Competitive Equilibria With Distortion Risk Measures

Boonen, Tim J.

doi:10.1017/asb.2015.11

Cited by 26 publications

(21 citation statements)

References 44 publications

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“…Every tranche is allocated to the firm that is endowed with the smallest distortion function on this quantile. This is interpreted as the locally least risk-averse firm (Boonen, 2015). It is here important to remark that the contract in (19) is analogous to Pareto optimal risk sharing contracts with distortion risk measures.…”

Section: Definition 31 Preference Relation V K K ∈ {I R} Is Givementioning

confidence: 99%

“…To conclude this section, we point out that suppose the insurer is a riskaverse distortion risk measure minimizer (i.e., g I is concave), and the reinsurer is risk-neutral, then it is optimal to reinsure all risk to the reinsurer, i.e., f (X) = X. This follows from E g I [Y] ≥ E [Y] for all Y ∈ L ∞ (see, e.g., Boonen, 2015). However, the reinsurer might ask for a mark-up above the expected value premium if α < 1, i.e., when the reinsurer has some bargaining power.…”

Section: Proposition 32 Suppose V I and V R Are Both Distortion Rismentioning

confidence: 99%

“…Both streams study roughly the same objective function in mathematical terms, but with different motivations. First, several authors study optimal risk sharing and Pareto equilibria (see, e.g., Heath and Ku, 2004; Barrieu and El Karoui, 2005;Filipović and Kupper, 2008;Jouini et al, 2008;Ludkovski and Young, 2009;Boonen, 2015). Second, there is a stream in the literature that studies optimal (re)insurance contract design with a given premium principle (see, e.g., Chi and Tan, 2011;Asimit et al, 2013;Cui et al, 2013;Chi and Meng, 2014;Assa, 2015;Boonen et al, 2015;Cheung and Lo, 2015).…”

Section: Introductionmentioning

confidence: 99%

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Pricing in Reinsurance Bargaining With Comonotonic Additive Utility Functions

Boonen¹,

Tan²,

Zhuang

2016

ASTIN Bull.

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Optimal reinsurance indemnities have widely been studied in the literature, yet the bargaining for optimal prices has remained relatively unexplored. Therefore, the key objective of this paper is to analyze the price of reinsurance contracts. We use a novel way to model the bargaining powers of the insurer and reinsurer, which allows us to generalize the contracts according to the Nash bargaining solution, indifference pricing and the equilibrium contracts. We illustrate these pricing functions by means of inverse-S shaped distortion functions for the insurer and the Value-at-Risk for the reinsurer.

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Section: Definition 31 Preference Relation V K K ∈ {I R} Is Givementioning

confidence: 99%

Section: Proposition 32 Suppose V I and V R Are Both Distortion Rismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Pricing in Reinsurance Bargaining With Comonotonic Additive Utility Functions

Boonen¹,

Tan²,

Zhuang

2016

ASTIN Bull.

Self Cite

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“…. , p. Due to concavity of the function g * and due to g * (s) ≤ g(s) for all s ∈ [0, 1], it holds that (see Boonen, 2015):…”

Section: Appendix: Proof Of Proposition 43mentioning

confidence: 99%

Optimal Reinsurance with One Insurer and Multiple Reinsurers

2015

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In this paper, we consider a one-period optimal reinsurance design model with n reinsurers and an insurer. For very general preferences of the insurer, we obtain that there exists a very intuitive pricing formula for all reinsurers that use a distortion premium principle. The insurer determines its optimal risk that it wants to reinsure via this pricing formula. This risk it wants to reinsure is then shared by the reinsurers via tranching. The optimal ceded loss functions among multiple reinsurers are derived explicitly under the additional assumptions that the insurer's preferences are given by an inverse-S shaped distortion risk measure and that the reinsurer's premium principles are some functions of the Conditional Value-at-Risk. We also demonstrate that under some prescribed conditions, it is never optimal for the insurer to cede its risk to more than two reinsurers.

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“…As a result, Pareto optima can be found in the class of comonotone allocations in a more tractable way. Examples include Carlier and Dana (2008) for a two-agent model with the so-called ranklinear utilities that generalize rank-dependent utilities but are still concave, Dana (2011) for a multiagent economy allowing short-selling with concave law-invariant utilities, Tsanakas and Christofides (2006) for rank-dependent utilities with convex probability weighting functions, and Boonen (2015Boonen ( , 2017 for expected utilities and dual utilities of Yaari (1987) with convex probability weighting functions. Xia and Zhou (2016) study full Arrow-Debreu equilibria and pricing for a single-period RDUT economy, without assuming any shape of the probability weighting function.…”

Section: Introductionmentioning

confidence: 99%

Arrow–Debreu equilibria for rank‐dependent utilities with heterogeneous probability weighting

Jin

Xia

2018

Mathematical Finance

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We study Arrow–Debreu equilibria for a one‐period‐two‐date pure exchange economy with rank‐dependent utility agents having heterogeneous probability weighting and outcome utility functions. In particular, we allow the economy to have a mix of expected utility agents and rank‐dependent utility ones, with nonconvex probability weighting functions. The standard approach for convex economy equilibria fails due to the incompatibility with second‐order stochastic dominance. The representative agent approach devised in Xia and Zhou (2016) does not work either due to the heterogeneity of the weighting functions. We overcome these difficulties by considering the comonotone allocations, on which the rank‐dependent utilities become concave. Accordingly, we introduce the notion of comonotone Pareto optima, and derive their characterizing conditions. With the aid of the auxiliary problem of price equilibria with transfers, we provide a sufficient condition in terms of the model primitives under which an Arrow–Debreu equilibrium exists, along with the explicit expression of the state‐price density in equilibrium. This new, general sufficient condition distinguishes the paper from previous related studies with homogeneous and/or convex probability weightings.

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Competitive Equilibria With Distortion Risk Measures

Cited by 26 publications

References 44 publications

Pricing in Reinsurance Bargaining With Comonotonic Additive Utility Functions

Pricing in Reinsurance Bargaining With Comonotonic Additive Utility Functions

Optimal Reinsurance with One Insurer and Multiple Reinsurers

Arrow–Debreu equilibria for rank‐dependent utilities with heterogeneous probability weighting

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