Innovating a Modern Model for Estimating the Amount of Money Laundering in Iran (The Application of Numerical and Inverse Problem Methods in Economy)

In this research, volume of dirty money is estimated using Inverse Problem Method and Tikhonov’s regularization strategy.
Corruption or money laundering encompasses a wide and multi-dimensional concept in such a way that this phenomenon might be regarded as a corruption in one society while being a social norm in another (De Saran, 1999). The occurrence of corruption or money laundering as an undesirable social phenomenon has a variety of different social and economic motives. Due to the importance of corruption or money laundering in different countries, extensive studies have been conducted into this issue in order to identify and analyze its causes. It should be reiterated that economic factors are the fundamental factors for all social structures and they leave significant effects on individual and group activities with regard to corruption.
Money laundering is a series of operations taken place to pretend that some illicit or illegal incomes are gained from legitimate or legal sources, However their origin is smuggling, bribery, extortion, kidnapping, fraud, forged invoices in the commercial sector, corruption, embezzlement and bribery in government organizations, financial fraud, wealth and income achieved from tax evasion, Internet fraud and other data tools and to-be-confiscated wealth.
Theoretical frame work: Quirk’s method (1996) has also been used in this article to identify the volume of dirty money and the effect of informal activities on money demand. In an article titled Major economic effects of money laundering, and according to Bhattacharyya's strategy, Quirk has considered the data on various types of crimes, the recommendations of the FATF to nineteen industrial countries on money demand function as a substitution variable to the illegal income, and investigated the effects of these criminal activities on monetary behavior in these countries.
Hence, there has been a high tendency to measure this phenomenon in recent years and there has been an attempt to use different methods to assess the quantity and volume of financial corruption along with other similar variables in the socio-economic context. Some others have used indirect methods that are mainly based on the assessment of opinions and perceptions of people and experts. However, this article aims at explaining the modeling of economic relationships as well as introducing a new algorithm for assessment of financial corruption in Iran that is totally based on mathematical techniques and is free of any particular premise. This is while other methods, due to their very nature, enjoy a variety of different premises and this has indeed created many problems, including the likelihood of having momentous errors. The present study applies a combination of Bhattacharyya method and arithmetic methods which are based on Tikhonov’s regularization strategy and inverse problem in order to introduce a new equation for assessment of the quantity of dirty money. In this method, firstly the illegal earning are estimated and then the volume of dirty money is calculated.
For the purpose of estimating illegal earning, in this article, we utilize inverse problem, in which inverse problem model is defined. But inverse problems are often ill-posed. It means that the problem is likely to have no answer or more than one answer or the answer is not stable. To overcome this problem, regularization methods are used for the stability of the answer. In regularization methods, the main problem is replaced by another problem which is close to the main problem, but does not have the awkward condition of being solvable and this is the nature of all regulation methods. There are many methods to organize regularization strategies. We use Tikhonov regularization strategy in this article and illegal earning is estimated using minimization function with Tikhonov regularization. Tikhonov regularization function leads to a consistent and congruent method for estimating illegal earning. We minimize Tikhonov regularization function to illegal earning. To do this, Euler-Lagrange equations will be applied. Using Euler-Lagrange equations leads us to a non-liner partial differential equation for estimation of illegal earning. The final non-liner partial differential equation cannot be solved using analytical methods and there is no closed form solution for this problem, or a closed form solution for this problem -if any- is very complicated. Therefore, we use numerical methods for solving it and obtain illegal earning. Since numerical methods are not accurate, one can find a method with a higher degree of congruence for the above mentioned problem at any time. In this paper, in addition to introducing an appropriate numerical for solving this method, we try to estimate illegal earning parameter, too. In this article, statistics and information of central bank during years 1973 to 2007 are utilized.
In this research, a non-liner partial differential equation is obtained for the estimation of illegal earning by Tikhonov regularization strategy and inverse problem and then volume of dirty money is determined. The results of the equation are as following table.
Table 1. Volume of dirty money growth rate in Iran Economy
1386 1385 1384 1383 1382 1381 year
11.4761 11.264 11.86 10.94 10.767 10.5391 volume of dirty money logarithm
1.88% -5.03% 8.41% 1.61% 2.16% 0.89% volume of dirty money growth rate
The results of this research represent the increasing progress of money laundering in Iran’s economy, which is seriously contradictory with developmental aims of Iran 1404; hence, serious device should be found in order to struggle with this phenomenon