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Autumn Semester 2023

Date / Time Speaker Title Location
7 September 2023
17:15-18:15 		Dr. David Itkin
Imperial College London
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Talks in Financial and Insurance Mathematics

Title Rank-based volatility stabilized models for equity markets
Speaker, Affiliation Dr. David Itkin, Imperial College London
Date, Time 7 September 2023, 17:15-18:15
Location HG G 43
Abstract Building on the previously proposed volatility stabilized models (Fernholz & Karatzas, 2005) in the framework of stochastic portfolio theory, we propose a rank-based extension to model an equity market over long time horizons. In this extended model, a collection of d stock capitalizations is driven by rank-dependent drift and diffusions coefficients normalized by their inverse market weight. Under an explicit condition on the parameters, we establish global weak existence to the market weight system as well as ergodicity of the induced ranked market weights. We also establish uniqueness of the reflected stochastic differential equation that the ranked system satisfies. Moreover, we show that the model admits relative arbitrage; that is the market portfolio can be outperformed with probability one in finite time. We then calibrate the model to three stable features of US equity data: (i) volatility of the ranked market capitalizations, (ii) frequency and intensity of "collisions" (i.e. changes in rank) and (iii) the capital distribution curve. Despite having only two parameters per asset to fit three distinct criteria, we are able to show that the model parsimoniously fits these stylized features of long-term US equity modelling. To the best of our knowledge this is the first model exhibiting relative arbitrage that has statistically been shown to have a good quantitative fit with the empirically estimable features (i)-(iii) above. We also generate simulated sample paths of the calibrated model and compare them to historical trajectories, both in and out of sample. Based on joint work in progress with Martin Larsson.
Rank-based volatility stabilized models for equity marketsread_more
HG G 43
15 September 2023
14:00-18:25
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Talks in Financial and Insurance Mathematics

Title Risk Day
Speaker, Affiliation
Date, Time 15 September 2023, 14:00-18:25
Location HG E 7
More information https://risklab.ethz.ch/news-and-events/risk-day.html
Risk Dayread_more
HG E 7
18 September 2023
17:15-18:15 		Prof. Dr. Dacheng Xiu
Booth School of Business, University of Chicago
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Talks in Financial and Insurance Mathematics

Title The Statistical Limit of Arbitrage
Speaker, Affiliation Prof. Dr. Dacheng Xiu, Booth School of Business, University of Chicago
Date, Time 18 September 2023, 17:15-18:15
Location HG D 3.2
More information https://finsuretech.ethz.ch/events/finsuretech-talks-.html
The Statistical Limit of Arbitrageread_more
HG D 3.2
28 September 2023
17:30-19:00
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Talks in Financial and Insurance Mathematics

Title Karl Brunner Distinguished Lecture
Speaker, Affiliation
Date, Time 28 September 2023, 17:30-19:00
Location HG F 30
Karl Brunner Distinguished Lecture
HG F 30
5 October 2023
17:15-18:15 		Prof. Dr. Marcus C. Christiansen
Universität Oldenburg
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Talks in Financial and Insurance Mathematics

Title A journey through multi-state modelling in life insurance
Speaker, Affiliation Prof. Dr. Marcus C. Christiansen, Universität Oldenburg
Date, Time 5 October 2023, 17:15-18:15
Location HG G 43
Abstract What is the probabilistic core of life insurance modelling? What kind of mathematical objects are premiums and reserves? Which modelling assumptions are really necessary and which are not? The presentation will take the audience on a journey through old concepts and modern interpretations. Traditions will be challenged and alternative views presented.
A journey through multi-state modelling in life insuranceread_more
HG G 43
12 October 2023
17:15-18:15 		Prof. Dr. Benjamin Jourdain
CERMICS
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Talks in Financial and Insurance Mathematics

