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Humboldt-Universität zu Berlin - Mathematisch-Naturwissenschaftliche Fakultät - Institut für Mathematik

FS Stochastische Analysis und Stochastik der Finanzmärkte

FS Stochastische Analysis und Stochastik der Finanzmärkte

Bereich für Stochastik

P. BANK, Ch. BAYER, Ch. BELAK, D. BECHERER, P. FRIZ, U. HORST, D. KREHER

Ort: HU Berlin,
Institut für Mathematik,
Rudower Chaussee 25, 12489 Berlin
Raum 1.115

Zeit: Donnerstag, 16 Uhr/17 Uhr c.t.

 24.10.2019 (16 Uhr c.t.) Jan Kallsen  (Universität Kiel) Should I invest in the market portfolio?   Abstract: Guided by stylised facts and inspired by Robert Fernholz' stochastic portfolio theory, we present a parsimonious stationary diffusion model for the entire stock market. Its ultimate purpose is to decide whether there is a simple more efficient alternative to the market portfolio. At this stage we discuss the qualitative implications of the model. A crucial role is played by the speed measure and by the local time at the boundary of the support of the diffusion process under consideration. 24.10.2019 (17 Uhr c.t.) N.N. tba   Abstract: 07.11.2019 (16 Uhr c.t.) Sara Svaluto-Ferro (University of Vienna) Polynomial processes - a universal modeling class   Abstract: We introduce polynomial jump-diffusions taking values in an arbitrary Banach space via their infinitesimal generator. We obtain two representations of the (conditional) moments in terms of solution of systems of ODEs. We illustrate the wide applicability of these formulas by analyzing several state spaces. We start by the finite dimensional setting, where we recover the well-known moment formulas. We then study the probability-measure valued setting, where we also obtain an existence result for the corresponding martingale problems. Moving to more recent results, we consider (potentially rough) forward variance polynomial models and we illustrate how to use the moment formulas to compute prices of VIX options. Finally, we show that the signature process of a d-dimensional Brownian motion is polynomial and derive its expected value via the polynomial approach. This is in fact just an illustrative example: the same applies to solutions of every SDE with analytic coefficients. 07.11.2019 (17 Uhr c.t.) Julio Backhoff (University of Twente) The Mean Field Schrödinger Problem   Abstract: I will introduce the mean field Schrödinger problem, concerned with finding the most likely evolution of a cloud of interacting Brownian particles conditionally on their initial and final configurations. New energy dissipation estimates are shown, yielding exponential convergence to equilibrium as the time between initial and final observations grows to infinity. The method reveals novel functional inequalities involving the mean field entropic cost, as well as an interesting connection with the theory of PDEs. (Joint work with Giovani Conforti, Ivan Gentil and Christian Léonard.) 21.11.2019  (16 Uhr c.t.) Stefan Gerhold (Technische Universität Wien)  Dynamic trading under integer constraints   Abstract: We first review results on arbitrage theory for some notions of "simple" strategies, which do not allow continuous portfolio rebalancing by  arbitrary amounts. Then, the focus of the talk is on trading under integer constraints, that is, we assume that the offered goods or shares are traded in integer quantities instead of the usual real quantity assumption. For finite probability spaces and rational asset prices this has little effect on the core of the theory of no-arbitrage pricing. For price processes not restricted to the rational numbers, a novel theory of integer arbitrage free pricing and hedging emerges. We establish an FTAP, involving a set of absolutely continuous martingale measures satisfying an additional property. The set of prices of a contingent claim is not necessarily an interval, but is either empty or dense in an interval. We also discuss superhedging with integral portfolios. Joint work with Paul Eisenberg. 21.11.2019 (17 Uhr c.t.) Tiziano De Angelis (University of Leeds) Some Explicit Results on Dynkin Games with Incomplete and Asymmetric Information   Abstract:  In this talk I will consider two types of Dynkin game with non-standard information structures. The first one is a zero-sum game between two players who observe a geometric Brownian motion but in which the minimiser knows the drift of the process whereas the maximiser doesn't know it. We construct an explicit Nash equilibrium in which the uninformed player uses a pure strategy and the informed player uses a randomised strategy. The second game is a non-zero sum game between two agents interested in the purchase of the same asset. Neither of the two players knows with certainty whether their competitor is `active' and in that sense that they have uncertain competition. Also in this case we construct explicitly a Nash equilibrium in which both players randomise their strategy. 05.12.2019 (16 Uhr c.t.) N.N. tba   Abstract: 05.12.2019 (17 Uhr c.t.) Frank Seifried (Universität Trier) Vortrag entfällt ! 