FS Stochastische Analysis und Stochastik der Finanzmärkte
Bereich für Stochastik
P. BANK, Ch. BAYER, D. BECHERER, P. FRIZ, S. KASSING, U. HORST, D. KREHER
- Das Seminar findet an der HU Berlin, Institut für Mathematik, Raum 1.115 (Rudower Chaussee 25) statt.
- Zeit: Donnerstag, 16 Uhr c.t. / 17 Uhr c.t.
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23.10.2025 16 Uhr c.t. |
Yilie Huang (Columbia University) Mean -Variance Portfolio Selection by Continuous-Time Reinforcement Learning: Algorithms, Regret Analysis, and Empirical Study
Abstract: We study continuous-time mean-variance portfolio selection in markets where stock prices are diffusion processes driven by observable factors that are also diffusion processes yet the coefficients of these processes are unknown. Based on the recently developed reinforcement learning (RL) theory for diffusion processes, we present a general data-driven RL algorithm that learns the pre-committed investment strategy directly without attempting to learn or estimate the market coefficients. For multi-stock Black-Scholes markets without factors, we further devise a baseline algorithm and prove its performance guarantee by deriving a sublinear regret bound in terms of Sharpe ratio. For performance enhancement and practical implementation, we modify the baseline algorithm and carry out an extensive empirical study to compare their performance, in terms of a host of common metrics, with a large number of widely used portfolio allocation strategies on S&P 500 constituents. The results demonstrate that the proposed continuous-time RL strategy is consistently among the best especially in a volatile bear market, and decisively outperforms the model-based continuous-time counterparts by significant margins. |
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23.10.2025 17 Uhr c.t. |
Carlo Sgarra (Università degli Studi di Bari Aldo Moro) Semi-static variance-optimal hedging with self-exciting jumps
Abstract: The aim of this talk is to investigate a quadratic, i.e., variance-optimal, semi-static hedging problem in an incomplete market model where the underlying log-asset price is driven by a diffusion process with stochastic volatility and a self-exciting jump process of Hawkes type. More precisely, we aim at hedging a claim at time T > 0 by using a portfolio of available contingent claims, so to minimize the |
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06.11.2025 16 Uhr c.t.
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Xueru Liu (University Nanjing)
The small mass limit of SDEs with arbitrary state-dependent friction driven by Lévy noise
Abstract: The small mass limit is also known as the Smoluchowski–Kramers approximation. It was first proposed by Smoluchowski (1916) and Kramers (1940) and is used in many mathematical and physical studies to describe the motion approximation problem of small mass particles. The small mass limit is the justification for using the first order equation to describe the motion of a small particle disturbed by a Wiener process instead of using the Newton second-order equation.We develop an approach to derive the small mass limit for stochastic differential equations with state dependent friction driven by non-Gaussian Lévy noise. For the case where the Lévy noise has a finite second moment, we identify the limiting equation in probability, with respect to Skorokhod topology as the mass tends to zero. For the case where the Lévy noise is α-stable, we use interlacing method, which provides effective estimate results for a system under an α--stable Lévy noise, with rigorous error estimates. Then, we obtain the same limiting equation as the case that Lévy noise has a finite second moment. In particular, compared to Gaussian noise, there are two more terms in the limit equation that are related to jumps, one is expressed entirely in terms of the solution itself and its jumps, and the other is expressed entirely by the integral of the state-dependent friction matrix with respect to jump increments. Finally, we give numerical simulation results to illustrate the validity of our theory. |
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06.11.2025 17 Uhr c.t.
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Sam Cohen (University of Oxford)
Neural networks, PDEs and control
Abstract: Optimal control problems often involve the solution of high dimensional nonlinear PDEs, which is a key computational bottleneck. In this talk we will consider how neural networks can be used as a computational tool for these problems, how simple test cases can work deceptively well, and how fine details of the approach can lead to different results. |
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20.11.2025 16 Uhr c.t. |
Ryoji Takano (The University of Osaka)
Large deviations for rough volatility
Abstract: A rough volatility model is a stochastic volatility model for an asset price process with rough volatility, meaning that the Hölder regularity of the volatility path is less than one half. In this talk, we will focus on the asymptotic behavior of implied volatility for short maturities under such models, and show that the large deviation principle for rough volatility models provides the short-time asymptotic behavior of implied volatility. Rough path theory sheds light on the calculus of these asymptotics.
