UNIVERSITA' DI SALERNO 

Dipartimento di Matematica   

AVVISO DI SEMINARI   

Mercoledì 1 giugno 2022, nella sala del consiglio del Dipartimento di Matematica, edificio F2, livello 1, si terranno i seguenti seminari in presenza e online (su Teams):

1) ore 15:00-15:45 - Prof. Enrico Scalas (University of Sussex, Brighton, UK) 

Limit theorems for prices of options written on semi-Markov processes 

link: https://teams.microsoft.com/l/meetup-join/19%3ameeting_ZmRiNmFjZmUtNmFlMS00OWY1LTk4ZTgtMGNlYWE1NzlmN2Y1%40thread.v2/0?context=%7b%22Tid%22%3a%22c30767db-3dda-4dd4-8a4d-097d22cb99d3%22%2c%22Oid%22%3a%2261e4e421-60a6-4cb9-8153-d04cb91c1edf%22%7d

We consider plain vanilla European options written on an underlying asset that follows a continuous time semi-Markov multiplicative process. We derive a formula and a renewal type equation for the martingale option price. In the case in which intertrade times follow the Mittag-Leffler distribution, under appropriate scaling, we prove that these option prices converge to the price of an option written on geometric Brownian motion time-changed with the inverse stable subordinator. For geometric Brownian motion time changed with an inverse subordinator, in the more general case when the subordinator's Laplace exponent is a special Bernstein function, we derive a time-fractional generalization of the equation of Black and Scholes.

This is joint work with Bruno Toaldo     

2) ore 16:00-16:45 - Dott. Giacomo Ascione (Scuola Superiore Meridionale, Napoli) 

Bulk behaviour of ground states for relativistic Schrödinger operators with spherical potential well   

link: https://teams.microsoft.com/l/meetup-join/19%3ameeting_OTMzYTBmYTAtZDFiYS00NDI0LThkNzQtYzg2NjE3MmQyYjRk%40thread.v2/0?context=%7b%22Tid%22%3a%22c30767db-3dda-4dd4-8a4d-097d22cb99d3%22%2c%22Oid%22%3a%2261e4e421-60a6-4cb9-8153-d04cb91c1edf%22%7d

In this talk, we show a probabilistic representation of the ground state of a massive or massless Schrödinger operator with a spherical potential well. Such a representation will lead to a two-sided approximation with different behaviours depending on the fact that we are inside or outside the well. Both of them rely on some functionals of the first exit time of a subordinated Brownian motion from a suitable open set (the well or its complement). We also develop a moving planes-type argument to prove the radial monotonicity of the ground state, which is one of the main tools of the two-sided bounds. This is joint work with József Lőrinczi.   

Gli interessati sono cordialmente invitati a partecipare,    

Cordiali saluti, 

Barbara Martinucci