FS Stochastische Analysis und Stochastik der Finanzmärkte
Bereich für Stochastik
P. BANK, C. BAYER, D. BECHERER, P. FRIZ, U. HORST, D. KREHER
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Sommersemester 2026
Ort: TU Berlin, MA 043
Zeit: Donnerstag, 16-18 Uhr
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07.05.2026
16:15
Benjamin Massat (Université de Toulouse)
Quantification of limit theorem for Hawkes processes
Abstract: Hawkes processes are a popular model for self-exciting phenomena, from
earthquakes to finance. In this talk, I will first present them in a simple way, using a
Poisson imbedding construction. I will then review what is known about their long-time behavior, through limit theorems for both linear and non-linear cases.
The focus will be on three regimes that appear when the process has a long memory and the branching ratio gets close to or above one: the Nearly Unstable, the Weakly Critical, and the Supercritical Nearly Unstable Hawkes processes. These regimes have been studied qualitatively, but quantitative convergence results have been missing. I will explain how we obtain explicit convergence rates, relying on a coupling with a Brownian sheet, Fourier analysis, and a careful approximation of the absolute value function.07.05.2026
17:15
Idris Karoubi (Sorbonne Université, Paris)
Mean-field control of non exchangeable systems
Abstract: We study the optimal control of mean-field systems with heterogeneous and
asymmetric interactions. This leads to considering a family of controlled Brownian diffusion processes with dynamics depending on the whole collection of marginal robability laws. We prove the well-posedness of such systems and define the control problem together with its related value function.
We next prove a law invariance property for the value function which allows us to work on the set of collections of probability laws. We show that the value function satisfies a dynamic programming principle (DPP) on the flow of collections of probability measures. We also derive a chain rule for a class of regular functions along the flows of collections of marginal laws of diffusion processes.
Combining the DPP and the chain rule, we prove that the value function is a viscosity solution of a Bellman dynamic programming equation in a L²-set of Wasserstein space-valued functions.
This talk is based on a joint work with A. De Crescenzo, M. Fuhrman and H. Pham.21.05.2026
16:15
Paolo Pigato (University of Rome)
Multivariate Rough Volatility
Abstract: We review some empirical facts of financial markets that have motivated the rough volatility paradigm for modelling financial volatility, both from the point of view of financial time series and options pricing.
Motivated by empirical evidence from the joint behavior of realized volatility time series, we propose to model the joint dynamics of log-volatilities using a multivariate fractional Ornstein-Uhlenbeck process. This model is a multivariate version of the Rough Fractional Stochastic Volatility model proposed in Gatheral, Jaisson, and Rosenbaum, Quant. Finance, 2018. It allows for different Hurst exponents in the different marginal components and non trivial interdependencies. We discuss the main features of the model, propose parameter estimators, derive their asymptotic theory and perform a simulation study that confirms the asymptotic theory in finite sample. We carry out an extensive empirical investigation on emprical realized volatility time series, showing that these time series are strongly correlated and can exhibit asymmetries in their empirical cross-covariance function, accurately captured by our model. These asymmetries lead to spillover effects, which we derive analytically within our model and compute based on empirical estimates of model parameters. Moreover, in accordance with the existing literature, we observe behaviors close to non-stationarity and rough trajectories.21.05.2026
17:15
John Armstrong (King's College London)
Collective Pensions
Abstract: This talk will explain when it is (and when it is not) possible for a group of investors to gain mutual benefit from a collective pension design. We will see that investors can obtain mutual benefit by completing the market with additional insurance products and will estimate the potential benefit that collective designs can provide over traditional pension products.
04.06.2026
16:15
Jim Gatheral (CUNY)
Magic strikes
Abstract: Rolloos and Arslan showed that the volatility swap strike can be approximated by the implied volatility evaluated at a single (magic) strike- the zero-vanna strike. We extend this idea systematically to a broad class of attainable claims, including variance swaps, gamma swaps, the leverage contract, and stochasticity. Using the forest expansion of Alòs, Gatheral and Radoičić, we derive a Bergomi-Guyon-type smile expansion and show that each contract’s fair value can be approximated, to arbitrary order, by the total implied variance evaluated at a small number of magic strikes determined by simple fixed-point equations. At leading order, these magic strikes recover known results; at higher orders, they provide corrections that are model-independent in the sense that they depend on the model only through the implied volatility smile. Numerical tests under the Heston and rough Bergomi models demonstrate these approximations are highly accurate even for strongly skewed smiles. The method does not require strike inversion and can be applied directly to interpolated market smiles.
