Risk- and value-based management for non-life insurers under solvency constraints.

*(English)*Zbl 1403.91194Summary: The aim of this paper is to study optimal risk- and value-based management decisions regarding a non-life insurer’s investment strategy by maximizing shareholder value based on preference functions, while simultaneously controlling for the ruin probability. We thereby extend previous work by deriving analytical solutions and by explicitly accounting for the policyholders’ willingness to pay depending on their risk sensitivity based on the insurer’s reported solvency status, which will be of great relevance under Solvency II. We further investigate the impact of the risk-free interest rate, (non-linear) dependencies between assets and liabilities, distributional assumptions as well as reinsurance. One main finding is that the consideration of default-risk-driven premiums is vital for optimal management decisions, since, e.g., the target ruin probability implying a higher shareholder value differs for various risk sensitivities of the policyholders. Furthermore, in the present setting, proportional reinsurance increases shareholder value only for non-risk sensitive policyholders.

##### MSC:

91B30 | Risk theory, insurance (MSC2010) |

##### Keywords:

non-life insurance; Solvency II; shareholder value optimization; default-risk-driven premium; copulas
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\textit{J. Eckert} and \textit{N. Gatzert}, Eur. J. Oper. Res. 266, No. 2, 761--774 (2018; Zbl 1403.91194)

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