In this in-depth exploration, I delve into the complex implications and costs of cybersecurity breaches. Venturing beyond just the immediate repercussions, the research unearths both the overt and concealed long-term ...In this in-depth exploration, I delve into the complex implications and costs of cybersecurity breaches. Venturing beyond just the immediate repercussions, the research unearths both the overt and concealed long-term consequences that businesses encounter. This study integrates findings from various research, including quantitative reports, drawing upon real-world incidents faced by both small and large enterprises. This investigation emphasizes the profound intangible costs, such as trade name devaluation and potential damage to brand reputation, which can persist long after the breach. By collating insights from industry experts and a myriad of research, the study provides a comprehensive perspective on the profound, multi-dimensional impacts of cybersecurity incidents. The overarching aim is to underscore the often-underestimated scope and depth of these breaches, emphasizing the entire timeline post-incident and the urgent need for fortified preventative and reactive measures in the digital domain.展开更多
We consider a structural stochastic volatility model for the loss from a large portfolio of credit risky assets.Both the asset value and the volatility processes are correlated through systemic Brownian motions,with d...We consider a structural stochastic volatility model for the loss from a large portfolio of credit risky assets.Both the asset value and the volatility processes are correlated through systemic Brownian motions,with default determined by the asset value reaching a lower boundary.We prove that if our volatility models are picked from a class of mean-reverting diffusions,the system converges as the portfolio becomes large and,when the vol-of-vol function satisfies certain regularity and boundedness conditions,the limit of the empirical measure process has a density given in terms of a solution to a stochastic initial-boundary value problem on a half-space.The problem is defined in a special weighted Sobolev space.Regularity results are established for solutions to this problem,and then we show that there exists a unique solution.In contrast to the CIR volatility setting covered by the existing literature,our results hold even when the systemic Brownian motions are taken to be correlated.展开更多
文摘In this in-depth exploration, I delve into the complex implications and costs of cybersecurity breaches. Venturing beyond just the immediate repercussions, the research unearths both the overt and concealed long-term consequences that businesses encounter. This study integrates findings from various research, including quantitative reports, drawing upon real-world incidents faced by both small and large enterprises. This investigation emphasizes the profound intangible costs, such as trade name devaluation and potential damage to brand reputation, which can persist long after the breach. By collating insights from industry experts and a myriad of research, the study provides a comprehensive perspective on the profound, multi-dimensional impacts of cybersecurity incidents. The overarching aim is to underscore the often-underestimated scope and depth of these breaches, emphasizing the entire timeline post-incident and the urgent need for fortified preventative and reactive measures in the digital domain.
基金supported financially by the United Kingdom Engineering and Physical Sciences Research Council (Grant No.EP/L015811/1)by the Foundation for Education and European Culture (founded by Nicos&Lydia Tricha).
文摘We consider a structural stochastic volatility model for the loss from a large portfolio of credit risky assets.Both the asset value and the volatility processes are correlated through systemic Brownian motions,with default determined by the asset value reaching a lower boundary.We prove that if our volatility models are picked from a class of mean-reverting diffusions,the system converges as the portfolio becomes large and,when the vol-of-vol function satisfies certain regularity and boundedness conditions,the limit of the empirical measure process has a density given in terms of a solution to a stochastic initial-boundary value problem on a half-space.The problem is defined in a special weighted Sobolev space.Regularity results are established for solutions to this problem,and then we show that there exists a unique solution.In contrast to the CIR volatility setting covered by the existing literature,our results hold even when the systemic Brownian motions are taken to be correlated.