insmatheco.2013.10.014

Cited by 20 publications

(17 citation statements)

References 17 publications

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“…Note that counter-monotonicity is a bivariate concept. An application of counter-monotonicity to merging risks was considered in Cheung et al (2014).…”

Section: Counter-monotonicitymentioning

confidence: 99%

Characterizing mutual exclusivity as the strongest negative multivariate dependence structure

Cheung

2014

Insurance: Mathematics and Economics

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Mutual exclusivity is an extreme negative dependence structure that was first proposed and studied in Dhaene and Denuit (1999) (The safest dependence structure among risks. Insurance: Mathematics and Economics 25, 11-21) in the context of insurance risks. In this article, we revisit this notion and present versatile characterizations of mutually exclusive random vectors via their pairwise counter-monotonic behaviour, minimal convex sum property, distributional representation and the characteristic function of the sum of their components. These characterizations highlight the role of mutual exclusivity in generalizing counter-monotonicity as the strongest negative dependence structure in a multi-dimensional setting.

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“…Note that counter-monotonicity is a bivariate concept. An application of counter-monotonicity to merging risks was considered in Cheung et al (2014).…”

Section: Counter-monotonicitymentioning

confidence: 99%

Characterizing mutual exclusivity as the strongest negative multivariate dependence structure

Cheung

2014

Insurance: Mathematics and Economics

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“…Second, the issue of moral hazard is not appropriately handled in many existing studies, resulting in counter-intuitive optimal solutions that are not marketable in practice. Throughout this paper, we restrict our analysis to non-decreasing and 1-Lipschitz ceded loss functions, so that both the insurer and reinsurer incur a higher loss with a heavier ground-up loss, ruling out ex post moral hazard issues arising from the manipulation of losses (see Cheung et al (2014) for how non-decreasing and 1-Lipschitz indemnity schedules appeal to both the insurer and reinsurer in an EU setting).…”

Section: Introductionmentioning

confidence: 99%

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

2016

Scandinavian Actuarial Journal

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The design of optimal reinsurance treaties in the presence of multifarious practical constraints is a substantive but underdeveloped topic in modern risk management. To examine the influence of these constraints on the contract design systematically, this article formulates a generic constrained reinsurance problem where the objective and constraint functions take the form of Lebesgue integrals whose integrands involve the unit-valued derivative of the ceded loss function to be chosen. Such a formulation provides a unifying framework to tackle a wide body of existing and novel distortion-risk-measure-based optimal reinsurance problems with constraints that reflect diverse practical considerations. Prominent examples include insurers' budgetary, regulatory and reinsurers' participation constraints. An elementary and intuitive solution scheme based on an extension of the cost-benefit technique in Cheung and .] is proposed and illuminated by analytically identifying the optimal risk-sharing schemes in several concrete optimal reinsurance models of practical interest. Particular emphasis is placed on the economic implications of the above constraints in terms of stimulating or curtailing the demand for reinsurance, and how these constraints serve to reconcile the possibly conflicting objectives of different parties. ARTICLE HISTORY

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“…The inequality above defines that Y is less risky than X in stop-loss order; see, for example, Kaas and van Heerwaarden (1992). Recently, Cheung et al (2014) introduced the concept of risk reducer in convex order as follows: Definition 1.1 For a given integrable random variable X, a random variable Z is said to be its risk reducer, denoted by Z ∈ R(X), if…”

Section: Introductionmentioning

confidence: 99%

“…( 1.3) In this paper we aim at a structural description of the set R(X). In other words, we follow the work of Cheung et al (2014) to investigate under what conditions adding a negatively dependent risk will decrease the overall level of risk. Dually, under the expected utility framework, Finkelshtain et al (1999), Denuit et al (2011), and Li et al (2016), among others, have investigated under what conditions adding a positively dependent risk will increase the overall level of risk.…”

Section: Introductionmentioning

confidence: 99%

Risk reducers in convex order

Tang

Zhang

2016

Insurance: Mathematics and Economics

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Given a risk position X, a random addition Z is called a risk reducer for X if the new position X + Z is less risky than X + E[Z] in convex order. We utilize the concept of convex hull to give a structural description of risk reducers in the case of an atomless probability space. Then we study risk reducers that are fully dependent on X. Applications to multivariate stochastic ordering, index-linked hedging strategies, and optimal reinsurance are proposed.

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Reducing risk by merging counter-monotonic risks

Cited by 20 publications

References 17 publications

Characterizing mutual exclusivity as the strongest negative multivariate dependence structure

Characterizing mutual exclusivity as the strongest negative multivariate dependence structure

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

Risk reducers in convex order

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