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Purpose This paper is aimed at developing a regression tree model useful to quantify the Money Laundering (ML) risk associated to a customer profile and his contracted products (customer’s inherent risk). ML is a risk to which different entities are exposed, but mainly the financial ones because of the nature of their activity, so that they are legally obliged to have an appropriate methodology to analyze and assess such a risk. Design/methodology/approach This paper uses the technique of regression trees to identify, measure and quantify the ML customer’s inherent risk. Findings After classifying customers as high- or low-risk based on a probability threshold of 0.5, this study finds that customers with 56 months or more of seniority are more risky than those with less seniority; the variables “contracted product” and “customer seniority” are statistically significant; the variables origin, legal entity and economic activity are not statistically significant for classifying customers; institution collection, business products and individual product are the most risky; and the percentage of effectiveness, suggested by the decision tree technique, is around 89.5 per cent. Practical implications In the daily practice of ML risk management, the two main issues to be considered are: 1) the knowledge of the customer, and 2) the detection of his inherent risk elements. Originality/value Information from the customer portfolio and his transaction profile is analyzed through BigData and data mining.

We consider the spectral stability problem for a family of standing pulse and wave front solutions to the one-dimensional version of the M 5-model formulated by Hillen [T. Hillen, M 5 mesoscopic and macroscopic models for mesenchymal motion, J. Math. Biol., 53 (2006), 585-616], to describe the mesenchymal cell motion inside tissue. The stability analysis requires the definition of spectrum, which is divided into two disjoint sets: the point spectrum and the essential spectrum. Under this partition the eigenvalue zero belongs to the essential spectrum and not to the point spectrum. By excluding the eigenvalue zero we can bring the spectral problem into an equivalent scalar quadratic eigenvalue problem. This leads, naturally, to deduce the existence of a negative eigenvalue which also turns out to belong to the essential spectrum. Beyond this result, the scalar formulation enables us to use the integrated equation technique to establish, via energy methods, that the point spectrum is empty. Our main result is that the family of standing waves is spectrally stable. To prove it, we go back to the original scalar problem and show that the rest of the essential spectrum is a subset of the open left-half complex plane.

In this paper we study the essential spectrum of the operator obtained by linearizing at traveling waves that occur in the one-dimensional version of the M$^5$-model for mesenchymal cell movement inside a directed tissue made up of highly aligned fibers. We show that traveling waves are spectrally unstable in $L^2(\mathbb{R};\mathbb{C}^3)$ as the essential spectrum includes the imaginary axis. Tools in the proof include exponential dichotomies and Fredholm properties. We prove that a weighted space $L^2_{w}(\mathbb{R};\mathbb{C}^3)$ with the same function for the tree variables of the linearized operator is no suitable to shift the essential spectrum to the left of the imaginary axis. We find a pair of appropriate weight functions whereby on the weighted space $L^2_{w_{\alpha}}(\mathbb{R};\mathbb{C}^2)\times L^2_{w_{\varepsilon}}(\mathbb{R};\mathbb{C})$ the essential spectrum lies on $\left\{\mathfrak{R}e\hspace{.03cm}\lambda<0\right\}$, outside the imaginary axis.