04.06.2026
17:15
Jonathan Tam (University of Oxford)
Bayesian dynamic portfolio optimization with informative constraints
Abstract: There is a recent debate on whether sustainable investing necessarily impact portfolio performance negatively. We model the financial impact of portfolio constraints by attributing the performance of dynamic portfolios to contributions from individual constraints. We consider a mean-variance portfolio problem with unknown asset returns. Investors impose a dynamic constraint based on a firm characteristic that contains information about returns, such as the environmental, social, and governance (ESG) score. We characterize the optimal investment strategy through two stochastic Riccati equations. Using this framework, we demonstrate that, depending on the correlation between returns and firm characteristics, incorporating the constraint can, in certain cases, enhance portfolio performance compared to a passive benchmark that disregards the information embedded in these constraints. Our results shed light on the role of implicit information contained in constraints in determining the performance of a constrained portfolio.
18.06.2026 No Seminar! (CRC TRR 388 Retreat) 16.07.2026
16:15
Wei Xu (Beijing Institute of Technology)
tba
16.07.2026
17:15
Chiara Rossato (ETH Zurich)
tba
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Wintersemester 2025/26
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)
Iterative Schemes for Markov perfect Equilibria
Abstract: We study Markov perfect equilibria in continuous-time dynamic games with finitely many symmetric players. The corresponding Nash system reduces to the Nash-Lasry-Lions equation for the commonvalue function, also known as the master equation in the mean-field setting. In the finite-state space problems we consider, this equation becomes a nonlinear ordinary differential equation admitting a unique classical solution. Leveraging this uniqueness, we prove the convergence of both Picard and weighted Picard iterations, yielding efficient computational methods. Numerical experiments confirm the effectiveness of algorithms based on this approach. This is joint work with Mathieu Laurière (NYU Shanghai), Mete Soner (Princeton), and Qinxin Yan (Princeton). |
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18.12.2025 17 Uhr c.t.
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Martin Keller-Ressel (Technische Universität Dresden)
Shape and dynamics of the term structure in multi-factor interest rate models Abstract: We examine the shapes that are attained by the forward- and yield-curve in several multi-factor interest rate models, in particular in the two-factor Vasicek model and the Svensson family of models. We provide a complete classification of all attainable shapes and partition the parameter space of each family according to these shapes. Building upon these results, we then examine the consistent dynamic evolution of the Svensson family under absence of arbitrage. Our analysis shows that consistent dynamics restrict the set of attainable shapes, and we demonstrate that certain complex shapes can no longer appear after a deterministic time horizon. As mathematical tools, the theory of total positivity and envelopes of plane curves are employed. The talk is based on joint work with Felix Sachse.
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29.01.2026 16 Uhr c.t.
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Xiaofei Sei (University of Toronto)
Dynamic Portfolio Choice with Intertemporal Hedging and Transaction Costs
Abstract: When returns are partially predictable and trading is costly, utility maximizing investors track a target portfolio at a constant trading speed. The target portfolio is optimal for a frictionless market, where asset returns are scaled back to account for trading costs and volatilities are adjusted to proxy the “execution risk” of holding assets that are costly to trade and exposed to volatile states. The trading speed solves an optimal execution problem, which describes how the legacy portfolio inherited from the past is traded towards the target portfolio in an optimal manner. Unlike for period-by-period mean-variance preferences as in Garleanu and Pedersen (2013), the target portfolio hedges changes in investment opportunities, and both it and the trading speed are linked and depend on execution risk. We set the problem out first in an “absolute” framework – price shocks independent of the price level and investors have CARA preferences – and then in a “relative” framework, with price shocks scaled by price levels and CRRA preferences.
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29.01.2026 17 Uhr c.t. |
Alessandro Bondi (École Polytechnique Paris)
Boundary attainment conditions for stochastic Volterra equations
Abstract: In this presentation, I will discuss boundary attainment conditions for one-dimensional stochastic Volterra equations (SVEs) of convolution type. In the first part of the talk, I will present an Osgood-type test for explosion to infinity of SVEs driven by additive noise, featuring kernels from a family that includes the fractional kernel. I will also investigate stability results for explosion times with respect to the kernels, including the case of an Euler-Maruyama approximation scheme. In the second part, I will present a Feller-type test that establishes, on a general open interval of the real line, necessary and sufficient conditions for boundary attainment of solutions to SVEs with possibly multiplicative noise. Here, I will consider dynamics governed by nonsingular kernels, which preserve the semimartingale property of the processes while introducing memory effects through a path-dependent drift. I will also show an application of these results to the Volterra square-root diffusion.
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12.02.2026 16 Uhr c.t. |
Guido Gazzani (University of Verona) VORTRAG ENTFÄLLT !! |
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12.02.2026 17 Uhr c.t. |
Beatrice Ongarato (Technische Universität Dresden) A stochastic Gordon-Loeb model for optimal security investment under clustered cyber-attacks
Abstract: We develop a continuous-time stochastic model for optimal cybersecurity investment under the threat of cyberattacks. The arrival of attacks is modeled using a Hawkes process, capturing the empirically relevant feature of clustering in cyberattacks. Extending the Gordon-Loeb model, each attack may result in a breach, with breach probability depending on the system’s vulnerability. We aim |
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Für Rückfragen wenden Sie sich bitte an:
Dr. Jana Bielagk
bielagk@math.hu-berlin.de