Analytical Formulas for Risk Assessment for a Class of Problems where Risk Depends on Three Interrelated Variables

We derive general analytical formulas for assessing risks in a problem domain where the risk depends on three interrelated variables. More specifically, we derive general analytical formulas for propagating beliefs in a network where three binary variables, A, B and C, are related to a fourth binary variable Z through an ‘AND’ relationship. In addition, we assume that variables A, B and C are interrelated in that a change in one variable may affect the value of each of the other two. The analytical formulas derived in this article determine the overall belief and plausibility that Z is true or not true, given that we have beliefs on variables A, B and/or C. To demonstrate the importance of the general results, we use the results to develop models applicable to three real-world situations. The first model can aid external auditors in assessing the quality of an audit client’s internal audit function to determine the extent to which the internal auditor’s work can be relied on in the conduct of a financial audit while the second can aid in assessing the risk of impaired auditor independence when conducting a financial statement audit. The third model can be used to assess the risk of management fraud in financial reporting. Assessment of such risks is of critical importance to external auditors, regulators, and the investing public. Analytical formulas to help address these types of important business and economic problems have not been available prior to these derivations

An Introduction to Evidential Reasoning for Decision Making under Uncertainty: Bayesian and Belief Functions Perspectives

The main purpose of this article is to introduce the evidential reasoning approach, a research methodology, for decision making under uncertainty. Bayesian framework and Dempster-Shafer theory of belief functions are used to model uncertainties in the decision problem. We first introduce the basics of the DS theory and then discuss the evidential reasoning approach and related concepts. Next, we demonstrate how specific decision models can be developed from the basic evidential diagrams under the two frameworks. It is interesting to note that it is quite efficient to develop Bayesian models of the decision problems using the evidential reasoning approach compared to using the ladder diagram approach as used in the auditing literature. In addition, we compare the decision models developed in this paper with similar models developed in the literature

The Dempster-Schafer Theory of Belief Functions for Managing Uncertainties: An Introduction and Fraud Risk Assessment Illustration

This is the author's final draft. The publisher's official version is available electronically from:<http://onlinelibrary.wiley. com/journal/10.1111/%28ISSN%291835-2561>.The main purpose of this paper is to introduce the Dempster-Shafer theory (“DS” theory) of belief functions for managing uncertainties, specifically in the auditing and information systems domains. We illustrate the use of DS theory by deriving a fraud risk assessment formula for a simplified version of a model developed by Srivastava, Mock, and Turner (2007). In our formulation, fraud risk is the normalized product of four risks: risk that management has incentives to commit fraud, risk that management has opportunities to commit fraud, risk that management has an attitude to rationalize committing fraud, and the risk that auditor’s special procedures will fail to detect fraud. We demonstrate how to use such a model to plan for a financial audit where management fraud risk is assessed to be high. In addition, we discuss whether audit planning is better served by an integrated audit/fraud risk assessment as now suggested in SAS 107 (AICPA 2006a, see also ASA 200 in AUASB 2007) or by the approach illustrated in this paper where a parallel, but separate, assessment is made of audit risk and fraud risk

METHODS AND MODELS FOR ASSESSMENT OF RELIABILITY OF STRUCTURAL-COMPLEX SYSTEMS

The article presents the main propositions of logical-probabilistic method of analysis the assurance and enhancement of reliability of structurally complex systems, in which the structure of the system is described by means of mathematical logic and quantitative assessment of reliability is performed using probability theory. An example build script the dangerous condition and performed a quantitative investigation of the reliability of complex systems with interdependent basic events. The methods and models are implemented in a computer system that provides the ability to objectively assess the reliability and safety of structurally complex systems and solving problems of operational decision-making in complex emergencies.The article presents the main propositions of logical-probabilistic method of analysis the assurance and enhancement of reliability of structurally complex systems, in which the structure of the system is described by means of mathematical logic and quantitative assessment of reliability is performed using probability theory. An example build script the dangerous condition and performed a quantitative investigation of the reliability of complex systems with interdependent basic events. The methods and models are implemented in a computer system that provides the ability to objectively assess the reliability and safety of structurally complex systems and solving problems of operational decision-making in complex emergencies

