Inf-convolution of risk measures and optimal risk transfer

In this paper we provide the complete solution to the existence and characterization problem of optimal capital and risk allocations for not necessarily monotone, law-invariant convex risk measures on the model space L p , for any p ∈ [1, ∞]. Our main result says that the capital and risk allocation problem always admits a solution via contracts whose payoffs are defined as increasing Lipschitz continuous functions of the aggregate risk.

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“…These convolutions are discussed thoroughly in e.g. [4] or [22] on L ∞ . In contrast, we provide our results on L 1 .…”

Section: Existence Of Optimal Allocationsmentioning

confidence: 99%

Optimal capital and risk allocations for law- and cash-invariant convex functions

Filipović

Svindland²

2008

Finance Stoch

114

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“…In recent years, formulations of the risk sharing problem in which the preferences of agents are specified by risk measures (monetary valuation functionals) have attracted considerable interest; see for instance Chateauneuf et al (2000); Barrieu and El Karoui (2005); Acciaio (2007);Jouini et al (2008);Filipovic and Svindland (2008); Kiesel and Rüschendorf (2008). When all agents use a translation invariant risk measure (as in Artzner et al (1999)) for evaluation, Pareto optimal solutions can only be unique up to addition of deterministic side payments which sum to zero.…”

Section: Introductionmentioning

confidence: 99%

The composite iteration algorithm for finding efficient and financially fair risk-sharing rules

Pazdera

Schumacher

Werker

2017

Journal of Mathematical Economics

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The composite iteration algorithm for finding efficient and financially fair risk-sharing rules Pazdera, J.; Schumacher, J.M.; Werker, B.J.M. Disclaimer/Complaints regulationsIf you believe that digital publication of certain material infringes any of your rights or (privacy) interests, please let the Library know, stating your reasons. In case of a legitimate complaint, the Library will make the material inaccessible and/or remove it from the website. Please Ask the Library: http://uba.uva.nl/en/contact, or a letter to: Library of the University of Amsterdam, Secretariat, Singel 425, 1012 WP Amsterdam, The Netherlands. You will be contacted as soon as possible. AbstractWe consider the problem of finding an efficient and fair ex-ante rule for division of an uncertain monetary outcome among a finite number of von Neumann-Morgenstern agents. Efficiency is understood here, as usual, in the sense of Pareto efficiency subject to the feasibility constraint. Fairness is defined as financial fairness with respect to a predetermined pricing functional. We show that efficient and financially fair allocation rules are in one-to-one correspondence with positive eigenvectors of a nonlinear homogeneous and monotone mapping associated to the risk sharing problem. We establish relevant properties of this mapping. On the basis of this, we obtain a proof of existence and uniqueness of solutions via nonlinear Perron-Frobenius theory, as well as a proof of global convergence of the natural iterative algorithm. We argue that this algorithm is computationally attractive, and discuss its rate of convergence.

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“…Very recently, research has focused on risk preferences given in terms of convex risk measures, as exemplified by the monograph of Föllmer and Schied [17]. In particular, Barrieu and El Karoui [4] studied optimal risk sharing under the exponential indifference measure, while Jouini et al [20] analyzed the case of two agents and convex, law-invariant risk measures. The related question of market equilibrium was addressed by Acciaio [2], Burgert and Rüschendorf [8] and Filipovic and Kupper [16].…”

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confidence: 99%

Optimal risk sharing under distorted probabilities

Ludkovski

Young

2009

Math Finan Econ

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We study optimal risk sharing among n agents endowed with distortion risk measures. Our model includes market frictions that can either represent linear transaction costs or risk premia charged by a clearing house for the agents. Risk sharing under third-party constraints is also considered. We obtain an explicit formula for Pareto optimal allocations. In particular, we find that a stop-loss or deductible risk sharing is optimal in the case of two agents and several common distortion functions. This extends recent result of Jouini et al. (Adv Math Econ 9:49-72, 2006) to the problem with unbounded risks and market frictions.

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Inf-convolution of risk measures and optimal risk transfer

Cited by 267 publications

References 25 publications

Optimal capital and risk allocations for law- and cash-invariant convex functions

Optimal capital and risk allocations for law- and cash-invariant convex functions

The composite iteration algorithm for finding efficient and financially fair risk-sharing rules

Optimal risk sharing under distorted probabilities

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