Talks in Financial and Insurance Mathematics

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

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Autumn Semester 2019

Date / Time

Speaker

Title

Location

26 September 2019
17:15-18:15

Juan-Pablo Ortega
Juan-Pablo Ortega (Universität Sankt Gallen, Switzerland and CNRS, France)

Event Details

Talks in Financial and Insurance Mathematics

Title	Dynamic and Control Theoretical Aspects of Reservoir Computing
Speaker, Affiliation	Juan-Pablo Ortega, Juan-Pablo Ortega (Universität Sankt Gallen, Switzerland and CNRS, France)
Date, Time	26 September 2019, 17:15-18:15
Location	HG G 43 ETHz
Abstract	Reservoir computing (RC) carries out the learning of input/output systems by using families of state space systems in which the training of a small portion of their parameters suffices for excellent generalization properties. In this talk we shall analyze in detail the connection between various dynamic and control theoretical features of widely used families of RC families and their impact in basic learning theoretical goals, in particular in the development of bounds for the approximation and estimation errors and in the design of dimension reduction techniques.

Dynamic and Control Theoretical Aspects of Reservoir Computingread_more

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ETHz

3 October 2019
17:15-18:15

Valérie Chavez-Demoulin
University of Lausanne

Event Details

Talks in Financial and Insurance Mathematics

Title	Causal mechanism of extremes on a river network
Speaker, Affiliation	Valérie Chavez-Demoulin, University of Lausanne
Date, Time	3 October 2019, 17:15-18:15
Location	HG G 43 ETHz
Abstract	Extreme hydrological events in the Danube river basin may severely impact human populations and economic activity. One often characterizes the joint structure of the extreme events using the theory of multivariate and spatial extremes and its asymptotically justified models. There is interest however in cascading extreme events and whether one event causes another. In this work, we argue that an improved understanding of the mechanism underlying severe events is achieved by combining extreme value modelling and causal discovery. We construct a causal inference method relying on the notion of the Kolmogorov complexity of extreme conditional quantiles. Tail quantities are derived using multivariate extreme value models and causal-induced asymmetries in the data are explored through the minimum description length principle. Our CausEV, for Causality for Extreme Values, approach uncovers causal relations between summer extreme river discharges in the upper Danube basin and finds significant causal links between the Danube and its Alpine tributary Lech.

Causal mechanism of extremes on a river networkread_more

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ETHz

10 October 2019
17:15-18:15

Zenghu Li
Beijing Normal University

Event Details

Talks in Financial and Insurance Mathematics

Title	The approach of stochastic equations for continuous-state branching processes
Speaker, Affiliation	Zenghu Li, Beijing Normal University
Date, Time	10 October 2019, 17:15-18:15
Location	HG G 43
Abstract	A continuous-state branching process is the mathematical model for the evolution of a large population of small individuals. The process can be constructed as the strong solution to a stochastic integral equation driven by Gaussian and Poisson time-space noises. The genealogical structures of the population are represented by continuum random trees. More general population models take into consideration the influence of immigration, competition, environments and so on. The research in the subject has been undergoing rapid development and has led to better understanding of deep structures including Brownian excursions, stochastic flows, L\'{e}vy trees and planar maps. In this talk, we present a number of stochastic equations for continuous-state branching processes without or with immigration. We explain how the equations can be used in the study the structural properties of the models including: 1) Distributions of jumps in continuous-state branching processes, 2) Exponential ergodicity of continuous-state branching processes with immigration, 3) Asymptotics of estimators of the stable Cox--Ingersoll--Ross model.

The approach of stochastic equations for continuous-state branching processesread_more

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17 October 2019
17:15-18:15

Pierre Patie
Cornell University

Event Details

Talks in Financial and Insurance Mathematics

Title	Interweaving Relations And Polynomial Processes
Speaker, Affiliation	Pierre Patie, Cornell University
Date, Time	17 October 2019, 17:15-18:15
Location	HG G 43
Abstract	In this talk, we introduce the concept of interweaving relations as a strengthening of usual intertwining relations between Markov semigroups. We proceed by providing some interesting applications of this new idea which include the spectral decomposition, the characterization of ergodic constants and hypercontractivity estimates for general Markov semigroups. After enumerating a list of interweaving relations that have emerged from the recent literature ranging from discrete-to-continuous interacting particle models, to degenerate hypoelliptic Ornstein-Uhlenbeck processes, we will present a very detailed analysis of some non-local extensions of the classical Jacobi process. This talk is based on joint works with P. Cheridito (ETHZ), A. Srapionyan and A. Vaidyanathan (Cornell University), and, L. Miclo (IMT Toulouse).

