Solvency Need Resulting from Reserving Risk in a ORSA Context

Geoffrey Nichil () and Pierre Vallois ()
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Geoffrey Nichil: Université de Lorraine
Pierre Vallois: Université de Lorraine

Methodology and Computing in Applied Probability, 2019, vol. 21, issue 2, 567-592

Abstract: Abstract The main goal of the paper is the evaluation of the Solvency Need SN(h), where h is the maximal duration of the insurance contracts that we will consider. We define it as the quantile of R(h, S) − 𝔼[R(h, S)], where R(h, S) is the reserve introduced in Nichil and Vallois (Insurance: Mathematics and Economics 66:29–43, 2016) and S := (Sx, x ⩾ 0) is a systemic risk. We prove that the normalized reserve converges in distribution, as h → + ∞, to the sum of a Gaussian RV and an independent RV which is an integral of a function of the systemic risk. In the case of mortgage guarantee we can go further in the description of the non-Gaussian RV and we propose three numerical schemes to estimate SN(h) when h is large and we compare the results of simulation.

Keywords: Solvency II; ORSA; Solvency need; Reserving risk; Quantile; Geometric Brownian motion; Poisson point process; Perpetual integral functional of Brownian motion; Gamma distribution; Monte-Carlo simulation; 60; 62; 65 (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s11009-017-9609-9

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