Mathematical Problems in Engineering

Volume 2016, Article ID 9191360, 7 pages

http://dx.doi.org/10.1155/2016/9191360

## Research on a Risk Assessment Method considering Risk Association

^{1}School of Business Administration, Northeastern University, Shenyang, China^{2}School of Economics and Management, Beijing Jiaotong University, Beijing, China

Received 26 August 2016; Revised 12 October 2016; Accepted 10 November 2016

Academic Editor: Yan-Wu Wang

Copyright © 2016 Zhan Zhang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Regarding risk assessment problems with multiple associated risks, a risk assessment method (RAM) is proposed in this paper. According to the risk-associated assessment information offered by expert panel, a comprehensive associated matrix is constructed to identify the influence relationship among risks so as to determine the hierarchical structure of risks. Then, based on the determined divided or undivided risk hierarchical structure as well as the possibility and loss of risks provided by expert panel, each value at risk (VAR) is calculated through knowledge related to probability theory. Finally, the feasibility and efficiency of the proposed method are demonstrated through a calculating case.

#### 1. Introduction

Risk assessment is quantifying the probable degree of influence or loss brought by a certain event or thing [1]. Risk assessment is an important segment of risk management, for instance, in financial risk management, credit risk management, engineering risk management, and other aspects; it plays a significant decision-support role for risk managers to adopt reasonable risk prevention measures and strategies [2–4]. Over the years, many scholars at home and abroad have attached great importance to researches on RAM and there have already been some outstanding research achievements [5–10], like analytic hierarchy process about risk assessment [5, 6], hazard degree calculation method [7, 8], risk matrix method [9–11] and artificial neural network [12, 13], and so on. Though all the RAMs mentioned above have solved various kinds of risk assessment problems from different perspectives, most of them do not take risk-associated situations into account. However, in reality there are usually connections among risks. For example, Baranoff and Sager [14] analyzed the associated situation between resource risk and production risk in life-insurance companies. Abdellaoui et al. [15] find that associated risks are valued differently than corresponding reduced simple risks. Thus, research on RAM in consideration of risk association has academic and practical application values. Now, there are few researches of this aspect. Liao et al. [16] adopted Bayesian Network approach to evaluate IT outsourcing risk meanwhile considering the association between IT outsourcing risk factors and IT outsourcing risks; Büyüközkan and Ruan [17] proposed a Choquet integrals-based software development risk evaluation approach regarding the association among development environment risk, code constraint risk, and engineering risk during the development of software. However, these RAMs mainly focus on specific risk assessment problems in risk-associated situations with no universal RAM proposed. Therefore, based on previous researches, we establish outsourcing risk hierarchy, introduce the interaction between different levels of risk, and give a RAM in consideration of multiple risk-associated situations.

There are four sections in this paper. In Section 1 we elaborate the research background and the problems that need to be explored or studied and then clarify the objectives and significance of the proposed method. In Section 2 we describe the RAM considering risk association in detail. In Section 3 we use a calculating case to prove feasibility and efficiency of the proposed method. Finally in Section 4 we summarize the conclusion and the main contributions of this paper and also the limitations and further research work to be carried out.

#### 2. Theories and Methods

##### 2.1. Description of Problems

In risk assessment problems, the occurrence of a certain risk may lead to another risk, that is, the association among risks. The following symbols are used to express the set and quantity of a risk assessment problem in consideration of risk-associated situations:(i): the set of risks, where means the risk number , (ii): the set of the expert panel, where means the expert number (iii): the weight vector of experts, where means the importance or weight of the expert ; it satisfies (iv): risk-associated matrix offered by the expert , where means the evaluation value offered by the expert for the direct influence degree of the risk on the risk , in which five-point scale is adopted. 0 means “no influence,” 1 means “weak influence,” 2 means “rather weak influence,” 3 means “medium influence,” 4 means “rather strong influence,” and 5 means “strong influence”(v): the thresholds offered by the expert for comprehensive influence degree. Setting up thresholds is to reject the influence relationship that is insignificant and has little comprehensive influence degree according to expert panel. (vi): the probability of occurrence of the risk offered by the expert (vii): the loss after the occurrence of the risk offered by the expert (viii): the comprehensive probability of the occurrence of the risk . (ix): the comprehensive loss of the risk , (x): the VAR of the risk

We propose the detailed procedure of RAM in consideration of risk association. Firstly, several risk-associated matrixes offered by expert panel are combined as group risk-associated matrix, while several thresholds of comprehensive influence degree offered by expert panel are combined as group threshold; secondly, risk relationship identification is performed through methods like matrix transform and there are usually two situations, divided and undivided risk hierarchical structures in the result of risk relationship identification. If the undivided risk hierarchical structure is set as situation A, each value at risk would be calculated according to the occurrence probability and loss of each risk offered by the expert panel; if the divided risk hierarchical structure is set as situation B, the expert panel are required to offer the occurrence probability of bottom risk and conditional probability according to the risk hierarchical structure. Furthermore, the comprehensive probability of the occurrence of each risk would be calculated through conditional probability formula and total probability formula specifically so as to calculate each value at risk in consideration of loss of each risk.

