Departement Mathematik

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Talks in financial and insurance mathematics

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Frühjahrssemester 2024

Datum / Zeit Referent:in Titel Ort
22. Februar 2024
17:15-18:15 		Dr. Salvatore Scognamiglio
Parthenope University of Naples
Details

Talks in Financial and Insurance Mathematics

Titel Explainable Least Square Monte Carlo for Solvency Capital Requirement Evaluation
Referent:in, Affiliation Dr. Salvatore Scognamiglio, Parthenope University of Naples
Datum, Zeit 22. Februar 2024, 17:15-18:15
Ort HG G 43
Abstract Solvency II requires that to be solvent, insurance and reinsurance undertakings that adopt the internal model should hold their own funds able to cover losses in excess of expected ones at a given confidence level over a one-year period. This Solvency Capital Requirement (SCR) is defined as the Value-at-Risk of the Net Asset Value probability distribution at a 99.5% confidence level over a one-year period. Estimating the SCR involves nested simulations, incurring prohibitive computational costs. While machine and deep learning methods exhibit accuracy, their lack of explainability impedes adoption in the highly regulated insurance sector. This paper introduces an extension of the Least Square Monte Carlo method based on recent advances in explainable deep learning known as ‘localGLMnet’. The proposed approach allows for an accurate estimation of the SCR without compromising model explainability. It allows for deriving some interesting insights into the impact of risk factors on the value of the insurance liabilities. Numerical experiments performed on two realistic insurance portfolios validate our proposal. Additionally, we illustrate that the ElasticNet regularisation can be applied to enhance the model’s performance further.
Explainable Least Square Monte Carlo for Solvency Capital Requirement Evaluationread_more
HG G 43
29. Februar 2024
17:15-18:15 		Prof. Dr. Mehdi Talbi
Université Paris-Cité
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Talks in Financial and Insurance Mathematics

Titel Sannikov’s contracting problem with many Agents
Referent:in, Affiliation Prof. Dr. Mehdi Talbi, Université Paris-Cité
Datum, Zeit 29. Februar 2024, 17:15-18:15
Ort HG G 43
Abstract This work aims to study an extension of the celebrated Sannikov’s Principal-Agent problem to the multi-Agents case. In this framework, the contracts proposed by the Principal consist in a running payment, a retirement time and a final payment at retirement. After discussing how the Principal may derive optimal contracts in the N-Agents case, we explore the corresponding mean field model, with a continuous infinity of Agents. We then prove that the Principal’s problem can be reduced to a mixed control-and-stopping mean field problem, and we derive a semi-explicit solution of the first best contracting problem. This is a joint work with Thibaut Mastrolia and Nizar Touzi.
Sannikov’s contracting problem with many Agentsread_more
HG G 43
7. März 2024
17:15-18:15 		Prof. Dr. Gregoire Loeper
BNP Paribas Global Markets
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Talks in Financial and Insurance Mathematics

Titel Black and Scholes, Legendre and Sinkhorn
Referent:in, Affiliation Prof. Dr. Gregoire Loeper, BNP Paribas Global Markets
Datum, Zeit 7. März 2024, 17:15-18:15
Ort HG G 43
Abstract This talk will be a unified overview of some recent contributions in financial mathematics. The financial topics are option pricing with market impact and model calibration. The mathematical tools are fully non-linear partial differential equations and semi-martingale optimal transport. Some new and fun results will be a Black-Scholes-Legendre formula for option pricing with market impact, a Measure Preserving Martingale Sinkhorn algorithm for martingale optimal transport, and a lognormal version of the Bass Martingale.
Black and Scholes, Legendre and Sinkhornread_more
HG G 43
14. März 2024
17:15-18:15 		Dr. Brandon Garcia Flores
Université de Lausanne
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Talks in Financial and Insurance Mathematics

