Insurance Mathematics and Stochastic Finance

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Post/Doctoral Seminar in Mathematical Finance

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Spring Semester 2023

Date / Time Speaker Title Location
8 March 2023
12:15-13:30 		David Pires Tavares Martins
ETH Zurich, Switzerland
Event Details

Post/Doctoral Seminar in Mathematical Finance

Title Mean-variance hedging in the rough Heston model
Speaker, Affiliation David Pires Tavares Martins, ETH Zurich, Switzerland
Date, Time 8 March 2023, 12:15-13:30
Location HG G 43
Abstract Rough volatility models, like the rough Heston model, have become popular recently, as they capture both the fractional scaling of the time series of the historic volatility and the implied volatility surface remarkably well. In this talk, we consider the hedging of derivatives in the rough volatility models. Combining mean-variance hedging with the affine structure of the rough Heston model allows us to obtain tractable formulas despite the fact that we are dealing with a non-Markovian and non-semimartingale underlying model and have to solve an infinite-dimensional optimal control problem. The talk is based on joint work with Christoph Czichowsky (LSE).
Mean-variance hedging in the rough Heston modelread_more
HG G 43
15 March 2023
12:15-13:30 		Dr. Matthieu Stigler
ETH Zürich, Switzerland
Event Details

Post/Doctoral Seminar in Mathematical Finance

Title With big data come big problems: pitfalls in measuring basis risk for crop index insurance
Speaker, Affiliation Dr. Matthieu Stigler, ETH Zürich, Switzerland
Date, Time 15 March 2023, 12:15-13:30
Location HG G 43
Abstract New satellite sensors will soon make it possible to estimate field-level crop yields, showing a great potential for agricultural index insurance. This paper identifies an important threat to better insurance from these new technologies: data with many fields and few years can yield downward biased estimates of basis risk, a fundamental metric in index insurance. To demonstrate this bias, we use state-of-the-art satellite-based data on agricultural yields in the US and in Kenya to estimate and simulate basis risk. We find a substantive downward bias leading to a systematic overestimation of insurance quality. In this paper, we argue that big data in crop insurance can lead to a new situation where the number of variables N largely exceeds the number of observations T . In such a situation where T << N , conventional asymptotics break, as evidenced by the large bias we find in simulations. We show how the high-dimension, low-sample-size (HDLSS) asymptotics, together with the spiked covariance model, provide a more relevant framework for the T << N case encountered in index insurance. More precisely, we derive the asymptotic distribution of the relative share of the first eigenvalue of the covariance matrix, a measure of systematic risk in index insurance. Our formula accurately approximates the empirical bias simulated from the satellite data, and provides a useful tool for practitioners to quantify bias in insurance quality.
With big data come big problems: pitfalls in measuring basis risk for crop index insuranceread_more
HG G 43
22 March 2023
12:15-13:30 		Songyan Hou
ETH Zurich, Switzerland
Event Details

Post/Doctoral Seminar in Mathematical Finance

Title Convergence of Adapted Empirical Measures on $\mathbb{R}^{d}$
Speaker, Affiliation Songyan Hou, ETH Zurich, Switzerland
Date, Time 22 March 2023, 12:15-13:30
Location HG G 43
Abstract We consider empirical measures of $\mathbb{R}^{d}$-valued stochastic process in finite discrete-time. We show that the adapted empirical measure introduced in the recent work by Backhoff et al. in compact spaces can be defined analogously on $\mathbb{R}^{d}$, and that it converges almost surely to the underlying measure under the adapted Wasserstein distance. Moreover, we quantitatively analyze the convergence of the adapted Wasserstein error between those two measures. We establish convergence rates of the expected error as well as the deviation error under different moment conditions. Furthermore, we propose a modification of the adapted empirical measure with smoothing on a non-uniform grid, which obtains the same convergence rate but under weaker assumptions. Indeed, for this measure, we obtain the optimal convergence rates of both expected error and exponential deviation error.
Convergence of Adapted Empirical Measures on $\mathbb{R}^{d}$read_more
HG G 43
29 March 2023
12:15-13:30 		Daniel Krsek
ETH Zurich, Switzerland
Event Details

Post/Doctoral Seminar in Mathematical Finance

Title Barycenters and Duality in Adapted Optimal Transport
Speaker, Affiliation Daniel Krsek, ETH Zurich, Switzerland
Date, Time 29 March 2023, 12:15-13:30
Location HG G 43
Abstract It has been noted by numerous mathematicians that the standard Wasserstein distance is not an appropriate metric on the space of stochastic processes since it does not comply with the temporal structure of information. The recently introduced adapted Wasserstein distance is believed to be an appropriate notion of distance resolving this issue. We consider the problem of causal and bicausal barycenters of stochastic processes. We study their properties, connection to multi-marginal adapted optimal-transport problems and duality. Moreover, we prove that the dual problem for adapted and causal optimal transport as well as for the barycenter problem is attained. The talk is based on ongoing work with Beatrice Acciaio and Gudmund Pammer.
Barycenters and Duality in Adapted Optimal Transportread_more
HG G 43
5 April 2023
12:15-13:30 		Robert Alexander Crowell
ETH Zurich, Switzerland
Event Details

