Fundamental Aspects of Operational Risk and Insurance Analytics: A Handbook of Operational Risk

Chapter Five Basic Probability Concepts in Loss Distribution Approach

In risk management in general, modelers attempt to assess the uncertain risk exposures or threats using past experiences and other information available. Probability theory seems to be the natural fit for these types of analyses. This chapter provides a description of basic concepts of the probability theory used in this book and introduces relevant notation. There is a range of important concepts that are required to be considered when developing OpRisk models in practical settings. This chapter establishes what will be considered in future chapters as basic presumed knowledge. It covers the following basic concepts:

• Loss Distributional Approach (LDA) modelling;
• Definitions of a probability distribution function and density functions in univariate and multivariate settings, as well as discrete, continuous and mixed type random variables;
• Statements of the Law of Large Numbers and distributional convergence of scaled and translated sums are briefly discussed;
• Then moments and quantile functions for random variables are discussed;
• Following this, the notion of frequency distributional models are discussed for the number of losses in a given year;
• Then naturally, the notion of severity loss models is briefly discussed for the size of each loss event in a given year;
• Next, the compound process is discussed with additional discussion on convolutions and transform methods;
• Finally, a very brief overview ...