Statistical analyses on actual data depict operational risk as an extremely heavy-tailed phenomenon, able to generate losses so extreme as to suggest the use of infinite-mean models. But no loss can actually destroy more than the entire value of a bank or of a company, and this upper bound...

According to the theory proposed by Acerbi & Scandolo (2008), the value of a portfolio is defined in terms of public market data and idiosyncratic portfolio constraints imposed by an investor holding the portfolio. Depending on the constraints, one and the same portfolio could have different...

We present four numerical methods to compute the Value-at-Risk and Expected Shortfall risk measure values of portfolios with financial options. The numerical methods are based on either wavelets or Fourier cosine approximations and belong to the class of Fourier inversion methods. We show that...