Title Convexity propagation and convex ordering of one-dimensional stochastic differential equations
Speaker, Affiliation Prof. Dr. Benjamin Jourdain, CERMICS
Date, Time 12 October 2023, 17:15-18:15
Location HG G 43
Abstract We consider driftless one-dimensional stochastic differential equations. We first recall how they propagate convexity at the level of single marginals. We show that some spatial convexity of the diffusion coefficient is needed to obtain more general convexity propagation and obtain functional convexity propagation under a slight reinforcement of this necessary condition. Such conditions are not needed for directional convexity.
Convexity propagation and convex ordering of one-dimensional stochastic differential equationsread_more
HG G 43
19 October 2023
17:15-18:15 		Dr. Eyal Neuman
Imperial College London
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Talks in Financial and Insurance Mathematics

Title Fast and Slow Optimal Trading with Exogenous Information
Speaker, Affiliation Dr. Eyal Neuman, Imperial College London
Date, Time 19 October 2023, 17:15-18:15
Location HG G 43
Abstract We model the interaction between a slow institutional investor and a high-frequency trader as a stochastic multiperiod Stackelberg game. The high-frequency trader exploits price information more frequently and is subject to periodic inventory constraints. We first derive the optimal strategy of the high-frequency trader given any admissible strategy of the institutional investor. Then, we solve the problem of the institutional investor given the optimal strategy of the high-frequency trader, in terms of the resolvent of a Fredholm integral equation, thus establishing the unique multi-period Stackelberg equilibrium of the game. Our results provide an explicit solution which shows that the high-frequency trader can adopt either predatory or cooperative strategies in each period, depending on the tradeoff between the order-flow and the trading signal. We also show that the institutional investor's strategy is more profitable when the order-flow of the high-frequency trader is taken into account. This talk is based on a joint work with Rama Cont and Alessandro Micheli.
Fast and Slow Optimal Trading with Exogenous Informationread_more
HG G 43
26 October 2023
17:15-18:15 		Prof. Dr. Ying Chen
National University of Singapore
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Talks in Financial and Insurance Mathematics

Title Optimal Market Making under Model Uncertainty: A Robust Reinforcement Learning Approach
Speaker, Affiliation Prof. Dr. Ying Chen, National University of Singapore
Date, Time 26 October 2023, 17:15-18:15
Location HG G 43
Abstract We study the optimal market making problem in order-driven electronic markets, with a focus on model uncertainty. We consider ambiguity in order arrival intensities and derive a robust strategy that can perform under various market conditions. To achieve this, we introduce a tractable model for the limit order book using Markov Decision Processes and develop robust Reinforcement Learning to solve the complex optimization problem. This approach enables us to accurately represent the order book dynamics with tick structures, as opposed to the usual price dynamics modeled in stochastic approaches. This is a joint work with Hoang Hai Tran, Julian Sester and Yijiong Zhang.
Optimal Market Making under Model Uncertainty: A Robust Reinforcement Learning Approachread_more
HG G 43
2 November 2023
17:15-18:15 		Prof. Dr. Alexander McNeil
University of York
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Talks in Financial and Insurance Mathematics

Title Copula-based models for financial and macroeconomic time series
Speaker, Affiliation Prof. Dr. Alexander McNeil, University of York
Date, Time 2 November 2023, 17:15-18:15
Location HG G 43
Abstract We present some new approaches to modelling and forecasting macroeconomic and financial time series using stationary d-vine (s-vine) copula processes. We show how non-Gaussian extensions of ARMA processes can be constructed to model data that have non-Gaussian marginal distributions and/or non-Gaussian and non-linear serial dependence structures. We also show how these models can be combined with uniform-measure-preserving transformations known as v-transforms to construct processes for volatile financial return series which can outperform classical econometric models in certain cases. Methods will be illustrated with a variety of applications to data.
Copula-based models for financial and macroeconomic time seriesread_more
HG G 43
9 November 2023
17:15-18:15 		Prof. Dr. Andrea Macrina
University College London
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Talks in Financial and Insurance Mathematics

