UPCOMING SEMINARS

25/05/22 Isaac González (University of Bath)

Title: Asymptotic moments of spatial branching processes

Abstract:

We consider a branching Markov process on a general space, with non-local branching mechanism. For a general setting in which the first moment semigroup of the process displays a Perron-Frobenius type behaviour, we identify the limit behaviour of the moments of the process in terms of the principal right eigen-function and left eigen-measure with an appropriate deterministic normalisation, which can be identified explicitly as either polynomial in time or exponential in time, depending on whether the process is critical, supercritical, or subcritical.

PAST SEMINARS

02/03/22, Peter Carr, NYU.

Optionality as a Binary Operation

Define optionality as the ability to choose at some fixed future time between receiving a constant vs receiving the realization of a just realized random variable. Suppose that the constant and the support of the random variable are in the same ordered set. Also suppose that the random variable has a finite mean in that same ordered set. Then the arbitrage-free value of this optionality can be treated as the outcome of using some binary operation to link the constant to the mean. We explore the interplay between standard properties of a binary operation eg commutativity and associativity, and standard properties of a risk-neutral probability density function eg symmetry and location-scale family. An application to an optimal stopping problem is also discussed.

26/01/22, María Elvira Mancino, U Firenze.

Volatility of volatility non-parametric estimation: Limiting results and Empirical study of the daily time series stylized facts We study the asymptotic normality of two estimators of integrated volatility of volatility based on the Fourier methodology, which does not require the pre-estimation of the spot volatility. We show that the bias-corrected estimator reaches the normal rate 1/4, while the estimator without bias-correction has a slower convergence rate and a smaller asymptotic variance. Additionally, we reconstruct the daily volatility of volatility of the SP&P500 and EUROSTOXX50 indices over long samples via the rate-optimal Fourier estimator and provide novel insight into the existence of stylized facts about its dynamic.

24/11/21, Archil Gulisashvili, Ohio U.

Time-inhomogeneous Gaussian stochastic volatility models: large deviations and super roughness

We study time-inhomogeneous stochastic volatility models, in which the volatility is described by a nonnegative function of a Volterra type continuous Gaussian process that may have very rough sample paths. Our main results are small-noise large deviation principles for the log-price process in a time-inhomogeneous Gaussian model under very mild restrictions. These results are used to find leading terms in small-noise asymptotic expansions of binary barrier options and call options.

29/09/2021, Soledad Torres, U Valparaíso.

Simple model sampled at random times

In this talk we give a simple model sampled at random times by a renewal process. The noise is derived from a fBm. Our motivation corresponds to the study of adaptive numerical methods for SDE.

27/10/2021, Adrián González Casanova, UNAM.

Lambda Selection and where to find it

There are many ways in which two populations can compete for resources and this leads to different forms of selection. A Lambda coalescent is a beautiful mathematical object that describes the genealogy of populations with skewed offspring distributions. We will discuss selection in the context populations in the Lambda universality class. Along the way, we will talk about a novel technique to relate coalescent processes with branching processes and about duality of Markov processes. Most of the talk is based on joint work with María Emilia Caballero (UNAM, México) and José Luis Pérez (CIMAT, México).