Talks in Financial and Insurance Mathematics

This is the regular weekly research seminar on Insurance Mathematics and Stochastic Finance.

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Spring Semester 2025

Date / Time

Speaker

Title

Location

6 February 2025
17:15-18:00

Prof. Dr. Andrea Macrina
University College London

Details

Talks in Financial and Insurance Mathematics

Title	From stressed carbon budgets to financial discounting with urgency
Speaker, Affiliation	Prof. Dr. Andrea Macrina, University College London
Date, Time	6 February 2025, 17:15-18:00
Location	HG G 43
Abstract	If the leading principle is that reducing carbon emissions today is more valuable than reducing emissions tomorrow, how should financial carbon discounting work? Starting from carbon budgets that limit global warming to under a specified level with a given probability, a carbon discount bond system is developed that depends on the stochastic carbon emissions and an associated emissions abatement plan. We show that the sooner and more capital is invested to reduce carbon emissions, the better. The proposed financial design and pricing approach also considers the notion of a carbon budget debt and its financial treatment in a tiered carbon discounting system. Hedge portfolios and carbon budget derivatives emerge that mitigate financial losses if emissions exceed a planned/mandated carbon budget. Initial observations point to a multicurve term structure underlying the constructed carbon discount bond system that is linked to the carbon budgets and emissions abatement urgency.

From stressed carbon budgets to financial discounting with urgencyread_more

HG G 43

6 March 2025
17:15-18:15

Dr. Aleksei Minabutdinov
ETH Zurich

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Talks in Financial and Insurance Mathematics

Title	Transversality Condition Matters: Ensuring Uniqueness of Deep Learning Solutions in Economics and Finance
Speaker, Affiliation	Dr. Aleksei Minabutdinov, ETH Zurich
Date, Time	6 March 2025, 17:15-18:15
Location	HG G 43
Abstract	Transversality is an important sufficient condition for identifying the solution in infinite horizon economic and financial models. Without such a condition, there exists a continuum of functions that satisfy the Hamilton-Jacobi-Bellman (HJB) functional equation. In this paper, we explore this manifold of solutions with numerical and analytical methods. Using a standard continuous-time model, we demonstrate that, without explicitly imposing the transversality condition, widely used numerical algorithms, including the (Deep) Galerkin-type methods, may converge to arbitrary points of this manifold, leading to significant and uncontrollable biases. Using an example of the AK-Ramsey model with logarithmic utility (a prototypical model for many financial mathematics and macro/environmental economics applications), the paper demonstrates that the area of direct applicability of projection-type algorithms is narrower than one might expect based on contemporary literature. We propose a novel approach using a functional transformation of the original HJB equation to effectively incorporate the transversality condition, ensuring convergence to the actual value function.

Transversality Condition Matters: Ensuring Uniqueness of Deep Learning Solutions in Economics and Financeread_more

HG G 43

20 March 2025
17:15-18:15

Sascha Günther
Université de Lausanne

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Talks in Financial and Insurance Mathematics

Title	Efficiently computing annuity conversion factors via feed-forward neural networks
Speaker, Affiliation	Sascha Günther, Université de Lausanne
Date, Time	20 March 2025, 17:15-18:15
Location	HG G 43
Abstract	Many pension plans and private retirement products contain annuity factors, converting the funds at some future time into lifelong income. In general model settings like for example the Li-Lee mortality model, analytical values for the annuity factors are not available and one has to rely on numerical techniques. Their computation typically requires nested simulations as they depend on the interest rate level and the mortality tables at the time of retirement. We exploit the flexibility and efficiency of feed-forward neural networks to value the annuity factors at the time of retirement. In a numerical study, we compare our deep learning approach to (least-squares) Monte-Carlo (LSMC) which can be represented as a special case of the neural network (NN).

