What is risk ?
Risk covers various concepts, some subjective and other objective, and this makes its definition often confusing.
The first concept refers to hazard, being the occurence in the future of a hazardous process that has to be caracterised in the best possible way, and modeled. In this domain, Insight Research Europe bases its research and development along three axis: (i) the modeling of returns distributions depending on assets types; (ii) the dependancy between financial assets, more often unstable and non-linear; and (iii) the phase transitions phenomena, which can for example lead to statistical "anomalies" such as crashes.
The second concept refers to the consequences of the occurence of the hazard. The consequences can be of financial nature (loss or gain) and psychological (satisfaction or unsatisfaction comparing the result to the objectives and possible changes to the investment strategies). This concept of risk also encompasses the subjectivity of the decision maker, notably his or her aversion to risk, that we formalize with a utility function that drives our optimization process.
Finally what we call the aryetic value of risk only refers to the hazard occurence that leads to negative consequences for the utility function. As such, Insight Research Europe distinguishes between negative and positive risk distributions in its modeling.
By grouping these concepts, risk becomes then the unwanted contingency of the utility function.