Abstract
In this short paper, we study a VaR-type risk measure introduced by Guérin and Renaud and which is based on cumulative Parisian ruin. We derive some properties of this risk measure and we compare it to the risk measures of Trufin et al. and Loisel and Trufin.
Highlights
Over the last few years, several dynamic risk measures, i.e., risk measures based on ruin-theoretic quantities, have been studied
In the classical compound Poisson risk model, Trufin et al (2011) considered a VaR-type risk measure defined as the smallest initial capital needed to ensure a certain probability of solvency throughout the lifetime of the surplus process
This risk measure has been extended by Mitric and Trufin (2016) who defined a risk measure taking into account both the probability of ruin and the expected deficit at ruin
Summary
Over the last few years, several dynamic risk measures, i.e., risk measures based on ruin-theoretic quantities, have been studied. In the classical compound Poisson risk model, Trufin et al (2011) considered a VaR-type risk measure defined as the smallest initial capital needed to ensure a certain probability of solvency throughout the lifetime of the surplus process. Implementation delays in the recognition of ruin and occupation times of the surplus process have been used as alternative risk management tools to assess the quality of an insurance portfolio In this direction, Guérin and Renaud (2017) introduced the concept of cumulative. Inspired by the risk measure of Trufin et al (2011), they defined a VaR-type risk measure based on cumulative Parisian ruin. We study this VaR-type risk measure based on cumulative Parisian ruin.
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