A soil sampling program for the Netherlands

Soil data users in The Netherlands were inventoried for current and future data needs. Prioritized data needs were used to design the Netherlands Soil Sampling Program (NSSP) as a framework containing 3 groups of related projects: map upgrading, map updating and upgrading of pedotransfer functions. In each one group, the sampling design, performance criteria and optimal sample size were defined. This paper focuses on the upgrading of the existing soil map of The Netherlands at scale 1:50,000, and extensively treats the user inventory and the sampling strategy. The sampling design, performance criteria of the sampling and associated optimal sample size were obtained by statistical analysis of soil data available before the sampling. The Phosphate Sorption Capacity (PSC) was chosen as target variable to optimize sampling, because it dominated total cost per sample. A prior analysis of a performance criterion related to the sampling error of PSC resulted in a cost saving of 13% relative to total cost determined earlier by expert judgment. A posterior analysis showed that the set quality criterion was reached or better in 6 out of 7 cases. The NSSP resulted in a data base with soil data from 2524 sample points selected by stratified random sampling, and a collection of 5764 aliquots taken at these points. The NSSP has been showing its usage potential for various kinds of environmental studies and could be a sound future basis for a national scale monitoring program

Representation of Interrelationships among Binary Variables under Dempster-Shafer Theory of Belief Functions

This is the peer reviewed version of the following article: Srivastava, R. P., L. Gao, and P. Gillett. " Representation of Interrelationships among Binary Variables under Dempster-Shafer Theory of Belief Functions" (pre-publication version), 2009, International Journal of Intelligent Systems, Volume 24 Issue 4, pp. 459 - 475, which has been published in final form at http://doi.org/10.1002/int.20347. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.This paper presents an algorithm for developing models under Dempster-Shafer theory of belief functions for categorical and 'uncertain' logical relationships among binary variables. We illustrate the use of the algorithm by developing belief-function representations of the following categorical relationships: 'AND', 'OR', 'Exclusive OR (EOR)' and 'Not Exclusive OR (NEOR)', and 'AND-NEOR' and of the following uncertain relationships: 'Discounted AND', 'Conditional OR', and 'Weighted Average'. Such representations are needed to fully model and analyze a problem with a network of interrelated variables under Dempster-Shafer theory of belief functions. In addition, we compare our belief-function representation of the 'Weighted Average' relationship with the 'Weighted Average' representation developed and used by Shenoy and Shenoy8. We find that Shenoy and Shenoy representation of the weighted average relationship is an approximation and yields significantly different values under certain conditions

Proposed audit guide : audit sampling;Audit sampling; Exposure draft (American Institute of Certified Public Accountants), 1982, Mar. 1

This exposure draft is a proposed Audit Guide entitled Audit Sampling. The proposed guide is important to all CPAs who do audits. It provides guidance to the auditor for implementing Statement on Auditing Standards no. 39, Audit Sampling. SAS no. 39 applies to all audit sampling — both statistical and nonstatistical. This proposed guide provides guidance to assist auditors using either approach in applying SAS no. 39. The guide is organized so that essentially all the guidance relating solely to statistical sampling is located beginning with Chapter 3, section 3. As a result, if an auditor is using this guide to assist him in applying nonstatistical sampling, the auditor would ordinarily follow the guidance in Chapters 1, 2, and 3 (sections 1 and 2). The audit guide is organized as follows: 1. The introduction to the guide describes the scope of the audit guide and provides guidance on the type of audit procedures covered by SAS no. 39 and this guide. 2. Chapter 1 provides an overview of the relationship of audit sampling to the audit process. 3. Chapter 2 provides guidance on the use of audit sampling for tests of compliance with prescribed internal accounting control procedures. This guidance applies to both nonstatistical and statistical sampling except where noted. 4. Chapter 3 provides guidance on the use of audit sampling for substantive tests of details. Chapter 3 is divided into four sections. Section one provides general guidance that applies to both nonstatistical and statistical sampling. Section 2 provides guidance for nonstatistical sampling applications for substantive tests. Two types of statistical sampling approaches for substantive tests are described in sections 3 and 4. Sections 2, 3, and 4 each include a case study illustrating the application of the guidance in the respective section. 5. The guide includes several appendices. Appendices A through E are primarily useful in applying certain statistical sampling approaches. Appendix F provides further guidance on the use of the risk model included in the appendix to SAS no. 39. Appendices G and H are a glossary and selected bibliography of further readings, respectively. Neither SAS no. 39 nor this guide requires the auditor using nonstatistical sampling to compare the sample size for the nonstatistical sampling application to a corresponding sample size calculated using statistical theory. However, the guide provides several quantitative illustrations of sample sizes based on statistical theory that should be helpful to an auditor applying professional judgment and experience in considering the effect of various planning considerations on sample size.https://egrove.olemiss.edu/aicpa_sop/1443/thumbnail.jp

