Forschungsgruppe "Stochastische Algorithmen und Nichtparametrische Statistik"
Seminar "Modern Methods in Applied Stochastics and Nonparametric Statistics" Summer Semester 2019
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| 16.04.2019 | Jérôme Lelong (Université Grenoble Alpes, France) |
| Pricing path-dependent Bermudan options using Wiener chaos expansion: An embarrassingly parallel approach In this work, we propose a new policy iteration algorithm for pricing Bermudan options when the payoff process cannot be written as a function of a lifted Markov process. Our approach is based on a modification of the well-known Longstaff Schwartz algorithm, in which we basically replace the standard least square regression by a Wiener chaos expansion. Not only does it allow us to deal with a non Markovian setting, but it also breaks the bottleneck induced by the least square regression as the coefficients of the chaos expansion are given by scalar products on the L^2 space and can therefore be approximated by independent Monte Carlo computations. This key feature enables us to provide an embarrassingly parallel algorithm. | |
| 23.04.2019 | n. n. |
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| 30.04.2019 | Dr. Melina Freitag (University of Bath, Uk) |
| A low-rank approach to the solution of weak constraint variational data assimilation problems | |
| 07.05.2019 | n. n. |
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| 14.05.2019 | Dr. Michele Coghi (WIAS Berlin) |
| Rough nonlinear Fokker-Planck equations Motivated by McKean-Vlasov diffusions with "common" noise, we present well-posedness of a nonlinear Fokker-Planck equation driven by a rough path. Joint work with Torstein Nilssen. | |
| 21.05.2019 | Dr. Fabian Telschow (University of California San Diego) |
| Seminar room ESH at MO 39 | Estimation of expected Euler characteristics of non-stationary Gaussian random fields |
| 28.05.2019 | Paul Hager (Tu Berlin) |
| The multiplicative chaos of fractional Brownian motions with vanishing Hurst parameters Empirical estimates attest the stochastic volatility process a small path regularity, which in the context of the rough volatility models are estimates of a small Hurst parameter of the underlying fractional Brownian motion. Ever smaller estimates have motivated Neuman and Rosenbaum to investigate the limit of fractional Brownian motions with vanishing Hurst parameters. Due to the vanishing H{\"o}lder regularity, the convergence can only be meaningful in the sense of generalised functions. The authors presented a normalised sequence of fractional Brownian motions and showed the convergence towards a log-correlated field, i.e. a generalised Gaussian field with a logarithmic singularity on the diagonal of the covariance kernel. Placed in the abstract ambient of the less known fractional Gaussian fields, we find the essential property of the normalisation that makes this convergence possible and we pose a general class of normalisations, which apply to fractional Brownian fields as well. The more interesting object from the finance perspective is the volatility process, i.e the exponential of the fractional Brownian motion. The limit process is not point-wise defined, yet we can make sense of the integrated volatility process as a random measure. The theory of Gaussian multiplicative chaos deals exactly with the latter problem: Defining the exponential of singular Gaussian fields. The usual construction of these measures uses a regularisation of the field, therefore most results are not directly applicable in our situation. This problem was treated by Neuman and Rosenbaum, however their proofs were incomplete. We are able to state an elementary proof for the convergence of the volatility measures in the so call L2-phase. |
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| 04.06.2019 | n. n. |
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| 11.06.2019 | Dr. Nikolas Tapia (WIAS/TU Berlin) |
| Signatures in shape analysis |
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| 18.06.2019 | Priv.-Doz. Dr. Peter Mathé (WIAS Berlin) | The modulus of continuity in Bayesian inverse problems We shall discuss how the convergence rates of direct and inverse problems are related through the modulus of continuity. |
| 25.06.2019 | Dr. Fabian Telschow (University of California San Diego) |
| Spatial confidence sets for raw effect size images |
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| 02.07.2019 | |
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| 30.07.2019 | |
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| 03.09.2019 | |
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last reviewed: June 24, 2019 by Christine Schneider