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.
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Nichil, G., Vallois, P. Solvency Need Resulting from Reserving Risk in a ORSA Context. Methodol Comput Appl Probab 21, 567–592 (2019). https://doi.org/10.1007/s11009-017-9609-9
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DOI: https://doi.org/10.1007/s11009-017-9609-9
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