Expectiles (EVaR) are a one-parameter family of coherent risk measures that have been recently suggested as an alternative to quantiles (VaR) and to Expected Shortfall (ES). In this work we review their known properties, we discuss their financial meaning, we compare them with VaR and ES and we...

Investments in security and cyber-insurance are two cyber-risk management strategies that can be employed together to optimize the overall security expense. In this paper, we provide a closed form for the optimal investment under a full set of insurance liability scenarios (full liability,...