Title Arcade Processes for Informed Martingale Interpolation and Transport
Speaker, Affiliation Prof. Dr. Andrea Macrina, University College London
Date, Time 9 November 2023, 17:15-18:15
Location HG G 43
Abstract Arcade processes are a class of continuous stochastic processes that interpolate in a strong sense between zeros at fixed pre-specified times. Their additive randomization allows one to match any finite sequence of target random variables, indexed by the given fixed dates, on the whole probability space. The randomized arcade processes can thus be interpreted as a generalization of anticipative stochastic bridges. The filtrations generated by these processes are utilized to construct a class of martingales which interpolate between the given target random variables. These so-called filtered arcade martingales (FAMs) are almost-sure solutions to the martingale interpolation problem and reveal an underlying stochastic filtering structure. In the special case of conditionally Markov randomized arcade processes, the dynamics of FAMs are informed through Bayesian updating. FAMs can be connected to martingale optimal transport (MOT) by considering optimally coupled target random variables. Moreover, FAMs allow to formulate an information-based martingale optimal transport problem, which enables the introduction of noise in MOT, in a similar fashion to how Schrödinger's problem introduces noise in optimal transport. This information-based transport problem is concerned with selecting an optimal martingale coupling for the target random variables under the influence of the noise that is generated by an arcade process.
Arcade Processes for Informed Martingale Interpolation and Transportread_more
HG G 43
9 November 2023
18:15-19:15 		Prof. Dr. Miquel Oliu Barton
Université Paris Dauphine
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Talks in Financial and Insurance Mathematics

Title Value positivity of matrix games
Speaker, Affiliation Prof. Dr. Miquel Oliu Barton, Université Paris Dauphine
Date, Time 9 November 2023, 18:15-19:15
Location HG G 43
Abstract Matrix games are the most basic problem in Game Theory, but robustness to small perturbations is not yet fully understood. A perturbed matrix game is one where the entries depend on a parameter which varies smoothly around zero. We introduce two new concepts: (a) value-positivity if, for every sufficiently small error, there is a strategy that guarantees the value of the error-free matrix game; and (b) uniform value-positivity if there exists a fixed strategy that guarantees, for every sufficiently small error, the value of the error-free matrix game. While the first concept captures the dependency of optimal strategies to small perturbations, the second naturally arises where the data is uncertain and a strategy is sought which remains optimal despite that uncertainty. In this paper, we provide explicit polynomial-time algorithms to solve these two problems for any polynomially perturbed matrix game. For (a), we further provide a functional form for the error-dependent optimal strategy. Last, we translate our results into robust solutions for LPs.
Value positivity of matrix gamesread_more
HG G 43
16 November 2023
17:15-18:15 		Prof. Dr. Denis Belomestny
Duisburg-Essen University
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Talks in Financial and Insurance Mathematics

Title Preference-based reinforcement learning with financial applications
Speaker, Affiliation Prof. Dr. Denis Belomestny, Duisburg-Essen University
Date, Time 16 November 2023, 17:15-18:15
Location HG G 43
Abstract Reinforcement learning (RL) algorithms aim to maximise the accumulated reward for a suitably chosen reward function. However, designing such a reward function often requires task-specific prior knowledge which may be not available in closed quantitative form. To alleviate these issues, preference-based reinforcement learning algorithms have been proposed that can directly learn from an expert’s preferences instead of a hand-designed numeric reward. In this talk I give an overview of preference-based reinforcement learning and illustrate its main principles on examples from mathematical finance. In particular, I discuss what type of human feedback can be assumed and how preferences can be build in the optimization problem via penalisation.
Preference-based reinforcement learning with financial applicationsread_more
HG G 43
23 November 2023
17:15-18:15 		Prof. Dr. Sergio Pulido
ENSIIE, Évry, France
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Talks in Financial and Insurance Mathematics

Title Affine Volterra processes with jumps
Speaker, Affiliation Prof. Dr. Sergio Pulido, ENSIIE, Évry, France
Date, Time 23 November 2023, 17:15-18:15
Location HG G 43
Abstract The theory of affine processes has been recently extended to continuous stochastic Volterra equations. These so-called affine Volterra processes overcome modeling shortcomings of affine processes by incorporating path-dependent features and trajectories with regularity different from the paths of Brownian motion. More specifically, singular kernels yield rough affine processes. This paper extends the theory by considering affine stochastic Volterra equations with jumps. This extension is not straightforward because the jump structure and possible singularities of the kernel may induce explosions of the trajectories. This study also provides exponential affine formulas for the conditional Fourier-Laplace transform of marked Hawkes processes. This is joint work with Alessandro Bondi and Giulia Livieri.
Affine Volterra processes with jumpsread_more
HG G 43
30 November 2023
17:15-18:15 		Prof. Dr. Anthony Réveillac
INSA Toulouse
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Talks in Financial and Insurance Mathematics