09.01.2020 (16 Uhr c.t.) Bruno Bouchard  (Université Paris Dauphine) Understanding the dual formulation for the hedging of path-dependent options with price impact.    Abstract: We consider a general path-dependent version of the hedging problem with price impact of Bouchard et al. (2019), in which a dual formulation for the super-hedging price is obtained by means of PDE arguments, in a Markovian setting and under strong regularity conditions. Using only probabilistic arguments, we prove, in a path-dependent setting and under weak regularity conditions, that any solution to this dual problem actually allows one to construct explicitly a perfect hedging portfolio. From a pure probabilistic point of view, our approach also allows one to exhibit solutions to a specific class of second order forward backward stochastic differential equations, in the sense of Cheridito et al. (2007). Existence of a solution to the dual optimal control problem is also addressed in particular settings. As a by-product of our arguments, we prove a version of It${\rm\hat{o}}$'s Lemma for path-dependent functionals that are only $C^{0,1}$ in the sense of Dupire. 09.01.2020 (17 Uhr c.t.) Guanxing Fu (National University of Singapore) Mean Field Utility Maximization Game with Partial Information   Abstract: We study a mean field utility maximization game, where each player manages a stock whose return process depends on a hidden factor, which cannot be observed by the manager. The manager needs to infer the return process and rewrite the dynamics of the stock price based on the information available to her. Moreover, each manager is concerned not only with her own terminal wealth but also with the relative performance of her competitiors. We use the probabilistic approach to consider exponential and power utilities. Due to the mean field interaction and the nature of the game, the FBSDE systems characterizing the equilibria of our problem become coupled mean-field FBSDEs with possibly quadratic growth. We establish the well-posedness result of the mean-field FBSDEs in some suitable BMO space; firstly we work on a short time interval and secondly the local solution is extended to an arbitrary interval by considering the corresponding variational FBSDEs. 23.01.2020 (16 Uhr c.t.) Peter Tankov (Université Paris-Saclay) The entry and exit game in the electricity markets: a mean-field game approach   Abstract:  We develop a model for the industry dynamics in the electricity market, based on mean-field games of optimal stopping. In our model, there are two types of agents: the renewable producers and the conventional producers. The renewable producers choose the optimal moment to build new renewable plants, and the conventional producers choose the optimal moment to exit the market. The agents interact through the market price, determined by matching th eaggregate supplyof the two types of producers with an exogenous demand function. We prove the existence of the Nash equilibrium and the uniqueness of the equilibrium price process. An empirical example, inspired by the UK electricity market is presented.  The example shows that while renewable subsidies clearly lead to higher renewable penetration, this may entail a cost to the consumer in terms of higher peakload prices. In order to avoid rising prices, the renewable subsidies must be combined with market or off-market mechanisms ensuring that sufficient conventional capacity remains in place to meet the energy demand during peak periods. 23.01.2020 (17 Uhr c.t.) Patrick Cheridito (ETH Zürich) Deep Optimal Stopping   Abstract: In this paper we develop a deep learning method for optimal stopping problems which directly learns the optimal stopping rule from Monte Carlo samples. As such, it is broadly applicable in situations where the underlying randomness can efficiently be simulated. We test the approach on three problems: the pricing of a Bermudan max-call option, the pricing of a callable multi barrier reverse convertible and the problem of optimally stopping a fractional Brownian motion. In all three cases it produces very accurate results in high-dimensional situations with short computing times. 06.02.2020 (16 Uhr c.t.) Berenice Neumann (Universität Hamburg) A Myopic Adjustment Process for Mean Field Games with Finite State and Action Space   Abstract: Why does the behaviour of agents constitue a Nash equilibrium? This question is classical in the theory of learning for games and even more important for mean field games. Indeed, dynamic mean field equilibria are characterized by forward-backward systems of differential equations, which are most of the time only numerically tractable. In this talk I introduce a learning rule for mean field games with finite state and action space and provide first results regarding its convergence behaviour. 06.02.2020 (17 Uhr c.t.) Thibaut Mastrolia (CMAP, Ecole Polytechnique, Palaiseau) tba   Abstract:

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Frau Sabine Bergmann
bergmann@mathematik.hu-berlin.de
Telefon: 2093 5811
Telefax: 2093 5848

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