Efficiently computing annuity conversion factors via feed-forward neural networksread_more

HG G 43

27 March 2025
17:15-18:15

Dr. Florian Huber
EPFL

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Talks in Financial and Insurance Mathematics

Title	An analyst's perspective on Markovian lifts of stochastic Volterra equations
Speaker, Affiliation	Dr. Florian Huber, EPFL
Date, Time	27 March 2025, 17:15-18:15
Location	HG G 43
Abstract	We investigate Markovian lifts of stochastic Volterra equations(SVEs) with completely monotone kernels and general coefficients within the framework of weighted Sobolev spaces. Our primary focus is developing a comprehensive solution theory for a class of non-local stochastic evolution equations (SEEs) encompassing these Markovian lifts. This enables us to extend known results for the lifted equation such as existence of solutions and of invariant measures. Additionally our Framework allows us to obtain an Itô-type formula for the stochastic Volterra equations.

An analyst's perspective on Markovian lifts of stochastic Volterra equationsread_more

HG G 43

3 April 2025
17:15-18:15

Dr. Adrian Riekert
University of Münster

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Talks in Financial and Insurance Mathematics

Title	Convergence of gradient methods in the training of neural networks
Speaker, Affiliation	Dr. Adrian Riekert, University of Münster
Date, Time	3 April 2025, 17:15-18:15
Location	HG G 43
Abstract	We study the situation of optimizing artificial neural networks (ANNs) with the rectified linear unit activation via gradient flow (GF), the continuous-time analogue of gradient descent. Under suitable regularity assumptions on the target function and the input data of the considered supervised learning problem, we prove that every non-divergent GF trajectory converges with a polynomial rate of convergence to a critical point. The proof relies on a generalized Kurdyka-Lojasiewicz gradient inequality for the risk function. Furthermore, in a simplified shallow ANN training situation, we show that the GF with suitable random initialization converges with high probability to a good critical point with a loss value very close to the global optimum of the loss.

Convergence of gradient methods in the training of neural networksread_more

HG G 43

17 April 2025
17:15-18:15

Dr. Gechun Liang
University of Warwick

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Talks in Financial and Insurance Mathematics

Title	Convergence Rates of the Universal Robust Limit Theorem for Nonlinear Lévy Processes under Sublinear Expectations: A Monotone Scheme Analysis
Speaker, Affiliation	Dr. Gechun Liang, University of Warwick
Date, Time	17 April 2025, 17:15-18:15
Location	HG G 43
Abstract	The Feynman-Kac formula bridges PDEs and probability theory by providing a probabilistic representation of PDE solutions, connecting the convergence of numerical schemes for PDEs to limit theorems in stochastic processes. In this talk, we extend this paradigm beyond linear frameworks to sublinear expectations—known as Peng’s G-expectations. We establish convergence rates for the Universal Robust Limit Theorem, including central limit theorems, laws of large numbers, and alpha-stable limit theorems, all under the sublinear expectation framework. Our analysis leverages the monotone scheme analysis of viscosity solutions to fully nonlinear second-order PIDEs associated with nonlinear Lévy processes. Based on joint work with Mingshang Hu and Lianzi Jiang.

Convergence Rates of the Universal Robust Limit Theorem for Nonlinear Lévy Processes under Sublinear Expectations: A Monotone Scheme Analysisread_more

HG G 43

8 May 2025
17:15-18:15

Prof. Dr. Jennifer Alonso-Garcia
Université Libre de Bruxelles

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Talks in Financial and Insurance Mathematics

Title	Variable annuities: a closer look at ratchet guarantees, hybrid contract designs, and taxation
Speaker, Affiliation	Prof. Dr. Jennifer Alonso-Garcia, Université Libre de Bruxelles
Date, Time	8 May 2025, 17:15-18:15
Location	HG G 43
Abstract	Recently, providers of variable annuity (VA) contracts have launched products which offer potentially higher guaranteed benefits through a ratcheting mechanism in conjunction with an array of investment options, including a cash fund. In some contract designs, the cash fund serves as an intermediate repository of earnings. For example, in a VA with a guaranteed minimum withdrawal benefit (GMWB), the policyholder has the option to withdraw less than the guaranteed withdrawal amount, with the difference being deposited into the cash fund, which appreciates at a benchmarked rate until the contract matures. We consider the valuation of a VA contract with a GMWB rider in which the policyholder has access to a cash fund. Assuming a ratcheting mechanism for the guarantee, we determine the optimal withdrawal strategy and provide numerical examples of cash flows emanating from the contract. We also investigate the implications of taxation on the value of the VA contract.