109 research outputs found
On the existence of a representative reinsurer under heterogeneous beliefs
No full textThis paper studies a one-period optimal reinsurance design model with n reinsurers and an insurer. The reinsurers are endowed with expected-value premium principles and with heterogeneous beliefs regarding the underlying distribution of the insurer’s risk. Under general preferences for the insurer, a representative reinsurer is characterized. This means that all reinsurers can be treated collectively by means of a hypothetical premium principle in order to determine the optimal total risk that is ceded to all reinsurers. The optimal total ceded risk is then allocated to the reinsurers by means of an explicit solution. This is shown both in the general case and under the no-sabotage condition that avoids possible ex post moral hazard on the side of the insurer, thereby extending the results of Boonen et al. (2016). We subsequently derive closed-form optimal reinsurance contracts in case the insurer maximizes expected net wealth. Moreover, under the no-sabotage condition, we derive optimal reinsurance contracts in case the insurer maximizes dual utility, or in case the insurer maximizes a generic objective that preserves second-order stochastic dominance under the assumption of a monotone hazard ratio
Bowley reinsurance with asymmetric information: A first-best solution
No full textBowley reinsurance solutions are reinsurance contracts for which the reinsurer optimally sets the pricing density while anticipating that the insurer will choose the optimal reinsurance indemnity given this pricing density. This Bowley solution concept of equilibrium reinsurance strategy has been revisited in the modern risk management framework by Boonen et al. [(2021). Bowley reinsurance with asymmetric information on the insurer's risk preferences. Scandinavian Actuarial Journal 2021 , 623–644], where the insurer and reinsurer are both endowed with distortion risk measures but there is asymmetric information on the distortion risk measure of the insurer. In this article, we continue to study this framework, but we allow the premium principle to be more flexible. We call this solution the first-best Bowley solution. We provide first-best Bowley solutions in closed form under very general assumptions. We implement some numerical examples to illustrate the findings and the comparisons with the second-best solution. The main result is further extended to the case when both the reinsurer and the insurers have heterogeneous beliefs on the distribution functions of the underlying risk
Equilibria and efficiency in a reinsurance market
No full textWe study equilibria in a reinsurance market with multiple reinsurers that are endowed with heterogeneous beliefs, where preferences are given by distortion risk measures, and pricing is done via Choquet integrals. We construct a model in the form of a sequential economic game, where the reinsurers have the first-mover advantage over the insurer, as in the Stackelberg setting. However, unlike the Stackelberg setting, which assumes a single monopolistic reinsurer on the supply side, our model accounts for strategic price competition between reinsurers. We argue that the notion of a Subgame Perfect Nash Equilibrium (SPNE) is the appropriate solution concept for analyzing equilibria in the reinsurance market, and we characterize SPNEs using a set of sufficient conditions. We then examine efficiency properties of the contracts induced by an SPNE, and show that these contracts result in Pareto-efficient allocations. Additionally, we show that under mild conditions, the insurer realizes a strict welfare gain, which addresses the concerns of Boonen and Ghossoub (2022) with the Stackelberg model and thereby ultimately reflects the benefit to the insurer of competition on the supply side. We illustrate this point with a numerical example.</p
IOF position statement: Vitamin D recommendations for older adults
No full textThis position paper of the International Osteoporosis Foundation makes recommendations for vitamin D nutrition in elderly men and women from an evidence-based perspective. © International Osteoporosis Foundation and National Osteoporosis Foundation 2010.Bischoff-Ferrari HA, 2009, BRIT MED J, V339, DOI 10.1136-bmj.b3692; Bischoff-Ferrari HA, 2005, JAMA-J AM MED ASSOC, V293, P2257, DOI 10.1001-jama.293.18.2257; Blum M, 2008, J AM COLL NUTR, V27, P274; Boonen S, 2007, J CLIN ENDOCR METAB, V92, P1415, DOI 10.1210-jc.2006-1404; DURAZOARVIZU RA, 2010, J NUTR, DOI DOI 10.3945-JM.109.116681; Flicker L, 2005, J AM GERIATR SOC, V53, P1881, DOI 10.1111-j.1532-5415.2005.00468.x; Fuleihan GEH, 2009, CLIN REV BONE MINER, V7, P77; Goussous R, 2005, J CLIN ENDOCR METAB, V90, P707, DOI 10.1210-jc.2004-1380; Harris SS, 2002, J AM COLL NUTR, V21, P357; Harris SS, 1998, J AM COLL NUTR, V17, P282; Heaney RP, 2003, AM J CLIN NUTR, V77, P204; Holick MF, 2008, J CLIN ENDOCR METAB, V93, P677, DOI 10.1210-jc.2007-2308; Mithal A, 2009, OSTEOPOROSIS INT, V20, P1807, DOI 10.1007-s00198-009-0954-6; OOMS ME, 1995, J CLIN ENDOCR METAB, V80, P1052, DOI 10.1210-jc.80.4.1052; Trang HM, 1998, AM J CLIN NUTR, V68, P854; Visser M, 2003, J CLIN ENDOCR METAB, V88, P5766, DOI 10.1210-jc.2003-030604; Wortsman J, 2000, AM J CLIN NUTR, V72, P690; Wortsman J, 2003, AM J CLIN NUTR, V77, P134217018816
UvA-DARE (Digital Academic Repository) Redistribution of Longevity Risk: The effect of heterogeneous mortality beliefs *