Titel Optimal reinsurance from an optimal transport perspective
Referent:in, Affiliation Dr. Brandon Garcia Flores, Université de Lausanne
Datum, Zeit 14. März 2024, 17:15-18:15
Ort HG G 43
Abstract We regard the optimal reinsurance problem as an iterated optimal transport problem between a (known) initial distribution and an (unknown) resulting risk exposure of the insurer. We also provide conditions that allow to characterize the support of optimal treaties, and show how this can be used to deduce the shape of the optimal contract, reducing the task to a finite-dimensional optimization problem, for which standard techniques can be applied. The proposed approach provides a general framework that encompasses many reinsurance problems, which we illustrate in several concrete examples, providing alternative proofs of classical optimal reinsurance results as well as establishing new optimality results, some of which contain optimal treaties that involve external randomness. Finally, we explain how in the current framework one can approach the problem of moral hazard in reinsurance and provide characterizations that avoid it.
Optimal reinsurance from an optimal transport perspectiveread_more
HG G 43
11. April 2024
17:15-18:15 		Prof. Dr. Erich Walter Farkas
ETH Zurich, Switzerland
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Talks in Financial and Insurance Mathematics

Titel Local-stochastic volatility and pricing autocallables
Referent:in, Affiliation Prof. Dr. Erich Walter Farkas, ETH Zurich, Switzerland
Datum, Zeit 11. April 2024, 17:15-18:15
Ort HG G 43
Abstract We investigate the pricing of single-asset autocallable barrier reverse convertibles in the Heston local-stochastic volatility (LSV) model. Despite their complexity, autocallable structured notes are the most traded equity-linked exotic derivatives. The autocallable payoff embeds an early redemption feature generating strong path- and model-dependency. Consequently, the commonly-used local volatility (LV) model is overly simplified for pricing and risk management. Given its ability to match the implied volatility smile and reproduce its realistic dynamics, the LSV model is, in contrast, better suited for exotic derivatives such as autocallables. We use quasi-Monte Carlo methods to study the pricing given the Heston LSV model and compare it with the LV model. In particular, we establish the sensitivity of the valuation differences of autocallables between the two models with respect to payoff features, model parameters, underlying characteristics, and volatility regimes. We find that the improved spot-volatility dynamics captured by the Heston LSV model typically result in higher prices, demonstrating the dependence of autocallables on the forward-skew and vol-of-vol risk. Moreover, we show that the parameters of the stochastic component of LSV models enable controlling for the autocallables price while leaving the fit to European options unaffected.The presentation is based on a joint work with Urban Ulrych and Francesco Ferrari and has grown from the Master Thesis of the latter.
Local-stochastic volatility and pricing autocallablesread_more
HG G 43
25. April 2024
17:15-18:15 		Dr. Xinwei Shen
ETH Zürich
Details

Talks in Financial and Insurance Mathematics

Titel Causality-oriented robustness: exploiting general additive interventions
Referent:in, Affiliation Dr. Xinwei Shen, ETH Zürich
Datum, Zeit 25. April 2024, 17:15-18:15
Ort HG G 43
Abstract Since distribution shifts are common in real-world applications, there is a pressing need for developing prediction models that are robust against such shifts. Existing frameworks, such as empirical risk minimization or distributionally robust optimization, either lack generalizability for unseen distributions or rely on postulated distance measures. Alternatively, causality offers a data-driven and structural perspective to robust predictions. However, the assumptions necessary for causal inference can be overly stringent, and the robustness offered by such causal models often lacks flexibility. In this paper, we focus on causality-oriented robustness and propose Distributional Robustness via Invariant Gradients (DRIG), a method that exploits general additive interventions in training data for robust predictions against unseen interventions, and naturally interpolates between in-distribution prediction and causality. In a linear setting, we prove that DRIG yields predictions that are robust among a data-dependent class of distribution shifts. We extend our approach to the semi-supervised domain adaptation setting to further improve prediction performance. Finally, we discuss an idea to go beyond specific characteristics but exploit shifts in overall aspects of the distribution, thus leading to potentially more robust predictions. The proposed methods are validated on a single-cell data application.
Causality-oriented robustness: exploiting general additive interventionsread_more
HG G 43
2. Mai 2024
17:15-18:15 		Prof. Dr. Luciano Campi
University of Milan
Details

