Bayesian modeling of risks of various origin

Abstract

Background. Financial as well as many other types of risks are inherent to all types of human activities. The problem is
to construct adequate mathematical description for the formal representation of risks selected and to use it for possible
loss estimation and forecasting. The loss estimation can be based upon processing available data and relevant expert
estimates characterizing history and current state of the processes considered. An appropriate instrumentation for mod-
elling and estimating risks of possible losses provides probabilistic approach including Bayesian techniques known today
as Bayesian programming methodology.
Objective. The purpose of the paper is to perform overview of some Bayesian data processing methods providing a
possibility for constructing models of financial risks selected. To use statistical data to develop a new model of Bayesian
type so that to describe formally operational risk that can occur in the information processing procedures.
Methods. The methods used for data processing and model constructing refer to Bayesian programming methodology.
Also Bayes theorem was directly applied to operational risk assessment in its formulation for discrete events and discrete
parameters.
Results. The proposed approach to modelling was applied to building a model of operational risk associated with in-
correct information processing. To construct and apply the model to risk estimation the risk problem was analysed,
appropriate variables were selected, and prior conditional probabilities were estimated. Functioning of the models con-
structed was demonstrated with illustrative examples.
Conclusions. Modelling and estimating financial and other type of risks is important practical problem that can be
solved using the methodology of Bayesian programming providing the possibility for identification and taking into
consideration uncertainties of data and expert estimates. The risk model constructed with the methodology proposed
illustrates the possibilities of applying the Bayesian methods to solving the risk estimation problems