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## Séminaires DSA

### Discretization error for the maximum of a Gaussian field

Jean-Marc Azaïs (Université de Toulouse, France)

4 avril 2017  -  14:00-15:00, salle Extranef 109

A Gaussian field $X$ defined on a square $T$ of $\R^2$ is considered. We assume that this field is only observed at some points of a regular grid with spacing $\frac{1}{n}$. We are interested in the discretization error $M - M_n$, with $M$ the global maximum of $X$ over $T$ and $M_n$ the maximum of $X$ over the observation grid. Using a model inspired by Slepian models, an asymptotic equivalent of the discretization error is given and thus an asymptotic bound for this error.

### Liste des prochaines séances

 26 octobre 2017 Means Testing Public Pensions under Population Ageing George Kudrna (CEPAR, UNSW Sydney, Australia) 15:00-16:00, salle Extranef 125 Plus d'informationMeans testing of public pensions facilitates the aims of containing pension expenditures by governments and of directing pension payments to those senior individuals most in need. In this project, we apply a lifecycle growth model to analyse the effects of means-tested public pensions under different population ageing scenarios. We consider the following demographic scenarios: (i) increases in longevity as measured by improved age-specific survival rates; (ii) different rates of population growth arising from changes in fertility profiles over time; and (iii) changing gradients in mortality across different income classes of individuals. The results indicate that more pronounced ageing scenarios together with widening mortality gaps between high- and low-income groups of individuals strengthen the role of means testing in providing sustainable and equitable pensions. 27 octobre 2017 About new approximations of the Value at Risk, Expected Shortfall and the distribution of bivariate aggregate claims Robert Mnatsakanov (West Virginia University, Morgantown, USA) 14:00-15:00, salle Extranef 118 Plus d'informationApproximations of the Value at Risk (VaR), the Expected Shortfall (ES) as well as the bivariate aggregate claims amount distribution in the Classical Risk model are discussed. The proposed approximations are based on the values of scaled Laplace transforms of the underlying distributions. The uniform rates of approximations are established and their asymptotic performance is illustrated in a simulation study. Some properties of the smoothed versions of approximations based on Bernstein and Szasz-Mirakyan operators are presented. Applications to the problem of estimating the ruin probability, the VaR and ES from corresponding empirical counterparts are discussed as well. 17 novembre 2017 The value of a liability cash flow in discrete time subject to capital requirements Filip Lindskog (Stockholm University, Sweden) 14:00-15:00, salle Internef 121 Plus d'informationThe aim of this talk is to define the market-consistent value of a liability cash flow in discrete time subject to repeated capital requirements, and explore its properties. Our multi-period market-consistent valuation approach is based on defining a criterion for selecting a static replicating portfolio and defining the value of the residual liability, whose cash flow is the difference between the original liability cash flow and that of the replicating portfolio. The value of the residual cash flow is obtained as a solution to a backward recursion that is implied by the procedure for financing the repeated capital requirements, and no-arbitrage arguments. We show that the liability value resulting from no-arbitrage pricing of the dividends to capital providers may be expressed as a multi-period cost-of-capital valuation. Explicit valuation formulas are obtained under Gaussian model assumptions.   The talk is based on joint work with Hampus Engsner and Kristoffer Lindensjö. 16 janvier 2018 Georgiy Shevchenko (Taras Shevchenko National University of Kyiv, Ukraine) 14:00-15:00, salle Extranef 109 16 janvier 2018 Yuliya Mishura (Taras Shevchenko National University of Kyiv, Ukraine) 15:00-16:00, salle Extranef 109
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