bluuebunny/crossref_metadata_2025_split huggingface dataset:
The Black–Scholes Formula and Its Applications in Finance
Authors: Kijima Masaaki , Muromachi Yukio 
Published: September 2014

AbstractThis chapter overviews a continuous‐time model for securities market and its applications in finance. Self‐financing and replicating portfolios play key roles for the pricing of derivative securities. The Black–Scholes model is explained in detail, and valuation of exotic options, interest‐rate derivatives, corporate bonds and real options is also discussed as applications of the Black–Scholes model.
Spearman Correlation Coefficients, Differences between
Authors: Myers Leann , Sirois Maria J. 
Published: September 2014

Abstract

Testing the equality of two population correlation coefficients when the data are bivariate normal and Pearson correlation coefficients are used as estimates of the population parameters is a straightforward procedure covered in many introductory statistics courses. The coefficients are converted using Fisher's
z
‐transformation with standard errors (
N
− 3)
−1/2
. The two transformed values are then compared using a standard normal procedure. When data are not bivariate normal, Spearman's correlation coefficient rho is often used as the index of correlation. Comparison of two Spearman rhos is not as well documented. Three approaches were investigated using Monte Carlo simulations. Treating the Spearman coefficients as though they were Pearson coefficients and using the standard Fisher's
z
‐transformation and subsequent comparison was more robust with respect to Type I error than either ignoring the nonnormality and computing Pearson coefficients or converting the Spearman coefficients to Pearson equivalents prior to transformation.
Chernoff‐Savage Theorem
Authors: Sen Pranab K. 
Published: September 2014

AbstractThe Chernoff‐Savage Theorem, in the setting of two independent samples, exploits the basic asymptotic properties of the two sample (empirical) distributions in a novel approach to the study of asymptotic normality of a general class of two‐sample linear rank statistics. Prior to the evolution of weak convergence of probability measures and contiguity of probability measures, both taking place in the 1960’s, this Theorem provided a completely new avenue of research in asymptotics in rank tests in a far more general set‐up comprising general linear models, time‐series, and multivariate as well as sequential models
Coincidences and Patterns in Sequences
Authors: Dasgupta Anirban 
Published: September 2014

AbstractThis entry provides a contemporary exposition at a moderately quantitative level of the distribution theory associated with sequences and patterns in iid multinomial trials, the birthday problem, and the matching problem. The section on patterns includes the classic distribution theory for waiting time for runs and more general patterns, and their means and moments. It also includes the central limit theorem and a.s. properties of the longest run, and modern applications to DNA sequence alignment. The section on birthdays reviews the Poisson approximation in the classical birthday problem, with new bounds on the total variation distance. It also includes a number of variants of the classic birthday problem, including the case of unequal probabilities, similar triplets, and the Bayesian version with Dirichlet priors on birthday probabilities. A new problem called the strong birthday problem with application to criminology is introduced. The section on matching covers the Poisson asymptotics, errors of Poisson approximations, and some variants such as near matches. It also briefly reviews the recent extraordinary developments in the area of longest increasing subsequences in random permutations. The entry provides a large number of examples, many not well known, to help a reader have a feeling for these questions at an intuitive level
Crop Area Estimation, Landsat Data Analysis in
Authors: Day Charles , Hanuschak George 
Published: September 2014

AbstractSince the early 1970s, the National Agricultural Statistics Service (NASS) has developed and applied statistical procedures that use Landsat satellite data to significantly improve the precision of estimates from ground‐gathered data from a stratified area frame sample. These procedures fall into two major categories:(1)Gaussian multivariate clustering and classification, and(2)direct expansion and regression estimation. This article describes these procedures in detail.
Forestry, Statistics and Biometry in
Authors: Gregoire Timothy , Lappi Juha 
Published: September 2014

AbstractStatistical methods are used in surveys of forest resources, and in the development of predictive models of individual‐tree size and growth, as well as the growth and yield of aggregations of trees in forest stands. Statistically designed experiments are conducted in order to understand better the responses to(i)management interventions, such as fertilization, genetic improvement, site preparation, harvesting; and to(ii)natural events like insect infestations, ice storms, hurricanes, temperature change.
Income Inequality Measures
Authors: Dagum Camilo 
Published: September 2014