Title Pseudo-chaotic expansion and explicit correlation formula for the Hawkes processes
Speaker, Affiliation Prof. Dr. Anthony Réveillac, INSA Toulouse
Date, Time 30 November 2023, 17:15-18:15
Location HG G 43
Abstract Hawkes processes have proved to be a powerful probabilistic model for various applications in neurosciences or insurance. These counting processes are defined through their intensity which is stochastic and pathwise dependent on the historical values of the process itself. This implicit definition leads to important drawbacks for performing explicit calculations involving simple quantities like for instance the inter-temporal correlation for which nothing is known to our knowledge outside the stationary case and some very particular examples. In this talk based on a joint work with C. Hillairet (ENSAE Paris), we will fill this gap by exploiting a specific decomposition named pseudo-chaotic expansion mixing some pathwise calculus together with some Malliavin calculus obtained in a previous joint work.
Pseudo-chaotic expansion and explicit correlation formula for the Hawkes processesread_more
HG G 43
7 December 2023
17:15-18:15 		Nicola Muça Cirone
Imperial College London
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Talks in Financial and Insurance Mathematics

Title Neural Signature Kernels
Speaker, Affiliation Nicola Muça Cirone, Imperial College London
Date, Time 7 December 2023, 17:15-18:15
Location HG G 43
Abstract Motivated by the paradigm of reservoir computing, we consider randomly initialised controlled ResNets defined as Euler-discretisations of neural controlled differential equations (Neural CDEs), a unified architecture which encompasses both RNNs and ResNets. We show that in the infinite-width-depth limit and under proper scaling, these architectures converge weakly to Gaussian processes indexed on some spaces of continuous paths and with kernels satisfying certain partial differential equations (PDEs) varying according to the choice of activation function, extending the results of Hayou (2022); Hayou & Yang (2023) to the controlled and homogeneous case. In the special, homogeneous, case where the activation is the identity, we show that the equation reduces to a linear PDE and the limiting kernel agrees with the signature kernel of Salvi et al. (2021a). We name this new family of limiting kernels neural signature kernels. Finally, we show that in the infinite-depth regime, finite-width controlled ResNets converge in distribution to Neural CDEs with random vector fields which, depending on whether the weights are shared across layers, are either time-independent and Gaussian or behave like a matrix-valued Brownian motion.
Neural Signature Kernelsread_more
HG G 43
14 December 2023
17:15-18:15 		Dr. Urban Ulrych
EPFL Lausanne
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Talks in Financial and Insurance Mathematics

Title Dynamic Currency Hedging with Non-Gaussianity and Ambiguity
Speaker, Affiliation Dr. Urban Ulrych, EPFL Lausanne
Date, Time 14 December 2023, 17:15-18:15
Location HG G 43
Abstract This paper introduces a non-Gaussian dynamic currency hedging strategy for globally diversified investors with ambiguity. It provides theoretical and empirical evidence that, under the stylized fact of non-Gaussianity of financial returns and for a given optimal portfolio, the investor-specific ambiguity can be estimated from historical asset returns without the need for additional exogenous information. Acknowledging non-Gaussianity, we compute an optimal ambiguity-adjusted mean-variance (dynamic) currency allocation. Next, we propose an extended filtered historical simulation that combines Monte Carlo simulation based on volatility clustering patterns with the semi-parametric non-normal return distribution from historical data. This simulation allows us to incorporate investor's ambiguity into a dynamic currency hedging strategy algorithm that can numerically optimize an arbitrary risk measure, such as the expected shortfall. The out-of-sample backtest demonstrates that, for globally diversified investors, the derived non-Gaussian dynamic currency hedging strategy is stable, robust, and highly risk reductive. It outperforms the benchmarks of constant hedging as well as static/dynamic hedging approaches with Gaussianity in terms of lower maximum drawdown and higher Sharpe and Sortino ratios, net of transaction costs.
Dynamic Currency Hedging with Non-Gaussianity and Ambiguityread_more
HG G 43

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