Abstract: Financial fraud detection is an important problem with a number of design aspects to consider. Issues such as problem representation, choice of detection technique, feature selection, and performance analysis will all affect the perceived ability of solutions, so for auditors and researchers to be able to sufficiently detect financial fraud it is necessary that these issues be thoroughly explored. In this paper we will analyse some of the relevant experimental issues of fraud detection with a focus on credit card fraud. Observations will be made on issues that have been explored by prior researchers for general data mining problems but not yet thoroughly explored in the context of financial fraud detection, including problem representation, feature selection, and performance metrics. We further investigated some of these issues with controlled simulations, concentrating on detection algorithms, feature selection, and performance metrics for credit card fraud.

Abstract: Motivated by the fact that the l1-penalty is piecewise linear, we proposed a ramp loss linear programming nonparallel support vector machine (ramp-LPNPSVM), in which the l1-penalty is applied for the RNPSVM, for binary classification. Since the ramp loss has the piecewise linearity as well, ramp-LPNPSVM is a piecewise linear minimization problem and a local minimum can be effectively found by the Concave Convex Procedure and experimental results on benchmark datasets confirm the effectiveness of the proposed algorithm. Moreover, the l1-penalty can enhance the sparsity.

Abstract: Banking systems, modelled with networks, evolve over time overcoming critical points. Topology-oriented indicators of tipping points and early-warning signals of criticality in networks do not reflect the gradual movement of a system towards a tipping point. Plenty of networks with SIR-like dynamics have restricted numbers of node states. In the case of banking networks, the range space of node states is continual, which allows an estimation of single bank remoteness from an insolvent state. Remoteness and velocity reflect change in the state per iteration and are considered in order to estimate the influence of node dynamics. Both node dynamics and topology are taken into account. We consider the positive and negative impact of interbank interactions (edge presence). Each edge is considered with weight and length parameters corresponding to the size of interbank lending and the number of iterations remaining before it expires. It was shown that the dropping well below zero of the presented indicator, is referred to as the potential of interactions, is a sign of a forthcoming tipping point. The introduced $\mathscr{T}$-Threatened set allows the detection of an approaching a tipping point in terms of nodes' states.

Abstract: This work presents a high order numerical method for the solution of generalized Black-Scholes model for European call option. The numerical method is derived using a two-step backward differentiation formula in the temporal discretization and a High-Order Difference approximation with Identity Expansion (HODIE) scheme in the spatial discretization. The present scheme gives second order accuracy in time and third order accuracy in space. Numerical experiments are conducted in support of the theoretical results.