AbstractThis study purports to present, analyze, and evaluate the following:The income inequality measures (IIMs) proposed since Pareto and Gini and to derive their corresponding utility and disutility functions from the specification of a fundamental equation of income. Furthermore, a dual relationship between utility and disutility functions and between IIMs and social welfare functions are established.The decomposition approach of the generalized entropy measure (GEM) and the Gini ratio showing the extreme limitations of GEM to meaningful account for the contribution of the between‐group inequalities.The directional distance ratio (DDR) between binary combinations of income distributions showing that it is a better alternative to the decomposition approach, and unlike the latter, DDR offers sound policy implications.The distance function between income distributions.
Large Insurance Losses Distributions
Authors: Fasen Vicky , Klüppelberg Claudia 
Published: September 2014

AbstractLarge insurance losses happen infrequently, but they happen. In this paper we present the standard distribution models used in fire, wind–storm, or flood insurance. We also present the Cramér–Lundberg model for the total claim amount and some more recent extensions. The classical insurance risk measure is the ruin probability, and we give a full account of the ruin event in such models. Finally, we present some results for an integrated insurance risk model, where investment risk is also taken into account.
Multistate Models for Life Insurance Mathematics
Authors: Norberg Ragnar 
Published: September 2014

Abstract
The subject matter and methodology of modern life insurance mathematics are surveyed in the framework of a multistate model for life‐history analysis. Standard insurance products with payments depending only on life‐ history events are described and analyzed in the commonly used Markov chain model under the assumption of deterministic interest rates. The actuarial equivalence principle for determining premiums and reserves is motivated by risk diversification in large portfolios. Differential equations for reserves and other conditional expected values are obtained and proclaimed basic, constructive, and computational tools. The traditional method for managing nondiversifiable risk arising from changes in e.g., mortality rates and interest rates is outlined; premiums are calculated under prudent assumptions, and systematic surpluses thus created are repaid as bonus. An alternative way of managing nondiversifiable risk is to link the contractual payments to the development of mortality, interest, and possibly other demographic or economic indexes. Examples of so‐called index‐linked products are given, and premiums and reserves are determined by combined use of classical actuarial principles and principles of pricing and hedging from financial mathematics. Transfer of nondiversifiable risk to the financial markets through creation of tradeable insurance derivatives is outlined as an idea. The present article is a revised and shortened version of an entry in the Encyclopedia of Actuarial Science published by Wiley in 2004.
Optimal Risk‐Sharing and Deductibles in Insurance
Authors: Aase Knut K. 
Published: September 2014

AbstractRisk sharing in insurance is analyzed, with a view toward explaining the prevalence of deductibles.First we introduce, in a modern setting, the main concepts of the theory of risk sharing in a group of agents. We apply this theory to the risk‐sharing problem between an insurer and an insurance customer. We develop the concept further through simple examples, illustrating some of the subtle points of this theory.To deduce deductibles endogenously, not explained in the neoclassical model, we separately introduce (a) the insurable asset as a decision variable, (b) administrative costs, and (c) moral hazard, and illustrate these with the help of examples.
Ruin Probabilities: Computational Aspects
Authors: Lefèvre Claude 
Published: September 2014

Abstract
This paper is concerned with the numerical evaluation of the probability of ruin or nonruin in insurance mathematics. Our attention is primarily focused on the classical model in collective risk theory, named the compound Poisson model. We present a review of the different methods that are usually proposed to calculate or approximate the (non)ruin probabilities, over an infinite horizon and in finite time.
Stochastic Control for Insurance Companies
Authors: Schmidli Hanspeter 
Published: September 2014

Abstract
We consider some (simple) optimization problems in insurance. In particular, we want to minimize the ruin probability by dynamic decisions, maximize the value of future dividends, and keep the contribution rate and the size of a pension fund close to some predefined values. The method is stochastic control theory. We illustrate how a Hamilton–Jacobi–Bellman equation can be obtained. We also show how to solve the equation and how the optimal strategies can be obtained.
Estimation of Mortality Rates From Insurance Data
Authors: Melnick Edward L. , Tenenbein Aaron 
Published: September 2014

Abstract
The problem of using insurance intercompany data to determine mortality rates has had a long history of development. The development of these mortality rates involves two steps, namely, the estimation of the rates from the data and the interpolation and smoothing of these rates to conform to known trends in the mortality rates by age, and time since first insured. This paper will discuss the different methods used to determine these rates and discuss the advantages and disadvantages of each approach.
Behavioral Decision Studies
Authors: Brandstätter Eduard , Riedl René 
Published: September 2014