##### 2.2. Risk Relationship Identification

According to the description of problems above, identification methods of relationship among several risks (or risk hierarchical structures) are listed below.

Firstly, risk-associated matrixes () are combined as a group-associated matrix , among which the calculating formula of is

In formula (1), means the number of experts who score the direct influence degree of the risk on the risk as 0. Furthermore, the group-associated matrix is transformed into regulated group-associated matrix , among which the calculating formula of is

Secondly, comprehensive influence matrix with indirect association is set up and the calculating formula is

Meanwhile, thresholds of comprehensive influence degree are combined as a group threshold , and the calculating formula is

According to the group threshold , the comprehensive influence matrix is transformed into -cut matrix , where

Assume as 0-1 comprehensive associated matrix, in which

Matrix reflects the preference of the expert panel for influence degree among each risk with indirect influence relationship. The influence of the risk on itself is 1.

According to matrix , hierarchical structure of each risk is divided. Assumewhere and . means the risk set corresponding to the element valued 1 in the list number in the matrix ; means the risk set corresponding to the element valued 1 in the row number in the matrix .

If formula (7) works for a certain , should be regarded as the bottom element in and the list number and the row number in should be deleted to form a new matrix. During the process, if the bottom element cannot be found, risk assessment should be performed regarding situation A. If there is bottom element, searching bottom element in the new matrix should be performed until all the elements in the matrix are deleted. Then the hierarchical structure of matrix should be built up according to the order of deleting. Finally, risk assessment should be performed for situation B.

##### 2.3. Risk Assessment

RAMs for situations A and B are listed below.

*Situation A*. As for the situation that risk hierarchical structure cannot be divided, each risk is regarded as elements of the same layer to process. Firstly, the probability of occurrence of risk offered by the expert panel () is combined as comprehensive probability of occurrence of risk , and the calculating formula is

Secondly, the loss of risks () offered by the expert panel is combined as comprehensive loss of risks , and the calculating formula is

Finally, on the basis of the comprehensive probability of occurrence of risk and comprehensive loss of risks , the value at risk is calculated, and the calculating formula is

*Situation B*. As for the situation that risk hierarchical structure can be divided, is assumed as the set of risk on the layer number , and is set as the risk number on the layer number , is the probability vector of the occurrence of the risk on the first layer (the bottom layer) offered by the expert , where is the probability of occurrence of the risk offered by the expert ; is the number of risks on the layer number . is assumed as the risk number on the layer number related to the risk ; is the number of risks on the layer number related to the risk . is assumed as the occurrence of the risk , and means that the risk does not happen. In consideration of two conditions, and , there will be conditional probabilities related to .

Furthermore, assuming that is the probability of occurrence of the risk offered by the expert with the risks happening simultaneously, is the probability of occurrence of the risk offered by the expert with the risks happening simultaneously but no risk , is the probability of occurrence of the risk without offered by the expert ; for convenience, ,, are recorded as , for abbreviation.

Firstly, the probability vectors are combined as the comprehensive probability vector and the calculating formula is

Secondly, the conditional probabilities are combined as the comprehensive conditional probability ; the conditional probabilities are combined as the comprehensive conditional probability ; the conditional probabilities are combined as the comprehensive conditional probability , and the calculating formulas are as follows:

According to formulas (11)–, total probability formula is adopted to calculate the comprehensive probability of occurrence of each risk specifically (from the bottom layer); for instance, the formula to calculate the comprehensive probability of occurrence of risk on the layer number iswhere

Finally, according to formulas (11)–, the comprehensive probability of occurrence of each risk is calculated. Furthermore, according to formula (10), each value at risk is calculated.

#### 3. The Calculating Case for Situations A and B

In the following part, 2 calculating cases for situations A and B are used to explain the RAM proposed above.

*Case 1 for Situation A*. In order to improve its competitive ability, Liaoning GTE Biopharmaceutical Company wants to outsource its clinical experiment business. Before outsourcing, the company needs risk assessment on this outsourcing activity. The company sets up a panel of experts including 5 experts , and according to experience and business proficiency of each expert, the weight vectors of experts provided by the company are . Through relevant analysis and arrangement of feedback suggestions from questionnaires, the group of experts determine 2 kinds of outsourcing risks: bad book () and contract modification (). These 2 risks cannot be divided to a hierarchical structure. It should be calculated by using formulas (8), (9), and (10). The 5 experts give the value as Tables 1 and 2 show.