Talks in Financial and Insurance Mathematics

Titel Mean field coarse correlated equilibria with applications
Referent:in, Affiliation Prof. Dr. Luciano Campi, University of Milan
Datum, Zeit 2. Mai 2024, 17:15-18:15
Ort HG G 43
Abstract Coarse correlated equilibria are generalizations of Nash equilibria which have first been introduced in Moulin et Vial (1978). They include a correlation device which can be interpreted as a mediator recommending strategies to the players, which makes it particularly relevant in a context of market failure. After establishing an existence and approximation results result in a fairly general setting, we develop a methodology to compute mean-field coarse correlated equilibria (CCEs) in a linear-quadratic framework. We identify cases in which CCEs outperform Nash equilibria in terms of both social utility and control levels. Finally, we apply such a methodology to a CO2 abatement game between countries (a slightly modified version of Barrett (1994)). We show that in that model CCEs allow to reach higher abatement levels than the NE, with higher global utility. The talk is based on joint works with F. Cannerozzi (Milan University), F. Cartellier (ENSAE) and M. Fischer (Padua University).
Mean field coarse correlated equilibria with applicationsread_more
HG G 43
16. Mai 2024
17:15-18:15 		Prof. Dr. Peter Hieber
Université de Lausanne
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Talks in Financial and Insurance Mathematics

Titel Management discretion and self-hedging equity-linked life insurance
Referent:in, Affiliation Prof. Dr. Peter Hieber, Université de Lausanne
Datum, Zeit 16. Mai 2024, 17:15-18:15
Ort HG G 43
Abstract The payoff of an equity-linked life insurance contract depends on granted investment guarantees and the performance of an investment fund, the assets of the insurance company. Given certain regulatory constraints, the investment in this fund is chosen by the insurance company. This suggests that this fund could – at the same time – be used as underlying fund of the insurance contract but also as its hedging portfolio. In other words, the insurance company might try to reduce risks by “self-hedging” the equity-linked life insurance contract payoff. This talk discusses the choice of such an optimal dynamic investment strategy. The result is compared to the case where the investment fund is exogenously given. (This is joint work with Karim Barigou, Université de Laval, Canada)
Management discretion and self-hedging equity-linked life insuranceread_more
HG G 43
23. Mai 2024
17:15-18:15 		Prof. Dr. Umut Çetin
London School of Economics
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Talks in Financial and Insurance Mathematics

Titel Kyle’s model with penalties, entropy and BSDEs
Referent:in, Affiliation Prof. Dr. Umut Çetin, London School of Economics
Datum, Zeit 23. Mai 2024, 17:15-18:15
Ort HG G 43
Abstract We consider the Kyle model in continuous time, where the informed traders face additional frictions. These frictions may arise due to difficulties in executing large portfolio, or legal penalties in case the informed trader is trading illegally on inside information. The equilibrium is characterised via the solution of a backward stochastic differential equation (BSDE) whose terminal condition is determined as the fixed point of a non-linear operator in equilibrium. A curious connection between the terminal condition of this BSDE and an entropic optimal transport problem appears in equilibrium. We find that informed traders consistently trade a constant multiple of the difference between the fundamental value and their anticipated market price just before their private information is disclosed to the public, reminiscent of the behaviour of a large trader in an Almgren-Chris model. If time permits, as an application to insider trading regulation, we also consider a regulator’s challenge of balancing price informativeness with minimising losses for uninformed traders, given a budget constraint. High legal penalties deter illegal trading and protect uninformed traders but make prices less efficient. An optimal policy suggests that if the cost of investigation exceeds its benefits, it’s best not to investigate.
Kyle’s model with penalties, entropy and BSDEsread_more
HG G 43
8. August 2024
17:15-18:15 		Dr. Florian Rossmannek
NTU Singapore
Details

Talks in Financial and Insurance Mathematics

Titel State-Space Systems as Dynamic Generative Models
Referent:in, Affiliation Dr. Florian Rossmannek, NTU Singapore
Datum, Zeit 8. August 2024, 17:15-18:15
Ort HG G 19.1
Abstract Reservoir computing is a powerful tool in learning temporal dynamics and forecasting time series. Although applications often have a stochastic flavour, the existing theory mainly deals with deterministic problems. This poses a significant gap between theory and practice, which we fill in this talk. We do so by establishing a stochastic version of the so-called echo state property, which is the key property needed for successful implementation. We will see that this equates to studying the behaviour of state-space systems as generative models and that the stochastic theory is much richer and much more intricate than its deterministic counterpart.
State-Space Systems as Dynamic Generative Modelsread_more
HG G 19.1

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