Abstract
Probability judgments are pivotal in guiding human decision making. The prevailing assumption in psychology is that human probability judgments are often biased. We challenge this view and present evidence of humans' remarkable capacities in judging probabilities. In particular, we discuss regression to the mean, probability judgments of conjunctive and disjunctive events, the consideration of base‐rate information, probability judgments based on small samples, judgments of personal risks, and external influences on probability judgments. We conclude that in real‐life contexts, in which the correct normative solutions are usually unknown, heuristics are useful tools for making fast and frugal judgments and decisions.
Decision Conferencing/Facilitated Workshops
Authors: Phillips Lawrence D. 
Published: September 2014

Abstract
Decision conferencing provides a structured group approach for assessing the risks associated with several options, with expert judgment providing some or all of the inputs and models based on decision theory used to combine the inputs into an overall assessment. A facilitated workshop brings together experts about a specific risk criterion, with an impartial facilitator taking the group through the process of discussing the meaning of each criterion, establishing measurement scales, and appraising options on the scales. At a subsequent decision conference attended by the key players, the facilitator guides participants through the process of making the final judgments about inputs and trade‐offs between criteria that allow the decision theory model to bring together all the inputs to provide an overall ordering of the options. This approach allows the collective experience of specialists and key players to be brought to bear on issues of risk assessment, and creates committed alignment backed by the authority of the entire group.
Expert Judgment
Authors: Hora Stephen C. 
Published: September 2014

AbstractExperts are often used to provide uncertainty distributions in risk analyses. They play an important role when insufficient data exist for quantification, or when the available data or models are conflicting. Multiple steps are required in constructing a successful expert judgment process. These steps include selecting and framing the issues, identifying the experts, deciding upon an organization structure, and possibly combining the distributions from multiple experts.Expert judgments are normally given as probabilities or probability distributions that express the uncertainty about future events or unmeasured quantities. The goodness of probabilistic judgments is measured through calibration and information, which, in turn, can be measured through a scoring rule.Various behavioral and mathematical methods have been proposed for combining the judgments of experts. There is, however, no single method that has emerged as the best.
Interpretations of Probability
Authors: Lenk Peter 
Published: September 2014

Abstract
Probability plays a central role in quantifying risk and uncertainty. In contrast to the laws of probability, which are well established, there are several different interpretations of probability. This article traces the major positions of the frequency, subjective, and logical schools, and summarizes the implications of these approaches for risk professionals. The article concludes that despite profoundly different interpretations and consequences, current industry demands require professionals to be facile in using different approaches to probability.
Multiattribute Value Functions
Authors: Stewart Theodor J. 
Published: September 2014

Abstract
The multiattribute value function is a means of systematically analyzing preferences in the context of multiattribute or multicriteria decision making. We discuss in some detail the axiomatic foundations of the additive form of the multiattribute value function as an ordinal measure of preference, and the implications of these axioms for eliciting the parameters of the function. Extensions of the basic model to cardinal preference measures (generally implying nonadditive forms of the value function), and to application in mathematical programming problems (multiobjective optimization) are then discussed. We conclude with a brief discussion on the treatment of risk and of time values within the context of multiattribute value functions.
Subjective Probabilities: Overview
Authors: Curley Shawn P. 
Published: September 2014

AbstractThe need for subjective probabilities arises from the variability that is pervasive in our world. A subjective probability is intended to meaningfully communicate the degree of uncertainty in the face of variability. Surrounding this common theme are several different approaches to defining and using subjective probabilities. The mathematical theory of probability is summarized as a basis for understanding these approaches. This article then describes the alternative perspectives on subjective probability relative to the mathematical theory: subjective probability as one of several interpretations for mathematical probability theory, as a behavioral assessment, as an inherent aspect of all uses of probability theory, and as an uncertainty measure that can be detached from the mathematical theory. The issue of assessing the quality of subjective probabilities is also discussed as it relates to these approaches.
Supra Decision Maker
Authors: Morton Alec 
Published: September 2014

Abstract
Decisions about the regulation of risks typically impact on a number of different sectors of society, and so have to take cognizance of the views of a variety of stakeholders. One way to conceptualize such decisions is to think of the regulatory or governmental decision maker as a “supra decision maker” (supra DM). The notion of a supra DM represents a distinctively decision‐theoretic take on the aggregation of individual preferences, whereby stakeholders' value functions are arguments in the supra DM's utility function. A normative theory of the supra DM exists, which provides conditions for an additive representation of the supra DM's value function, but this theory avoids key questions about securing honest statements of stakeholders' values, and about the comparability of these statements. Despite this drawback, the idea of a supra DM is a useful frame for thinking about, and for private analysis of, decisions that impact multiple stakeholders.
Computer Security: A Historical Perspective
Authors: Schell Roger R. , Reed Edwards E. 
Published: September 2014

