This paper aims to develop optional semimartingale methods in risk theory to allow for a larger class of risk models. Optional semimartingales are left-continuous with right-limit stochastic processes defined on a probability space where the usual conditions - completeness and right-continuity...

By examining the significant flaws in multivariate risk analysis and integrated risk analysis, this article introduces a new approach to evaluating the total risk within complex risk systems: the principle of multi-dimensional risk (MDR) analysis. Under this framework, the scope of each...