Interweaving Relations And Polynomial Processesread_more

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24 October 2019
17:15-18:15

Hansjörg Albrecher
Université de Lausanne

Event Details

Talks in Financial and Insurance Mathematics

Title	Inhomogeneous phase-type constructions, matrix distributions and the modeling of heavy-tailed risks
Speaker, Affiliation	Hansjörg Albrecher, Université de Lausanne
Date, Time	24 October 2019, 17:15-18:15
Location	HG G 43
Abstract	In this talk we discuss the extension of the construction principle of phase-type (PH) distributions to allow for inhomogeneous transition rates and show that this naturally leads to direct probabilistic descriptions of certain transformations of PH distributions. In particular, the resulting matrix distributions enable to carry over fitting properties of PH distributions to distributions with heavy tails, providing a general modelling framework for heavy-tail phenomena. We also discuss related randomized versions involving Mittag-Leffler distributions and illustrate the versatility and parsimony of the proposed approach for the modelling of real-world insurance data.

Inhomogeneous phase-type constructions, matrix distributions and the modeling of heavy-tailed risksread_more

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31 October 2019
17:15-18:15

Jean Pinquet
Université Paris Nanterre

Event Details

Talks in Financial and Insurance Mathematics

Title	Poisson models with dynamic random effects and nonnegative credibilities per period
Speaker, Affiliation	Jean Pinquet, Université Paris Nanterre
Date, Time	31 October 2019, 17:15-18:15
Location	HG G 43
Abstract	This paper provides a toolbox for the credibility analysis of frequency risks, with allowance for the seniority of claims and of risk exposure. We use Poisson models with dynamic and second-order stationary random effects that ensure nonnegative credibilities per period. We specify classes of autocovariance functions that are compatible with positive random effects and that entail nonnegative credibilities regardless of the risk exposure. Random effects with nonnegative generalized partial autocorrelations are shown to imply nonnegative credibilities. This holds for ARFIMA(0,d,0) models. The AR(p) time series that ensure nonnegative credibilities are specified from their precision matrices. The compatibility of these semiparametric models with log-Gaussian random effects is verified. Gaussian sequences with ARFIMA(0,d,0) specifications, which are then exponentiated entrywise, provide positive random effects that also imply nonnegative credibilities. Dynamic random effects applied to Poisson distributions are retained as products of two uncorrelated and positive components: the first is time-invariant, whereas the autocovariance function of the second vanishes at infinity and ensures nonnegative credibilities. The limit credibility is related to the three levels for the length of the memory in the random effects. The limit credibility is less than one in the short memory case, and a formula is provided.

Poisson models with dynamic random effects and nonnegative credibilities per periodread_more

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7 November 2019
17:15-18:15

Daniel Bartl
Universität Wien

Event Details

Talks in Financial and Insurance Mathematics

Title	All Adapted Topologies are Equal
Speaker, Affiliation	Daniel Bartl, Universität Wien
Date, Time	7 November 2019, 17:15-18:15
Location	HG G 43
Abstract	Several researchers have introduced topological structures on the set of laws of stochastic processes. A unifying goal of these authors is to strengthen the usual weak topology in order to adequately capture the temporal structure of stochastic processes. We find that all of these seemingly independent approaches define the same topology in finite discrete time. Moreover, we explain how optimal transport theory can be used obtain a compatible metric that is both tractable ensures Lipschitz continuity of optimal stopping and several problems in mathematical finance. Joint work of J. Backhoff, M. Beiglboeck, M. Eder

All Adapted Topologies are Equalread_more

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21 November 2019
17:15-18:15

Mathias Millberg Lindholm
Stockholm University

Event Details

Talks in Financial and Insurance Mathematics

Title	Claims reserving when making use of claim counts
Speaker, Affiliation	Mathias Millberg Lindholm, Stockholm University
Date, Time	21 November 2019, 17:15-18:15
Location	HG G 43
Abstract	In this talk we will discuss how claim counts can be used in order to obtain separate RBNS and IBNR reserves starting from a constructive discrete time description of the claim dynamics. This will allow us to start at a "micro" level, but, given certain circumstances, obtain "macro" level predictors closely connected to well-studied regression models for which it is possible to obtain e.g. analytical prediction error estimates. Further, it is possible to show that the classical chain ladder technique may be seen as a large exposure (i.e. no. of contract) approximation of the introduced models. Finally, based on these observations for constructive models, we argue that it is reasonable to mimic these dynamics for algorithmic ("black-box" models) and illustrate how this, again, allows us to obtain separate RBNS and IBNR reserves together with simulation based prediction error estimates following the route laid out in a recent paper by Gabrielli et al. (2019). This talk will mainly be based on work done in collaboration with Richard Verrall and Felix Wahl.

