Splitting and composition methods for explicit time dependence in separable dynamical systems

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The Role of Gender and Education in Peer-to-peer Lending Activities: Evidence from a European Cross-country Study

The wide use of peer-to-peer lending platforms coupled with the Fintech global race has emphasized the role of social lending activities and their impact on consumers in recent years. Starting from the publicly available Bondora database, we analyse determinants of loan default during the 2013-2021 period by studying individual economic and social factors of borrowers. We apply a Logit model to estimate the ex-post probability of default on both original variables provided by the database and factors obtained by Principal Component Analysis. Results show the fundamental role of borrowers’ education in reducing the probability of default, as with financial awareness obtained by loan characteristics. In addition, gender plays an important role in determining loan default, with a particular focus on women's conditions within the family. Regarding financial inclusion and its social implications, our findings suggest different ways to improve financial literacy and promote peer-to-peer lending

The Role of Gender and Education in Peer-to-peer Lending Activities: Evidence from a European Cross-country Study

The wide use of peer-to-peer lending platforms coupled with the Fintech global race has emphasized the role of social lending activities and their impact on consumers in recent years. Starting from the publicly available Bondora database, we analyse determinants of loan default during the 2013-2021 period by studying individual economic and social factors of borrowers. We apply a Logit model to estimate the ex-post probability of default on both original variables provided by the database and factors obtained by Principal Component Analysis. Results show the fundamental role of borrowers’ education in reducing the probability of default, as with financial awareness obtained by loan characteristics. In addition, gender plays an important role in determining loan default, with a particular focus on women's conditions within the family. Regarding financial inclusion and its social implications, our findings suggest different ways to improve financial literacy and promote peer-to-peer lending

Peer-to-Peer (P2P) Lending in Europe: Evaluating the Default Risk of Borrowers in the Context of Gender and Education

In recent years, the importance of social lending activities and their effects on consumers have been highlighted by the widespread use of peer-to-peer lending platforms and the global race in fintech. Our study focuses on factors that affect the likelihood that European borrowers on peer-to-peer lending platforms, which are currently based in Estonia, Finland, and Spain, will default on their loans. Starting with the publicly accessible Bondora database, we examine the different economic and social characteristics of the borrowers to analyze the factors that contributed to loan default between 2013 and 2021. We use a Logit model to calculate the ex-post probability of default for factors derived from Principal Component Analysis as well as the original variables supplied by the database. The results show how crucially important education is for borrowers in lowering the risk of default, along with loan characteristics like high debt levels, long loan terms, and high interest rates. In addition, gender plays an important role in determining loan default, with a particular focus on women's conditions within the family. Regarding financial inclusion and its social implications, our findings suggest different ways to improve financial literacy and promote peer-to-peer lending. Future research could develop on the findings by applying them to other lending platforms and countries

A constructive method for parabolic equations with opposite orientations arising in optimal control

An optimal control model governed by parabolic equations is usually analyzed by carrying out the formulation of the so called “optimality system”, that consists of equations with opposite orientations. PDE-constrained optimization is employed in different fields, such as in economics and in ecology for allocating resources and managing ecosystems. Under the assumption that any solution exists, we provide an original proof of its uniqueness. This result is original and can be applied to a wide range of problems. Moreover, the same proof can be exploited to carry out a constructive method for approximating the solution, which is not available in closed form in the most cases. The method is based on successive approximations converging to a fixed-point that is the required solution. Due to the structure of the problem, this kind of approximation performs a forward-backward integration, giving raise to different iterative schemes. We investigate their convergence in the continuous setting under an original approach, by adapting the same proof provided for the exact solution uniqueness. Another innovative issue is related to the numerical implementation which involves exponential integration in time: up to our knowledge, the use of exponential integrators is new and original in the setting of PDE-constrained optimization. The effectiveness of the proposed approach is shown by providing some numerical results

Rational Krylov methods in exponential integrators for European option pricing

The aim of this paper is to analyze efficient numerical methods for time integration of European option pricing models. When spatial discretization is adopted, the resulting problem consists of an ordinary differential equation that can be approximated by means of exponential Runge–Kutta integrators, where the matrix-valued functions are computed by the so-called shift-and-invert Krylov method. To our knowledge, the use of this numerical approach is innovative in the framework of option pricing, and it reveals to be very attractive and efficient to solve the problem at hand. In this respect, we propose some a posteriori estimates for the error in the shift-and-invert approximation of the core-functions arising in exponential integrators. The effectiveness of these error bounds is tested on several examples of interest. They can be adopted as a convenient stopping criterion for implementing the exponential Runge–Kutta algorithm in order to perform time integration

A fixed-point iteration method for optimal control problems governed by parabolic equations

The analysis of an optimal control model governed by parabolic differential equations is usually developed by carrying out the formulation of the so called “optimality system”, which consists of partial differential equations with opposite orientations. Even though existence and uniqueness of the solution may be investigated, in most cases the solution itself is not available in closed form. For this reason, our aim consists of evaluating an accurate approximation. Thus, we provide a constructive method based on a scheme of successive approximations which converge to a fixed-point representing the required solution. Successive approximations are evaluated by applying Finite Element method for the spatial semi-discretization; then the resulting ODE system is solved by exponential integrators. Some numerical results are provided in order to show the effectiveness of the proposed approach

Multiscale modelling of the circulatory system

Tesi di Dottorato di ricerca in Matematica Computazionale e Ricerca Operativa (MACRO), XIII Ciclo, Università degli Studi di Milano, (Abstract in Boll. Unione Mat. Ital., Sez. A, Mat. Soc. Cult. (8) 4, No.3, 535-538 (2001)

Existence of solutions and numerical approximation of a non-local tumor growth model

In order to model the evolution of a heterogeneous population of cancer stem cells and tumor cells, we analyse a nonlinear system of integro-differential equations. We provide an existence and uniqueness result by exploiting a suitable iterative scheme of functions which converge to the solution of the system. Then, we discretize the model and perform some numerical simulations. Numerical approximations are obtained by applying finite differences for space discretization and an exponential Runge-Kutta scheme for time integration. We exploit the numerical tool in order to investigate the effects that niches have on cancer development. In this respect, the numerical procedure is applied in the case when the function of cell redistribution is assumed to be spatially explicit. It allows for finding an approximate solution which is spatially inhomogeneous as time progresses. In this framework, numerical investigation may help in understanding the process of niche construction, which plays an important role in cancer population biology