Professor of Financial & Actuarial Mathematics
Home
Research
About
How to Reach Me
More
December 23, 2011

Alexey Kuznetsov & Manuel Morales
Ever since the first introduction of the expected discounted penalty function (EDPF), it has been widely acknowledged that it contains information that is relevant from a risk management perspective. Expressions for the EDPF are now available for a wide range of models, in particular for a general class of Lévy risk processes. Yet, in order to capitalize on this potential for applications, these expressions must be computationally tractable enough as to allow for the evaluation of associated risk measures such as Value at Risk (VaR) or Conditional Value at Risk (CVaR). Most of the models studied so far offer few interesting examples for which computation of the associated EDPF can be carried out to the last instances where evaluation of risk measures is possible. Another drawback of existing examples is that the expressions are available for an infinitetime horizon EDPF only. Yet, realistic applications would require the computation of an EDPF over a finitetime horizon. In this paper we address these two issues by studying examples of risk processes for which numerical evaluation of the EDPF can be readily implemented. These examples are based on the recently introduced meromorphic processes, including the beta and theta families of Lévy processes, whose construction is tailormade for computational ease. We provide expressions for the EDPF associated with these processes and we discuss in detail how a finitetime horizon EDPF can be computed for these families. We also provide numerical examples for different choices of parameters in order to illustrate how ruinbased risk measures can be computed for these families of Lévy risk processes.
Research (20)
Applied Research (4)
Research Program (5)
Partnership (4)
Article (11)
Published Article (9)
Working Paper (2)
Conference (15)
Education (8)
Course (4)