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20.11.2025 17 Uhr c.t. |
Ofelia Bonesini (London School of Economics and Political Sciences)
Continuous-time persuasion by filtering
Abstract: We frame dynamic persuasion in a partial observation stochastic control game with an ergodic criterion. The receiver controls the dynamics of a multidimensional unobserved state process. Information is provided to the receiver through a device designed by the sender that generates the observation process.
The commitment of the sender is enforced and an exogenous information process outside the control of the sender is allowed. We develop this approach in the case where all dynamics are linear and the preferences of the receiver are linear-quadratic.
We prove a verification theorem for the existence and uniqueness of the solution of the HJB equation satisfied by the receiver’s value function. An extension to the case of persuasion of a mean field of interacting receivers is also provided. We illustrate this approach in two applications: the provision of information to electricity consumers with a smart meter designed by an electricity producer; the information provided by carbon footprint accounting rules to companies engaged in a best-in-class emissions reduction effort. In the first application, we link the benefits of information provision to the mispricing of electricity production. In the latter, we show that when firms declare a high level of best-in-class target, the information provided by stringent accounting rules offsets the Nash equilibrium effect that leads firms to increase pollution to make their target easier to achieve.
This is a joint work with Prof. René Aïd, Prof. Giorgia Callegaro and Prof. Luciano Campi.
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04.12.2025 16 Uhr c.t.
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Kristoffer Andersson (University of Verona) Exponential convergence of fictitious-play FBSDEs in finite player stochastic differential games
Abstract: We study finite player stochastic differential games on possibly bounded spatial domains. The equilibrium problem is formulated through the dynamic programming principle, leading to a coupled Nash system of HJB equations and, in probabilistic form, to a corresponding Nash FBSDE with stopping at the first exit from the parabolic domain (covering both boundary and terminal conditions). The main focus of the talk is the analysis of a fictitious-play procedure applied at the level of FBSDEs. At each iteration, a player solves a best-response FBSDE against fixed opponent strategies, giving rise to a sequence of fictitious-play FBSDEs.
We show that this sequence converges exponentially fast to the Nash FBSDE.
In unbounded domains, this holds under a small-time assumption; in bounded domains, exponential convergence is obtained for arbitrary horizons under additional regularity conditions.For completeness, we also discuss how the fictitious-play FBSDE is approximated by a numerically tractable surrogate FBSDE, which itself converges exponentially to the fictitious-play equation. Since the surrogate FBSDE admits a standard time-discrete approximation of order 1/2, this provides a transparent overall error structure for the numerical approximation of the Nash FBSDE.
We conclude with representative numerical illustrations of the full approximation scheme.
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04.12.2025 17 Uhr c.t.
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Alex Tse (University College London) Portfolio Selection in Contests
Abstract: In an investment contest with incomplete information, a finite number of agents dynamically trade assets with idiosyncratic risk and are rewarded based on the relative ranking of their terminal portfolio values. We explicitly characterize a symmetric Nash equilibrium of the contest and rigorously verify its uniqueness. The connection between the reward structure and the agents' portfolio strategies is examined. A top-heavy payout rule results in an equilibrium portfolio return distribution with high positive skewness, which suffers from a large likelihood of poor performance. Risky asset holding increases when competition intensifies in a winner-takes all contest. This is joint work with Yumin Lu.
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18.12.2025 16 Uhr c.t.
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Felix Höfer (University of Princeton)
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18.12.2025 17 Uhr c.t.
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Martin Keller-Ressel (Technische Universität Dresden)
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15.01.2026
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N.N.
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29.01.2026 16 Uhr c.t.
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Xiaofei Sei (University of Toronto)
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29.01.2026 17 Uhr c.t. |
Alessandro Bondi (École Polytechnique Paris)
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12.02.2026 16 Uhr c.t. |
Guido Gazzani (University of Verona) tba Abstract:
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12.02.2026 17 Uhr c.t. |
Beatrice Ongarato (Technische Universität Dresden) tba
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Interessenten sind herzlich eingeladen.
Für Rückfragen wenden Sie sich bitte an:
Frau Sabine Bergmann
bergmann@math.hu-berlin.de
Telefon: 2093 45450
Telefax: 2093 45451