Constantinos T. Artikis

Properties and applications in risk management operations of a stochastic discounting model

Abstract Stochastic discounting models have been widely adopted in many practical disciplines. In particular, the contribution of these models to the development of risk management as an organizational discipline has been proved very important. This paper is mainly devoted to the formulation, practical applications and investigation of a stochastic discounting model. More precisely, a stochastic discounting model for the present value of a continuous uniform cash flow, incorporating some fundamental concepts of probability theory, is formulated. Applications of the model in several areas of risk management are also provided. Moreover, sufficient conditions for embedding the distribution corresponding to the model into an important class of transformed distributions are established.

Incorporating an Integral equation for characteristic functions in investigating a class of distributions

Abstract Integral equations of characteristic functions are very strong analytical tools for investigating the distributions of stochastic models. The paper makes use of an integral equation, incorporating the characteristic function of a renewal distribution and the characteristic function of a uniform random contraction, for establishing a characterization of a class of selfdecomposable distributions. Moreover, the paper establishes interpretations in stochastic modeling of risk severity reduction operations of the uniform random contraction and the characterization of that class of selfdecomposable distributions.

Discounted maximum of a random number of random cash flows in optimal decision making

The paper makes use of an important concept of extreme value theory in order to formulate a stochastic discounting model for the present value of a random cash flow under random timing and constant force of interest. Sufficient conditions for evaluating the distribution function of the formulated model are established. Moreover, applications in optimal decision making of the proposed stochastic discounting model are provided.

Formulating Discrete Geometric Random Sums for Facilitating Intelligent Behaviour of a Complex System under a Major Risk

The contribution of random sums as strong analytical tools of many areas of probability theory is generally recognized as very important. Infinitely divisible distributions, counting stochastic processes, stochastic integrals, service systems, stochastic processes with stationary and independent increments and branching processes are significant areas of probability theory making extensive use of random sums. Moreover, economics, management, insurance, reliability, quality control and engineering are examples of practical disciplines utilizing random sums as powerful stochastic models. The present paper formulates a geometric random sum of discrete, independent and identically distributed random variables. A stochastic derivation of such a random sum is also provided. Moreover, the paper establishes an interpretation of the formulated discrete geometric random sum as a research tool of computational intelligence for describing and analyzing the evolution of a complex system under the occurrences of a major risk. The paper makes quite clear that research activities on the formulations, stochastic derivations and practical applications of discrete random sums can substantially facilitate the use of computational intelligence principles and methodologies in investigating the structure and evolution of complex systems operating under the negative consequences of a severe risk.

Discounted minimum of a random number of random variables in replacement of computer systems

The paper concentrates on the formulation, investigation and applications of a stochastic discounting model. More precisely, the paper makes use of the minimum of a random number of nonnegative random variables and a nonnegative random variable for formulating a stochastic discounting model and also establishes applications in replacement of computer systems of such a stochastic model.

Discrete random sums in processes of systemics arising in cybernetics and informatics

Abstract Discrete random sums are generally recognized as powerful analytical tools with particularly important applications in many practical fields. The present paper formulates a very wide class of discrete random sums. Applications of the formulated class in systemics, cybernetics and informatics are also established. Moreover, the paper makes quite clear the role of such applications in the description, investigation and control of the performance and evolution of a modern very complex educational organization.

Stochastic modelling of risk control operations for recovery of systems

The paper uses a discrete random variable and two sequences of nonnegative random variables formulating a stochastic model which is the maximum of a random number of stochastic multiplicative models. Sufficient conditions for the distribution function of the model are established. The paper also provides applications of this model assessing certain risk control operations applied to a random number of systems which have been affected by a major risk. Moreover, the paper makes clear that a concept of extreme value theory can contribute to the improvement of the applicability of risk management in a class of systems.

Incorporating concepts of extreme value theory in formulating a discounting model for making optimal decisions in competing risks management

Abstract Stochastic discounting models incorporating concepts of extreme value theory constitute very strong analytical tools for making optimal risk management decisions. The paper makes use of two fundamental concepts of extreme value theory for formulating a stochastic discounting model. The paper also establishes properties and applications in optimal competing risks management decisions of the formulated stochastic discounting model.

Stochastic derivation and application in information risk frequency reduction of a class of discrete random variables

Abstract The class of discrete random variables taking values in the set of nonnegative integers and having probability functions with a unique mode at the point zero is generally recognized as a very strong analytical tool for stochastic modelling in many practical disciplines. The present paper establishes a stochastic derivation of this class by making use of an integral part model. Applications of the stochastic derivation in the area of risk frequency reduction operations are also provided.

Combinations of risk control and risk financing operations

Risk treatment operations combining risk control and risk financing operations constitute very strong tools of modern risk management. The cost of such a risk treatment operation is a fundamental factor for developing and implementing proactive and reactive risk management processes. The present paper mainly concentrates on the formulation and applicability of a stochastic model in the description, analysis and manipulation of the cost of a risk treatment operation incorporating a risk frequency reduction operation and a risk retention operation.