Model-based measurement of latent risk in time series with applications

Risk is at the center of many policy decisions in companies, governments and other institutions. The risk of road fatalities concerns local governments in planning counter-measures, the risk and severity of counterparty default concerns bank risk managers on a daily basis and the risk of infection has actuarial and epidemiological consequences. However, the risk can not be observed directly and it usually varies over time. Measuring risk is therefore an important exercise. In this paper a general multivariate framework for the time series analysis of risk is introduced that is modelled as a latent process. The latent risk time series model extends existing approaches by the simultaneous modelling of (1) the exposure to an event, (2) the risk of that event occurring and (3) the severiy of the event. First, existing time series approaches are discussed for the analysis of risk which have been applied to road safety, actuarial and epidemiological problems. Second, a general model for the analysis of risk is presented and its statistical treatment based on linear state space methods is discussed. Third, the methodology is applied to time series of insurance claims, credit card purchases and road safety. It is shown that the general methodology can be effectively used in the assessment of risk.