Optimal reinsurance with general risk measures

This work studies Good Deals in a scenario in which a fir uses decision-making tools based on a coherent risk measure, and in which the market prices are determined with a sub-linear pricing rule. The most important observation of this work is that the existence of a Good Deal is equivalent to the incompatibility between the pricing rule and the risk measure. In this paper, we look into this situation from a regulatory point of view to rule out Good Deals with the purpose of stabilizing financia markets. We propose some practical ways of modifying a risk measure so a regulator can set appropriate levels of capital requirements for a financia institution.

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“…This problem has been studied in Balbás et al [3,2,4]. The dual of problem (3.4) is found in Balbás et al [3] as…”

Section: A Hedging Problemmentioning

confidence: 99%

“…By means of the Hahn-Banach Separation Theorem, one can easily prove that if ρ ⊂ L q is convex, σ (L q , L p )-compact and ρ satisfie (2.3), then there exists a unique continuous ρ satisfying (1), (2), (3) and (4) such that (2.2) holds.…”

Section: Remarkmentioning

confidence: 99%

Good Deals and compatible modification of risk and pricing rule: a regulatory treatment

Assa

Balbás

2011

Math Finan Econ

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“…These pioneering results are later extended to situation where there is a more sophisticated objective function and/or more realistic premium principles (see, e.g. Young 1999, Gajek & Zagrodny 2000, 2004, Kaluszka 2001, 2005, Cai & Tan 2007, Balbás et al 2009, 2015, Chi 2012, Asimit et al 2013, 2015, Cai et al 2013, Forthcoming, Chi & Tan 2013, Cui et al 2013, Cheung et al 2014, 2015, Bernard et al 2015, Cheung et al 2015, Boonen et al 2016. In the above-mentioned papers, the risk of the insurer is typically given and the objective boils down to determining an optimal strategy of transferring part of its risk to a reinsurer.…”

Section: Introductionmentioning

confidence: 99%

Optimal insurance in the presence of reinsurance

Zhuang

Boonen

Tan

et al. 2016

Scandinavian Actuarial Journal

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This paper studies an optimal insurance and reinsurance design problem among three agents: policyholder, insurer, and reinsurer. We assume that the preferences of the parties are given by distortion risk measures, which are equivalent to dual utilities. By maximizing the dual utility of the insurer and jointly solving the optimal insurance and reinsurance contracts, it is found that a layering insurance is optimal, with every layer being borne by one of the three agents. We also show that reinsurance encourages more insurance, and is welfare improving for the economy. Furthermore, it is optimal for the insurer to charge the maximum acceptable insurance premium to the policyholder. This paper also considers three other variants of the optimal insurance/reinsurance models. The first two variants impose a limit on the reinsurance premium so as to prevent insurer to reinsure all its risk. An optimal solution is still layering insurance, though the insurer will have to retain higher risk. Finally, we study the effect of competition by permitting the policyholder to insure its risk with an insurer, a reinsurer, or both. The competition from the reinsurer dampens the price at which an insurer could charge to the policyholder, although the optimal indemnities remain the same as the baseline model. The reinsurer will however not trade with the policyholder in this optimal solution. ARTICLE HISTORY

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“…The robust pricing and hedging strategies of Cox and Ob÷ ój (2011b) and Cox and Ob÷ ój (2011a) serve as an example of this approach. A di¤erent line of research in model-free hedging is based directly on the concepts of hedging and minimization of risk (see Xu (2006), Assa and Balbás (2011), Balbás, Balbás, and Heras (2009), Balbás, Balbás, and Garrido (2010), and Balbás, Balbás, and Mayoral (2009)). In this setting, the investor or portfolio manager minimizes the risk of a global position given the budget constraint on a set of manipulatable positions (a set of accessible portfolios, for instance).…”

Section: Introductionmentioning

confidence: 99%

Hedging and Pricing in Imperfect Markets Under Non-Convexity

Assa

Gospodinov

2014

SSRN Journal

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Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Abstract: This paper proposes a robust approach to hedging and pricing in the presence of market imperfections such as market incompleteness and frictions. The generality of this framework allows us to conduct an in-depth theoretical analysis of hedging strategies for a wide family of risk measures and pricing rules, which are possibly non-convex. The practical implications of our proposed theoretical approach are illustrated with an application on hedging economic risk. Terms of use: Documents inJEL classification: G11, G13, C22, E44

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Optimal reinsurance with general risk measures

Cited by 108 publications

References 34 publications

Good Deals and compatible modification of risk and pricing rule: a regulatory treatment

Good Deals and compatible modification of risk and pricing rule: a regulatory treatment

Optimal insurance in the presence of reinsurance

Hedging and Pricing in Imperfect Markets Under Non-Convexity

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