No full textRedistribution of longevity risk: The effect of heterogeneous mortality beliefs Boonen, T.J.; De Waegenaere, A.; Norde, H. General rights It is not permitted to download or to forward/distribute the text or part of it without the consent of the author(s) and/or copyright holder(s), other than for strictly personal, individual use, unless the work is under an open content license (like Creative Commons). Disclaimer/Complaints regulations If 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: https://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. Abstract Existing literature regarding the natural hedge potential that arises from combining different longevity-linked liabilities typically does not address the question how changes in the liability mix can be obtained. We consider firms who aim to exploit the benefits of natural hedge potential by redistributing their risks, and characterize the risk redistributions that will arise when the parties bargain for a redistribution of risk that weakly benefits them all. We analyze the effects of heterogeneity in the beliefs regarding the probability distribution of future mortality rates on the properties of these risk redistributions, and provide a numerical illustration for a case where an insurer with a portfolio of term assurance contracts and a pension fund with a portfolio of life annuities redistribute their risks. JEL-Classification: C71, C78, G22, J1
Optimal reinsurance with heterogeneous reference probabilities
No full textThis paper studies the problem of optimal reinsurance contract design. We let the insurer use dual utility, and the premium is an extended Wang’s premium principle. The novel contribution is that we allow for heterogeneity in the beliefs regarding the underlying probability distribution. We characterize layer-reinsurance as an optimal reinsurance contract. Moreover, we characterize layer-reinsurance as optimal contracts when the insurer faces costs of holding regulatory capital. We illustrate this in cases where both firms use the Value-at-Risk or the conditional Value-at-Ris
Effects of physical exercise and body weight on disease-specific outcomes of people with rheumatic and musculoskeletal diseases (rmds): systematic reviews and meta-analyses informing the 2021 eular recommendations for lifestyle improvements in people with
No full textThis work was funded by the European League Against Rheumatism.
SMMV and JMG are supported by Versus Arthritis (grant number 21755) and the
NIHR Manchester Biomedical Research Centre. The views expressed are those of
the author(s) and not necessarily those of the NHS, the NIHR or the Department of
Health.Gwinnutt J.M., Wieczorek M., Cavalli G., Balanescu A., Bischoff-Ferrari H.A., Boonen A., De Souza S., De Thurah A., Dorner T.E., Moe R.H., Putrik P., Rodríguez-Carrio J., Silva-Fernández L., Stamm T., Walker-Bone K., Welling J., Zlatković-Švenda M.I., Guillemin F., Verstappen S.M.M
Solvency II Solvency Capital Requirement for life insurance companies based on Expected Shortfall
No full textThis paper examines the consequences for a life annuity insurance company if the solvency II solvency capital requirements (SCR) are calibrated based on expected shortfall (ES) instead of value-at-risk (VaR). We focus on the risk modules of the SCRs for the three risk classes equity risk, interest rate risk and longevity risk. The stress scenarios are determined using the calibration method proposed by EIOPA in 2014. We apply the stress-scenarios for these three risk classes to a fictitious life annuity insurance company. We find that for EIOPA’s current quantile 99.5% of the VaR, the stress scenarios of the various risk classes based on ES are close to the stress scenarios based on VaR. Might EIOPA choose to calibrate the stress scenarios on a smaller quantile, the longevity SCR is relatively larger and the equity SCR is relatively smaller if ES is used instead of VaR. We derive the same conclusion if stress scenarios are determined with empirical stress scenarios
A discussion of ’Optimal reinsurance designs based on risk measures: A review’
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Risk sharing with expected and dual utilities
No full textThis paper analyzes optimal risk sharing among agents that are endowed with either expected utility preferences or with dual utility preferences. We find that Pareto optimal risk redistributions and the competitive equilibria can be obtained via bargaining with a hypothetical representative agent of expected utility maximizers and a hypothetical representative agent of dual utility maximizers. The representative agent of expected utility maximizers resembles an average risk-averse agent, whereas representative agent of dual utility maximizers resembles an agent that has lowest aversion to mean-preserving spreads. This bargaining leads to an allocation of the aggregate risk to both groups of agents. The optimal contract for the expected utility maximizers is proportional to their allocated risk, and the optimal contract for the dual utility maximizing agents is given by “tranching” of their allocated risk. We show a method to derive equilibrium prices. We identify a condition under which prices are locally independent of the expected utility functions, and given in closed form. Moreover, we characterize uniqueness of the competitive equilibrium
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