A stochastic model for capital requirement assessment for mortality and longevity risk, focusing on idiosyncratic and trend components

Abstract

This paper provides a stochastic model, consistent with Solvency II and the Delegated Regulation, to quantify the capital requirement for demographic risk. In particular, we present a framework that models idiosyncratic and trend risks exploiting a risk theory approach in which results are obtained analytically. We apply the model to non-participating policies and quantify the Solvency Capital Requirement for the aforementioned risks in different time horizons.

A Discrete Risk-Theory Approach to Manage Equity-Linked Policies in an Incomplete Market

“…From a practical standpoint, this approach highlights how the insurance company can fully immunize itself from financial risk, provided it obtains less coverage for demographic risk. Following the approach of Clemente et al (2022) and Wüthrich et al (2010), we define the r.v. Y t n as…”

“…This is because, if it were to apply the same effective safety loading as an insurer quantifying the derivative price fairly λ E f f = λ Max , it would propose a price that is too high. This approach, known in risk theory as "safety loading calculation through the ruin probability principle" (see Clemente et al 2022), is perfectly aligned with insurance practice, where implicit safety loading is incorporated into pricing through the use of prudential demographic bases, commonly referred to as first-order technical bases.…”

“…With reference to policyholders, let us assume that the insurer sells the policy at time t = 0 to a cohort of 10,000 policyholders with the same characteristics (for further information on the definition of a homogeneous cohort, see Savelli and Clemente (2013) or Clemente et al (2022)); in particular, they all have an age of 50 years and a probability of reaching the age of 51 equal to 99.5%. The vector of 10,000 sums insured was drawn from a LogNormal distribution with a mean of 100,000 and a Coefficient of Volatility (CoV) of 1.…”

What do we know about ESG and risk? A systematic and bibliometric review

“…Firms invest in CRS projects to control their risk using CRS as an insurance mechanism against risk. Mefteh‐Wali et al (2022) and Clemente et al (2022) propose innovative methodologies to manage idiosyncratic risk. Based on various copula functions, Mefteh‐Wali et al (2022) depicts the complex dependence structures between the firm specific risk and idiosyncratic risk levels, showing a directional causality between CSR and the idiosyncratic risk.…”

“…Based on various copula functions, Mefteh‐Wali et al (2022) depicts the complex dependence structures between the firm specific risk and idiosyncratic risk levels, showing a directional causality between CSR and the idiosyncratic risk. Clemente et al (2022) provides a stochastic model to quantify the capital requirement and risk (focusing on demographic risk) in different time horizons. The results of these research shed new light on how CSR can be integrated in any risk management strategy to speed up the transition to a more sustainable, low‐carbon economy.…”