Claims reserving when making use of claim countsread_more

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28 November 2019
17:15-18:15

Sabrina Mulinacci
University of Bologna

Event Details

Talks in Financial and Insurance Mathematics

Title	Joint Life Insurance Pricing Using Extended Marshall-Olkin Models
Speaker, Affiliation	Sabrina Mulinacci, University of Bologna
Date, Time	28 November 2019, 17:15-18:15
Location	HG G 43
Abstract	Bivariate copula functions have been widely used to model the dependence structure between the residual lifetimes of the two individuals in a couple. However, most commonly used copulas are absolutely continuous and do not allow for the case of a simultaneous death due to some catastrophic event. In order to include this case, we consider the Extended Marshall-Olkin model which is based on the combination of two approaches: the absolutely continuous copula approach,where the copula is used to capture dependencies due to environmental factors shared by the two lives, and the classical Marshall-Olkin model, where the association is given by accounting for a fatal event causing the simultaneous death of the two lives. Relevant properties of the Extended Marshall-Olkin model are analyzed and the behaviour of the induced mortality intensities studied. The model is then applied to a sample of censored residual lifetimes of couples of insureds extracted from a dataset of annuities contracts of a large Canadian life insurance company. Finally, some possible extensions of the model will be discussed. The talk is based on joint work with Fabio Gobbi (Department of Statistics, University of Bologna, Italy) and Nikolai Kolev (Institute of Mathematics and Statistics, University of São Paulo, Brazil).

Joint Life Insurance Pricing Using Extended Marshall-Olkin Modelsread_more

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12 December 2019
17:15-18:15

Christian Furrer
University of Copenhagen

Event Details

Talks in Financial and Insurance Mathematics

Title	On Forward Transition Rates And Representation of Some Non-classic Payment Processes via Change-of-measure Techniques
Speaker, Affiliation	Christian Furrer, University of Copenhagen
Date, Time	12 December 2019, 17:15-18:15
Location	HG G 43
Abstract	There is an increasing interest in representation and efficient computation of expected accumulated life insurance cash flows in the presence of policyholder behavior and double stochasticity. The inclusion of policyholder behavior leads to scaled payments with the scaling factor depending on the time of specific events such as retirement. We associate to these modified payments a new probability measure allowing for standard representation of the expected cash flows. In the context of doubly stochastic Markov models, we explore the concept of forward transition rates. We provide a unified theoretical framework and compare recent proposals in the literature. Finally, an assessment of the scope and limits of the aforementioned methods in relation to current actuarial practice is given.

On Forward Transition Rates And Representation of Some Non-classic Payment Processes via Change-of-measure Techniquesread_more

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9 January 2020
17:15-18:15

Christian Bayer
Weierstrass Institute (Berlin)

Event Details

Talks in Financial and Insurance Mathematics

Title	Pricing American Options by Exercise Rate Optimization
Speaker, Affiliation	Christian Bayer, Weierstrass Institute (Berlin)
Date, Time	9 January 2020, 17:15-18:15
Location	HG G 43
Abstract	We present a novel method for the numerical pricing of American options based on Monte Carlo simulation and the optimization of exercise strategies. Previous solutions to this problem either explicitly or implicitly determine so-called optimal exercise regions, which consist of points in time and space at which a given option is exercised. In contrast, our method determines the exercise rates of randomized exercise strategies. We show that the supremum of the corresponding stochastic optimization problem provides the correct option price. By integrating analytically over the random exercise decision, we obtain an objective function that is differentiable with respect to perturbations of the exercise rate even for finitely many sample paths. The global optimum of this function can be approached gradually when starting from a constant exercise rate. Numerical experiments on vanilla put options in the multivariate Black--Scholes model and a preliminary theoretical analysis underline the efficiency of our method, both with respect to the number of time-discretization steps and the required number of degrees of freedom in the parametrization of the exercise rates. Finally, we demonstrate the flexibility of our method through numerical experiments on max call options in the classical Black--Scholes model, and vanilla put options in both the Heston model and the non-Markovian rough Bergomi model.

Pricing American Options by Exercise Rate Optimizationread_more

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