AbstractThe pervasive dependence on computers today gives us no choice but to use them in the face of professional attackers. That threat, for which software subversion is often the tool of choice, is serious and growing, so computers are increasingly a major source of risk. Responsible risk assessment and risk management requires that we not only create computers that are secure but also verify that we have succeeded. A productive history of more than 30 years of research and practical experience has produced a theory of computer security rich with solutions and tools. The greatest achievement is the demonstrated ability to build and operationally deploy truly bulletproof systems having verifiable protection. This remains the most powerful solution available for many of today's hard computer and network security problems.
Truncation
Authors: Rai Shesh N. , Sun Jianguo 
Published: September 2014

AbstractIn collection and analysis of real‐life data, we always encounter incomplete data. Censoring and truncation are types of incomplete data that arise owing to a type of sampling scheme. We describe the differences and similarities between censoring and truncation. We also describe types of truncation and the role of truncation in the analysis of real‐life data.
Warranty Analysis
Authors: Murthy D.N. Prabhakar , Blischke Wallace R. 
Published: September 2014

Abstract
For products sold with warranty, an important element of risk for the manufacturer is the potential cost resulting from the servicing of failures occurring under warranty. These costs depend on several factors, the most important being the reliability of the product. For planning purposes, the manufacturer must estimate (a) the expected cost of warranty per unit sold and (b) the expected cost per unit time over the product life cycle. This must be done in the product development stage. This article deals with models that may be used to obtain these cost estimates for products sold with free‐replacement and pro rata warranties.
Ultrahigh Reliability
Authors: Resnick Marc L. 
Published: September 2014

Abstract
Ultrareliability is a system of systems approach to modeling and achieving reliability. It seeks to increase reliability metrics and mission success by an order of magnitude or more by going beyond traditional approaches to reliability. It involves a rigorous examination of the interacting relationships among system components, people, and the external context at all stages of the system life cycle from determining requirements to system disposal. Interactions are evaluated to quantify their effects on system reliability and mission success and to discover ways to mitigate sources of error and component failure. Interactions include communication, training, operating processes and procedures, and human factors. The external context includes customers, supply chains, and culture.
There are many benefits when organizations achieve ultrareliability in their systems. Maintenance costs can often be reduced significantly because breakdowns become rare. Systems fail rarely and last longer. There are also indirect benefits such as streamlined development, increased customer satisfaction, and a better understanding of how systems operate. For many organizations, even the process of attempting ultrareliability yields several of these benefits, increasingly so as the organization develops its ultrareliability capability.
Common Cause Failure Modeling
Authors: Vaurio Jussi K. 
Published: September 2014

AbstractModeling and quantification of simultaneous failures of multiple components due to common causes is a frequent and often crucial task in safety system reliability and risk assessments. Several models of common cause failures (CCF) are introduced. Their mutual relationships, limitations, and advantages, as well as sources of parametric values, are described. The models are presented in terms of basic multiple‐failure rates and probabilities that are independent of system testing schemes and intervals, and have direct connection to the basic event probabilities needed in system logic models.The early CCF models such as the β factor, binomial failure rate, common load, and distributed failure probability models are all special cases of stochastic reliability analysis. Even if mathematically attractive, these models are inherently constrained by certain mutual couplings between the CCF rates or CCF probabilities.More general α factor and multiple Greek letter models are based on the ratios of multiple‐failure rates or probabilities. In applications, both models need some additional failure rate from outside of the model to yield CCF rates and basic event probabilities.Extensive national and international common cause failure data collection efforts are making it feasible to estimate plant‐specific multiple‐failure rates and probabilities by combining data from many similar systems with empirically oriented Bayesian methods without assuming common generic parametric values. This methodology is briefly described. It takes into account both statistical and assessment uncertainties due to limited observations, interpretations, and documentation of CCF events.
Probabilistic Design
Authors: Gelder Petrus H.A.J.M. , Vrijling Johannes K. 
Published: September 2014

AbstractIn this article, the probabilistic approach to design and risk analysis in civil engineering is outlined. The application of probabilistic design methods offers the designer a way to unify the design of engineering structures, processes, and management systems. For this reason, there is a growing interest in the use of these methods. This article begins with an introduction to probabilistic analysis, a discussion on uncertainties, and a reflection on the deterministic approach versus the probabilistic approach. The article then addresses the tools, design, and calculation methods for a probabilistic systems analysis. Failure probability calculation for an element is reviewed and the article concludes with a description of the evaluation methods of a calculated risk level.