Si avvisa che in data 19/3/2019, alle ore 12:30 precise, presso Aula Seminari al Sesto Piano, si svolgerà il seguente seminario:

Titolo: Risk measures and progressive enlargement of filtrations: a BSDE approach
Relatore: Alessandro Calvia, Università degli Studi di Milano-Bicocca

Abstract:

Risk measures are nowadays well-established tools in mathematical finance to evaluate the riskiness of a future financial position, both in a static and in a dynamic (i.e., time dependent) setting. Also, Backward Stochastic Differential Equations (or BSDEs, for short) are widely adopted tools in mathematical finance. From the beginning of the 21st century, connections between dynamic risk measures and BSDEs have been studied in the literature. Thanks to the theory of g-expectations, introduced by S. Peng, one can induce a dynamic risk measure from a BSDE. This can be done mapping the terminal condition of the BSDE (modeling a future financial position) into the first component of the corresponding solution. Clearly, this kind of risk measures depend on the noise and on the map g (called driver) appearing in the BSDE. The case of noise given by either a Brownian motion or a Brownian motion and an independent Poisson random measure is studied in the literature. Properties of the driver g, such as monotonicity, convexity, homogeneity, etc., are reflected in the properties of the dynamic risk measure and vice versa. The aim of this talk is to show that it is possible to induce a dynamic risk measure from a BSDE whose driving noise is given by a Brownian motion and a marked point process. In terms of the underlying information flow, this corresponds to the progressive enlargement of a Brownian reference filtration with the information brought by the occurrence of random events at some random times. We will prove that the original risk measure can be split into different risk measures, evaluating future financial position between each of these random events, that are induced, in turn, by a family of indexed Brownian BSDEs. We also show connections between properties of the driver of the BSDE and the induced risk measure and its time-consistency. This is joint work with Emanuela Rosazza Gianin.