Portfolio optimization models for project valuation

This dissertation presents (i) a framework for selecting and managing a portfolio of risky multi-period projects, called Contingent Portfolio Programming (CPP), and (ii) an inverse optimization procedure that uses this framework to compute the value of a single project. The dissertation specifically examines a setting where the investor can invest both in private projects and securities in financial markets, but where the replication of project cash flows with securities is not necessarily possible. This setting is called a mixed asset portfolio selection (MAPS) setting. The valuation procedure is based on the concepts of breakeven selling and buying prices, which are obtained by first solving an optimization problem and then an inverse optimization problem. In the theoretical part of the dissertation, it is shown that breakeven prices are consistent valuation measures, exhibiting sequential consistency, consistency with contingent claims analysis (CCA), and sequential additivity. Due to consistency with CCA, the present approach can be regarded as a generalization of CCA to incomplete markets. It is also shown that, in some special cases, it is possible to derive simple calculation formulas for breakeven prices which do not require the use of inverse optimization. Further, it is proven that breakeven prices for a mean-variance investor converge towards the prices given by the Capital Asset Pricing Model (CAPM) as the investor's risk tolerance goes to infinity. The numerical experiments show that CPP is computationally feasible for relatively large portfolios both in terms of projects and states, and illustrate the basic phenomena that can be observed in a MAPS setting.reviewe

An Evidential Reasoning Approach to Fraud Risk Assessment under Dempster-Shafer Theory: A General Framework

This paper develops a general framework under Dempster-Shafer theory for assessing fraud risk in a financial statement audit by integrating the evidence pertaining to the presence of fraud triangle factors (incentives, attitude and opportunities), and evidence concerning both account-based and evidence-based fraud schemes. This framework extends fraud risk assessment models in prior research in three respects. 1) It integrates fraud schemes, both account schemes through which accounts are manipulated, and evidence schemes through which frauds are concealed, into a single framework. 2) It incorporates prior fraud frequency information obtained from the Accounting and Auditing Enforcement Releases issued by the Securities and Exchange Commission into an evidential network which uses Conditional OR relationships among assertions. 3) The framework provides a structured approach for connecting risk assessment, audit planning, and evaluation of audit results. The paper uses a real fraud case to illustrate the application of the framework

A hybrid simulation approach to modelling the impact of public interventions on poverty

*An earlier version of this article has been presented in ICABE 2019 www.icabe.grPurpose: The aim of the article is to present the concept of a hybrid simulation model to study the impact of public intervention on the level of poverty at the local, regional and national levels. Design/Methodology/Approach: The proposed model is the hybrid of two computer simulation methods Agent-Based Simulation (ABS) and System Dynamics (SD). Findings: Counteracting the phenomenon of poverty is one of the tasks of public administration units. Various tools and instruments can be used to fight poverty, as a part of numerous programs financed from public funds, but their implementation should be preceded by a thorough analysis of the effects arising after their application. This is not easy, because the phenomenon of poverty is very complex, it results from the arrangement of many interrelated elements, and the outcomes of actions are visible only after a longer period of time. This system is characterized by the heterogeneity of elements. Some of them are on a macro scale (e.g. GDP level, labour market), while others refer to the micro scale (e.g. households and their members). Building a model of households requires the use of a method that allows to reflect the behaviour and decision-making rules of individuals and the interaction between them in a disaggregated form. Agent-Based Simulation (ABS) is such a method. On the other hand, modelling elements occurring in the macro scale, where we usually deal with aggregate quantities, is best matched by System Dynamics (SD) simulation method, which allows for reflecting dynamic behaviour through feedback loops. Practical Implications: The proposed concept can be used both by public administration units at various levels as well as by scientists - to conduct socio-economic research. Originality/Value: The applied simulation approach allows to capture the interrelations between the modelled effects in a dynamic manner for a long-time horizon, which is extremely important in the case of public management activities.peer-reviewe