For some time now, Solvency II requires that insurance companies calculate minimum capital requirements to face the risk of insolvency, either in accordance with the Standard Formula or using a full or partial Internal Model. An Internal Model must be based on a market-consistent valuation of assets and liabilities at a 1-year time span, where a real-world probabilistic structure is used for the first year of projection. In this paper, we describe the major risks of a non-life insurance company, i.e. the non-life underwriting risk and market risk, and their interactions, focusing on the non-life premium risk, equity risk, and interest rate risk. This analysis is made using some well-known stochastic models in the financial- actuarial literature and practical insurance business, i.e. the Collective Risk Model for non-life premium risk, the Geometric Brownian Motion for equity risk, and a real-world version of the G2++ Model for interest rate risk, where parameters are calibrated on current and real market data. Finally, we illustrate a case study on a single-line and a multi-line insurance company in order to see how the risk drivers behave in both a stand-alone and an aggregate framework.

Capital requirement modeling for market and non-life premium risk in a dynamic insurance portfolio / Cotticelli, Stefano; Savelli, Nino. - In: ANNALS OF ACTUARIAL SCIENCE. - ISSN 1748-4995. - (2023), pp. 1-32. [10.1017/S1748499523000234]

Capital requirement modeling for market and non-life premium risk in a dynamic insurance portfolio

Stefano Cotticelli
;
Nino Savelli
2023

Abstract

For some time now, Solvency II requires that insurance companies calculate minimum capital requirements to face the risk of insolvency, either in accordance with the Standard Formula or using a full or partial Internal Model. An Internal Model must be based on a market-consistent valuation of assets and liabilities at a 1-year time span, where a real-world probabilistic structure is used for the first year of projection. In this paper, we describe the major risks of a non-life insurance company, i.e. the non-life underwriting risk and market risk, and their interactions, focusing on the non-life premium risk, equity risk, and interest rate risk. This analysis is made using some well-known stochastic models in the financial- actuarial literature and practical insurance business, i.e. the Collective Risk Model for non-life premium risk, the Geometric Brownian Motion for equity risk, and a real-world version of the G2++ Model for interest rate risk, where parameters are calibrated on current and real market data. Finally, we illustrate a case study on a single-line and a multi-line insurance company in order to see how the risk drivers behave in both a stand-alone and an aggregate framework.
2023
capital requirements; time horizon; risk management; real-world valuation; market risk; non-life premium risk; Geometric Brownian Motion; G2++ Model; Collective Risk Model; Solvency II; ORSA
01 Pubblicazione su rivista::01a Articolo in rivista
Capital requirement modeling for market and non-life premium risk in a dynamic insurance portfolio / Cotticelli, Stefano; Savelli, Nino. - In: ANNALS OF ACTUARIAL SCIENCE. - ISSN 1748-4995. - (2023), pp. 1-32. [10.1017/S1748499523000234]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1695813
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