Sometimes more, sometimes less: Prudence and the diversification of risky insurance coverage

Reichel, Lukas; Schmeiser, Hato; Schreiber, Florian

doi:10.1016/j.ejor.2020.10.046

Cited by 4 publications

(2 citation statements)

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“…This matters because solvency impacts insurance demand and also optimal reinsurance decisions (see, e.g. Eckert and Gatzert, 2018;Reichel, Schmeiser, and Schreiber, 2021). It is also a major consideration for Enterprise Risk Management and in the regulation of financial institutions (e.g.…”

Section: Statement Of Contributionsmentioning

confidence: 99%

Optimal reinsurance design under solvency constraints

Avanzi¹,

Lau²,

Steffensen³

2022

Preprint

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Optimal reinsurance is a perennial problem in insurance. The problem formulation considered in this paper is closely connected to the optimal portfolio problem in finance, with some important distinctions. In particular, the surplus of an insurance company is routinely approximated by a Brownian motion, as opposed to the geometric Brownian motion used to model assets in finance. Furthermore, exposure to risk is controlled "downwards" via reinsurance, rather than "upwards" via risky investments. This leads to interesting qualitative differences in the optimal solutions.In this paper, using the martingale method, we derive the optimal proportional, non cheap reinsurance control that maximises the quadratic utility of the terminal value of the insurance surplus. We also consider a number of realistic constraints on the terminal value: a strict lower boundary, the probability (Value at Risk) constraint, and the expected shortfall (conditional Value at Risk) constraints under the P and Q measures, respectively. Comparison of the optimal strategies with the optimal solutions in finance are of particular interest. Results are illustrated.

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Section: Statement Of Contributionsmentioning

confidence: 99%

Optimal reinsurance design under solvency constraints

Avanzi¹,

Lau²,

Steffensen³

2022

Preprint

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“…6 See also M. Ibragimov et al (2015) for a comprehensive review of the effects of heavy-tailedness on diversification and the related literature. 7 Recently, Reichel et al (2021) investigate optimal insurance demand when policyholders are able to diversify default risk across several insurance companies. 8 Furthermore, our methodology for sharing the default loss between policyholders is related to ideas that have been applied to the pricing of default risk in multiline insurance companies (R. Ibragimov et al, 2010;Myers & Read, 2001;Phillips et al, 1998).…”

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confidence: 99%

Risk pooling and solvency regulation: A policyholder's perspective

Huggenberger

Albrecht

2022

J of Risk & Insurance

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We investigate the benefits of risk pooling for the policyholders of stock insurance companies under different solvency standards. Using second-degree stochastic dominance, we document that the utility of risk-averse policyholders is increasing in the pool size if the equity capital is proportional to the premiums written. To the contrary, an increase in the pool size can reduce the policyholders' utility if the equity capital is determined using the Value-at-Risk (VaR). We show that pooling with a larger number of risks is also beneficial for all risk-averse policyholders under a VaR-based regulation if the pool satisfies an excess tail risk restriction. Our analysis provides new insights for the design of solvency standards and reveals a potential disadvantage of risk-based capital requirements for policyholders. K E Y W O R D Sexcess wealth order, exchangeable risks, risk pooling, solvency regulation, value-at-risk | INTRODUCTIONRisk reduction through pooling can be viewed as a defining characteristic of the insurance mechanism from the insurer's perspective. For example, Houston (1964, p. 538) argues that while individuals see insurance as a risk transfer, insurance companies consider it as a pooling process that reduces risk by increasing the number of policies. Following this view, the benefits

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