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AVVISO DI SEMINARI DI PROBABILITÀ E STATISTICA MATEMATICA

Title: The risk model with stochastic premiums and a multi-layer dividend strategy

by Olena Ragulina

Faculty of Mechanics and Mathematics, Taras Shevchenko National University of Kyiv

Abstract: The lecture is devoted to a generalization of the risk model with stochastic premiums where dividends are paid according to a multi-layer dividend strategy. First of all, we derive piecewise integro-differential equations for the Gerber-Shiu function and the expected discounted dividend payments until ruin. Next, we concentrate on the detailed investigation of the model in the case of exponentially distributed claim and premium sizes and find explicit formulas for the ruin probability as well as for the expected discounted dividend payments. Moreover, we obtain an exponential bound for the ruin probability under certain conditions and study these conditions for some special distributions of claim and premium sizes. Lastly, numerical illustrations for some multi-layer dividend strategies are presented. --

Title: The first-passage time properties of the Jacobi process and applications to neuronal modeling

by Giuseppe D'Onofrio

Dipartimento di Matematica "Giuseppe Peano", Università di Torino

Abstract: Nonlinear dynamical systems are often affected by different sources of noise and the usual belief is that the presence of noise can hinder or deteriorate the signal transmission in the system. However it has been observed, both in theoretical models and experiments, that random fluctuations can sometimes improve information processing. Mathematical models in neuroscience are one of the most prominent examples of phenomena for which the noise is of primary importance or even a part of the signal itself rather than a source of inefficiency and unpredictability. Our aim is to contribute to the discussion on the role of noise, studying the effects of a multiplicative noise on the performance of single neuron models using an analytical approach on the related first-passage-time problem. We consider a model where the evolution of the neuronal membrane depolarization between two consecutive spikes is described by a Jacobi process. We analyze the spiking activity of the neuron under study through the firing rate and the variability of the output related to the first two moments of the random variable first-passage time and we describe the occurrence of a phenomenon of coherence resonance. In particular we present counterintuitive effects due to the presence of the multiplicative noise and its dependence on the input parameters. Based on joint work with Petr Lansky (Czech Academy of Sciences) and Massimiliano Tamborrino (University of Warwick).

I seminari si terranno il 23 Gennaio 2020 ore 15:00 e ore 15:45, rispettivamente, in Aula G terzo livello del Dipartimento di Matematica e Applicazioni, Università di Napoli FEDERICO II, Complesso di Monte Sant'Angelo, Via Cintia, Napoli.