Value at Risk and Inventory Control

The purposes of this paper are two-fold. On the one hand, we shall provide a decision analysis justification for the Value at Risk (VaR) approach based on ex-post, disappointment decision making arguments. We shall show that the approach is justified by a disappointment criterion. In other words, the asymmetric valuation between ex-ante expected returns above an appropriate target return and the expected returns below that same target level, provide an explanation for the VaR criterion when it is used as a tool for VaR efficiency design. Second, this paper provides applications to inventory management based on VaR risk exposure. Although the mathematical problems arising from an application of the VaR approach, tuned to current practice in financial risk management, are difficult to solve analytically, solutions can be found by application of standard computational and simulation techniques. A number of cases are solved and formulated to demonstrate the paper’s applicability.Inventory; VaR; Disappointment

Environmental Games and Queue Models

This paper considers a pollution and control game which uses a queuing framework. This framework allows an accounting of pollution events, environmental pollution quality and the application of controls to maintain a desirable quality of the environment. A number of examples are used to highlight the approach and demonstrates both its theoretical and practical usefulness.Environment; Control; Quality; Queuing

Risk Management: An Interdisciplinary Framework

Risk is shown to be based on both theory and practice. It is shown to be conceptual and technical, blending behavioral psychology, financial economics and decision making under uncertainty into a coherent whole that justify the selection of risky choices. Its applications are also broadly distributed across many areas and fields of interest. The examples treated here have focused on both finance, insurance and on a few problems in industrial management howeverRisk; Management; Interdisciplinarity

Diffusion of New Products in Heterogeneous Populations: Incorporating Stochastic Coefficients

Diffusion models have had a major impact on the literature and practice of marketing science. Following the pioneering work of Bass (1969), which suggested a deterministic model for homogeneous populations, the basic diffusion model has been extended to incorporate: changes in the market potential over time (Mahajan & Peterson 1978); complimentarity, substitutability, contigent & independent relations of the new product with other brands in the market place (Peterson & Mahajan 1978); spatial diffusion pattern (Mahajan & Peterson 1979); varying word-of-mouth effects (Easingwood, Mahajan & Muller 1983); various marketing mix effects including the effect of price on both innovation and imitation coefficients (Robinson and Lakhani 1975) or advertising effect on the innovation coefficient (Horsky and Simon 1983). competitive effects (Eliashberg & Jeuland 1982, Fershtman, Mahajan and Muller 1983

Volatility Estimators and the Inverse Range Process in a Random Volatility Random Walk and Wiener Processes

International audienceThe purpose of this paper is to study the mean, the variance, the probability distribution and the hazard rate of the inverse range process of an a-priori unknown volatility random walk. Motivation for this process arises when it is necessary to obtain statistics that pertain to a process volatility in addition to the usual variance statistics. As a result, range process statistics are indicated as an additional source of information in the study of processes' volatility. Examples and applications are considered

A Claims Persistence Process and Insurance

International audienceThe purpose of this paper is to introduce and construct a state dependent counting and persistent random walk. Persistence is imbedded in a Markov chain for predicting insured claims based on their current and past period claim. We calculate for such a process, the probability generating function of the number of claims over time and as a result are able to calculate their moments. Further, given the claims severity probability distribution, we provide both the claims process generating function as well as the mean and the claim variance that an insurance firm confronts over a given period of time and in such circumstances. A number of results and applictions are then outlined (such as a Compound Claim Persistence Process)

Quality, Risk and the Taleb Quadrants

Abstract The definition and the management of quality has evolved and assumed a variety of approaches, responding to an increased variety of needs. In industry, quality and its control has responded to the need of maintaining an industrial process operating as "expected", reducing the process sensitivity to uncontrolled disturbances (robustness) etc. By the same token, in services, quality has been defined as "satisfied customers obtaining the services they expect". Quality management, like risk management, has a general negative connotation, arising from the consequential effects of "non-quality". Quality, just as risk, is measured as a consequence resulting from factors and events defined in terms of the statistical characteristics that underlie these events. Quality and risk may thus converge, both conceptually and technically, expanding the concerns that both domains are confronted with and challenged by. In this paper, we analyze such a prospective convergence between quality and risk, and their management. In particular we emphasize aspects of integrated quality, risk, performance and cost in industry and services. Throughout such applications, we demonstrate alternative approaches to quality management, and their merging with risk management, in order to improve both the quality and risk management processes. In the analysis we apply the four quadrants proposed by Nassim Taleb for mapping consequential risks and their probability structure. Three case studies are provided, one on risk finance, a second one on risk management of telecommunication systems and a third one on quality and reliability of web based services