Post/Doctoral Seminar in Mathematical Finance

Title Weak existence for McKean-Vlasov SDEs with common noise and propagation of chaos (I)
Speaker, Affiliation Robert Alexander Crowell, ETH Zurich, Switzerland
Date, Time 5 April 2023, 12:15-13:30
Location HG G 43
Abstract We consider weak solutions of McKean-Vlasov SDEs with common noise. The aim of this overview talk is to discuss the main steps to prove weak existence and identify more nuanced assumptions under which chaos propagates. The results are obtained through a marriage of probabilistic and analytic techniques for general non-linear but uniformly elliptic coefficients that posses only low spatial regularity.
Weak existence for McKean-Vlasov SDEs with common noise and propagation of chaos (I)read_more
HG G 43
19 April 2023
12:15-13:30 		Robert Alexander Crowell
ETH Zurich, Switzerland
Event Details

Post/Doctoral Seminar in Mathematical Finance

Title Weak existence for McKean-Vlasov SDEs with common noise and propagation of chaos (II)
Speaker, Affiliation Robert Alexander Crowell, ETH Zurich, Switzerland
Date, Time 19 April 2023, 12:15-13:30
Location HG G 43
Abstract This is a more specialized follow-up talk, intended to focus on some details of the convergence problem for finite interacting particle systems and McKean-Vlasov SDEs. After recalling the formulation from the first talk and the a priori regularity estimates, we show how these elements combine to let us conclude convergence of the finite particle systems, and existence of solutions to McKean-Vlasov SDEs more generally.
Weak existence for McKean-Vlasov SDEs with common noise and propagation of chaos (II)read_more
HG G 43
26 April 2023
12:15-13:30 		Christopher Blier-Wong
Université Laval
Event Details

Post/Doctoral Seminar in Mathematical Finance

Title The generating function of expected allocations with applications to risk-sharing
Speaker, Affiliation Christopher Blier-Wong, Université Laval
Date, Time 26 April 2023, 12:15-13:30
Location HG G 43
Abstract The conditional mean risk-sharing rule, which can be expressed as expected allocations, plays an important role in P2P insurance risk decomposition and capital allocation. In this talk, we introduce an ordinary generating function for expected allocations, a power series representation of the expected allocation of an individual risk given the total risks in the portfolio when all risks are discrete. First, we provide a simple relationship between the ordinary generating function for expected allocations and the probability generating function. Then, leveraging properties of ordinary generating functions, we reveal new theoretical results on closed-formed solutions to risk allocation problems, especially when dealing with Katz or compound Katz distributions. Then, we present an efficient algorithm to recover the expected allocations using the fast Fourier transform, providing a new practical tool to compute expected allocations quickly. The latter approach is exceptionally efficient for a portfolio of independent risks.
The generating function of expected allocations with applications to risk-sharingread_more
HG G 43
3 May 2023
12:15-13:30 		Philipp Zimmermann
ETH Zurich, Switzerland
Event Details

Post/Doctoral Seminar in Mathematical Finance

Title Fractional p-Calderón problems
Speaker, Affiliation Philipp Zimmermann, ETH Zurich, Switzerland
Date, Time 3 May 2023, 12:15-13:30
Location HG G 43
Abstract The main purpose of this talk is to discuss my recent results on fractional p-biharmonic systems and a related inverse problem. To make the exposition as self-contained as possible, we start by reviewing the classical p-Calderón problem and discussing preliminaries on nonlocal operators. Afterwards we introduce anisotropic fractional p-biharmonic operators and the related inverse problem. Finally, we state the main theorems, showing that under a monotonicity assumption they are uniquely solvable, and comment on the essential ingredients to establish these results.
Fractional p-Calderón problemsread_more
HG G 43
17 May 2023
12:15-13:30 		Jakob Heiss
ETH Zurich, Switzerland
Event Details

Post/Doctoral Seminar in Mathematical Finance

Title Bayesian Optimization-based Combinatorial Assignment
Speaker, Affiliation Jakob Heiss, ETH Zurich, Switzerland
Date, Time 17 May 2023, 12:15-13:30
Location HG G 43
Abstract The main challenge in combinatorial assignment (including combinatorial auction) is the exponential growth of the bundle space in the number of items. To address this, several papers have recently proposed ML-based preference elicitation algorithms that aim to elicit only the most important information from agents. Our key technical contribution is to integrate a method for capturing model uncertainty into an iterative combinatorial auction mechanism. This enables the mechanism to curiously explore (and not just greedily exploit) the bundle space during its preference elicitation phase.
Bayesian Optimization-based Combinatorial Assignmentread_more
HG G 43
31 May 2023
12:15-13:30 		Benjamin Nathaniel Kotlov
ETH Zurich, Switzerland
Event Details

Post/Doctoral Seminar in Mathematical Finance

Title Time-Inconsistent Mean-Field Optimal Stopping: a Limit Approach
Speaker, Affiliation Benjamin Nathaniel Kotlov, ETH Zurich, Switzerland
Date, Time 31 May 2023, 12:15-13:30
Location HG G 43
Abstract In this talk I will present the paper “Time-Inconsistent Mean-Field Optimal Stopping: a Limit Approach” by Boualem Djehiche and Mattia Martini. The authors consider an optimal stopping problem whose Snell envelope depends on the mean. This dependence makes the problem time-inconsistent, and thus the classical theory is not immediately applicable. To get around this, the authors solve a sequence of time-consistent approximations, and then pass to the limit.
Time-Inconsistent Mean-Field Optimal Stopping: a Limit Approachread_more
HG G 43

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