Double STAR seminar: Asma Khedher and Michèle Vanmaele

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The webinars will take place on Zoom and a link to the virtual room will be sent out to all those who registered at the registration page.

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Speaker at 10:00: Asma Khedher (University of Amsterdam)

Title: An infinite-dimensional affine stochastic volatility model

Abstract: We introduce a flexible and tractable infinite-dimensional stochastic volatility model. More specifically, we consider a Hilbert space valued Ornstein–Uhlenbeck-type process, whose instantaneous covariance is given by a pure-jump stochastic process taking values in the cone of positive self-adjoint Hilbert-Schmidt operators. The tractability of our model lies in the fact that the two processes involved are jointly affine, i.e., we show that their characteristic function can be given explicitly in terms of the solutions to a set of generalised Riccati equations. The flexibility lies in the fact that we allow multiple modeling options for the instantaneous covariance process, including state-dependent jump intensity.

Infinite dimensional volatility models arise e.g. when considering the dynamics of forward rate functions in the Heath-Jarrow-Morton-Musiela modeling framework using the Filipović space. In this setting we discuss various examples: an infinite-dimensional version of the Barndorff-Nielsen–Shephard stochastic volatility model, as well as a model involving self-exciting volatility.

Speaker at 11:00: Michèle Vanmaele (Ghent University)

Title: Mortality/Longevity Risk-Minimization with or without Securitization

Abstract: In this talk we will address the risk-minimization problem, with and without mortality securitization, à la Föllmer–Sondermann for a large class of equity-linked mortality contracts when no model for the death time is specified. This framework includes situations in which the correlation between the market model and the time of death is arbitrary general, and hence leads to the case of a market model where there are two levels of information—the public information, which is generated by the financial assets, and a larger flow of information that contains additional knowledge about the death time of an insured. We will derive the dynamics of the value processes of the mortality/longevity securities used for the securitization, and decompose any mortality/longevity liability into the sum of orthogonal risks by means of a risk basis. Next, we will quantify, as explicitly as possible, the effect of mortality on the risk-minimizing strategy by determining the optimal strategy in the enlarged filtration in terms of strategies in the smaller filtration. We will obtain risk-minimizing strategies with insurance securitization by investing in stocks and one (or more) mortality/longevity derivatives such as longevity bonds.
The talk is based on joint work with Tahir Choull (University of Alberta)i and Catherine Daveloose (Ghent University).

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This series of webinars addresses all interested people in probability, stochastic analysis, control, risk evaluation, statistics, with a view towards applications, in particular to renewable energy markets and production. This series brings together the major research themes of the projects STORM, SCROLLER, and SPATUS

Published Oct. 7, 2021 11:39 AM - Last modified Oct. 18, 2021 12:08 PM