# Seminar on Financial and Actuarial Mathematics

The seminar is organized by Prof. Biagini, Prof. Czado, Prof. Glau, Prof. Klüppelberg, Prof. Meyer-Brandis, Prof. Scherer, Prof. Svindland and Prof. Zagst. The venue of the seminar changes on a regular basis between the TUM (Garching, Business Campus, Parkring 11)* *and the *Mathematical Institute of the LMU* (München, Theresienstraße 39).

Currently the Seminar takes place at the Ludwig-Maximilians-Universität München, Theresienstraße 39, Munich, Room No. B349 (on Mondays, 14:15 to 17:00)

The dates of the Graduate Seminar in Financial and Actuarial Mathematics (SoSe 2018) are:

- May 7, 2018
- June 11, 2018
- July 9, 2018

## Upcoming talks

(no entries)

## Previous talks

### 07.05.2018 14:15 Prof. Michael Ludkowski: Marrying Stochastic Control and Machine Learning: from Bermudan Options to Natural Gas Storage and Microgrids

Simulation-based strategies bring the machine learning toolbox to numerical resolution of stochastic control models. I will begin by reviewing the history of this idea, starting with the seminal work by Longstaff-Schwartz and through the popularized Regression Monte Carlo framework. I will then describe the Dynamic Emulation Algorithm (DEA) that we developed, which unifies the different existing approaches in a single modular template and emphasizes the two central aspects of regression architecture and experimental design. Among novel DEA implementations, I will discuss Gaussian process regression, as well as numerous simulation designs (space-filling, sequential, adaptive, batched). The overall DEA template is illustrated with multiple examples drawing from Bermudan option pricing, natural gas storage valuation, and optimal control of back-up generator in a power microgrid. This is partly joint work with Aditya Maheshwari (UCSB).

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### 07.05.2018 15:00 Dr. Tobias Kley, Berlin: Quantile-Based Spectral Analysis of Time Series

Classical methods for the spectral analysis of time series account for covariance-related serial dependencies. This talk will begin with a brief introduction to these traditional procedures. Then, an alternative method is presented, where, instead of covariances, differences of copulas of pairs of observations and the independence copula are used to quantify serial dependencies. The Fourier transformation of these copulas is considered and used to define quantile-based spectral quantities. They allow to separate marginal and serial aspects of a time series and intrinsically provide more information about the conditional distribution than the classical location-scale model. Thus, quantile-based spectral analysis is more informative than the traditional spectral analysis based on covariances. For an observed time series the new spectral quantities are then estimated. The asymptotic properties, including the order of the bias and process convergence, of the estimator (a function of two quantile levels) are established. The results are applicable without restrictive distributional assumptions such as the existence of finite moments and only a weak form of mixing, such as alpha-mixing, is required.

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### 07.05.2018 16:00 Dr. Gregor Kastner, Wien: Bayesian Time-Varying Covariance Estimation in Many Dimensions using Sparse Factor Stochastic Volatility Models

We address the curse of dimensionality in dynamic covariance estimation by modeling the underlying co-volatility dynamics of a time series vector through latent time-varying stochastic factors. The use of a global-local shrinkage prior for the elements of the factor loadings matrix pulls loadings on superfluous factors towards zero. To demonstrate the merits of the proposed framework, the model is applied to simulated data as well as to daily log-returns of 300 S&P 500 members. Our approach yields precise correlation estimates, strong implied minimum variance portfolio performance and superior forecasting accuracy in terms of log predictive scores when compared to typical benchmarks. Furthermore, we discuss the applicability of the method to capture conditional heteroskedasticity in large vector autoregressions.

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### 04.12.2017 14:15 Alexander Szimayer: Rating Under Asymmetric Information

We analyze how a firm’s reputation and track record affect its rating and cost of debt. We model a setting in which outsiders such as a rating agency and the firm’s creditors continuously update their assessment of the firm’s true state described by its cash flow. They observe the latter only imperfectly due to asymmetric information. Other things equal, the rating agency optimally rates a firm with the same observed cash flow higher, if the historical minimum is sufficiently low. Thus, the rating is not only driven by the most recent information, but history matters. The rating agency refines its unbiased cash flow estimate by ruling out the most overestimated types, leading to an overestimation at default. In response, the firm delays default and lower asset values are available to creditors upon default.

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### 04.12.2017 15:00 Harry Joe: Estimation of tail dependence coefficients and extreme joint tail probabilities

Let C be a d-dimensional copula. With a random sample from this copula, several methods are introduced for estimation of the upper and lower tail dependence coefficients, as well as extreme joint tail probabilities such as the probability that all variables exceed their 0.99 quantiles and all variables are below their 0.01 quantiles.
The main theory is based on (i) a tail expansion of the distribution D() of maximum or minimum of the random vector on the copula scale and (ii) a tail expansion of an integral of D(). Item (ii) comes from investigating a tail-weighted dependence measure that is related to an estimate of the extremal index for multivariate extreme value data. The estimation methods for extreme joint tail probabilities consist of (a) likelihood-based threshold methods (for observations of appropriate maxima/minima that lie beyond a threshold, or (b) weighted regression
methods. Examples will be used for illustration of the main ideas.

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### 24.07.2017 14:15 Stefan Weber: Models and Measures of Systemic Risk

Systemic risk refers to the risk that a financial system is susceptible to failures due to the characteristics of the system itself. The tremendous cost of this type of risk requires the design and implementation of tools for the efficient macroprudential regulation of financial institutions. The first part of the talk presents a comprehensive model of a financial system that integrates network effects, bankruptcy costs, cross-holdings, and fire sales. The second part discusses a multivariate approach to measuring systemic risk.
The talk is based on joint work with Zachary G. Feinstein, Birgit Rudloff, and Kerstin Weske.

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### 19.06.2017 16:30 Sascha Desmettre: Generalized Pareto processes and liquidity

Motivated by the modeling of liquidity risk in fund management in a dynamic setting, we propose and investigate a class of time series models with generalized Pareto marginals: the autoregressive generalized Pareto process (ARGP), a modified ARGP (MARGP) and a thresholded ARGP (TARGP). These models are able to capture key data features apparent in fund liquidity data and reflect the underlying phenomena via easily interpreted, low-dimensional model parameters. We establish stationarity and ergodicity, provide a link to the class of shot-noise processes, and determine the associated interarrival distributions for exceedances. Moreover, we provide estimators for all relevant model parameters and establish consistency and asymptotic normality for all estimators (except the threshold parameter, which as usual must be dealt with separately). Finally, we illustrate our approach using real-world fund redemption data, and we discuss the goodness-of-fit of the estimated models.

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