This article explores and analyzes the implementation problem of International Financial Reporting Standard 9 (IFRS 9) which is in use from 1 January 2018. IFRS 9 is most relevant for financial institutions, but also for all business subjects with a significant share of financial assets in their Balance sheet. The main objective of this article is the implementation of new impairment model for financial instruments, which is measurable through Expected Credit Losses (ECL). The use of this model is in correlation with a credit risk of the company for which it is necessary to determine basic variables of the model: Exposure at Default (EAD), Loss Given Default (LGD) and Probability of Default (PD). Basel legislation could be used for LGD calculation while PD calculation is based on specific methodology with two different solutions. In the first option, PD is taken as an external data from reliable rating agencies. When there is no external rating, an internal model for PD calculation has to be created. In order to develop an internal model, authors of this article propose application of multi-criteria decision-making model based on Analytic Hierarchy Process (AHP) method. Input data in the model are based on information from financial statements while MS Excel is used for calculation of such multi-criteria problem. Results of internal model are mathematically related with PD values for each analyzed company. Simple implementation of this internal model is an advantage compared to other much more complicated models.

In this paper, a mathematical formalism for defining the J-Curve phenomenon is set up in the form of a corresponding differential equation with practical application. An explicit form of the differential equation to describe the J-Curve, as well as the solution of the differential equations in terms of polynomials with coefficients satisfying a particular property was presented for the first time. The J-Curve and S-Curve are modelled as Riccati's nonlinear differential equation of the 1 st order. A mathematical form of the differential equation is proposed that corresponds in structure to the Laguerre Polynomials (linear differential equation of the 2 nd order), resulting in J-Curve as a solution. To confirm this, it is necessary to fulfil two main criteria for the mathematical validation of the J-Curve -confirmation of the structure of Laguerre polynomials (a polynomial equation with coefficients of alternating sign) and an R-squared score greater than 0.6. Two case studies are presented to validate the theoretical concepts and demonstrate the application of J-Curve mathematical modelling -Returns on Venture Investments (where returns from start-up investments are analysed over a 12-year period) and Returns on Long-Term Stock Investments (based on actual financial data for the period from 2016 to 2020 for the NIFTY 500 Index of the National Stock Exchange of India). A direct connection between the mathematical formulation and the graphs obtained is shown, which corresponds to the mathematical validation of the J-Curve phenomenon. It is mathematically shown how the financial data manifest the J-Curve behaviour, satisfying the initial assumptions of such a model. The mathematical model set up in this way can be verified in practice on different other types of data, which could create interest in an interdisciplinary approach in such research. This could include studies particularly from other economic fields such as micro-or macroeconomics.

višnja vojvodić rosenzweig, hrvoje volarević, mario varović: a multi-criteria analysis of the banking system in the republic of croatia financial theory and practice 37 (4) 403-422 (2013) 403A multi-criteria analysis of the banking system in the Republic of Croatia introductionThe purpose of the paper is to show the usefulness of multi-criteria decision-making in an analysis of the strategies of economic agents that are all in the same economic activity. The analysis will use a mathematical model of multi-criteria decision making, which will contain a number of the different individual criteria that are usually used in the framework of this branch of the economy. The analysis and ranking of the banking system according to the criteria selected in the model are applied in accordance with the preferences of the decision makers. The mathematical model for multi-criteria decision making presented will contain nine individual criteria classified into three basic groups -profitability, security (or risk) and liquidity -which are the interlinked components of financial management. The paper will formulate the problem of goal programming in which the goal of the bank is determined by the level of a single indicator from a group of cognate indicators, and the closest operational performance to the goal established is sought.

Background:The ranking of commercial banks is usually based on using a single criterion, the size of assets or income. A multicriteria approach allows a more complex analysis of their business efficiency. Objectives: This paper proposes the ranking of banks based on six financial criteria using a multicriteria approach implementing a goal programming model. The criteria are classified into three basic groups: profitability, credit risk and solvency. Methods/Approach: Business performance is evaluated using a score for each bank, calculated as the weighted sum of relative values of individual indicators. Results: In the process of solving the corresponding goal programming problem, the weights are calculated. It is assumed that the goal of each bank is the highest profitability. Because of the market competition among banks, the weights of indicators depend on the performance of each bank. This method is applied to the five biggest Croatian banks (ZABA, PBZ, ERSTE, RBA and HYPO). Conclusion: For the observed period (2010), the highest priority is given to profitability and then to credit risk. The ranking is achieved by using a multicriteria model.

The selection of an investment project is seen as a problem of multi-criteria decision-making. In this paper, a decision-maker uses six attributes i.e. criteria most used by the international companies in practice (net present value, internal rate of return, payback period, accounting rate of return, operating profit margin and return on equity).Individual utility functions are made for each attribute separately and the global utility function as a weighted sum of individual utility functions. For each criterion a final set of arranged pairs i.e. points of utility is determined based on the decision-maker’s assessments. Then, the points obtained are approximated by the utility function.Finally, the optimization issue solved in order to obtain the optimal performance of the selected project according to decision-maker’s opinion. The negotiation procedure enables the offered performances to approach optimal performance of the selected project aimed at decision-maker and investor reaching an agreement.