# 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 Technichal University of Munich, Business Campus, Garching (Monday, 14:15 to 17:00 - Garching, Business Campus, Parkring 11, Room BC1 2.02.01)

The dates of the Graduate Seminar in Financial and Actuarial Mathematics (WiSe 2017/2018) are:

- December 4, 2017
- January 8, 2018
- February 5, 2018

## Upcoming talks

(keine Einträge)

## Previous talks

### 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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### 08.05.2017 14:15 Aditi Dandapani: Martingales and strict local martingales

When discussing the nature of nonnegative solutions of SDEs,
making the distinction between a strict local martingale and a true
martingale can be very important. The papers of Delbaen, Shirakawa,
Mijatovic, Urusov, Lions, Musiela, Andersen, Piterbarg, Bernard, Cui, and
finally McLeish have studied the case of a one dimensional SDE, with or
without stochastic volatility. We present two concepts: how a solution of an
SDE which is a martingale can become a strict local martingale by the
addition of new information to the underlying filtration, and how various
components of a vector of SDEs can be strict local martingales for some
components of the system, and martingales for others. This is based on joint
work with Philip Protter, Professor at Columbia University.

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### 08.05.2017 15:00 Giorgia Riveccio (Parthenope University): Copula quantile regression for analysis of multiple time series

In financial researches and among risk management practitioners the analysis of multiple time-series is often conducted in a non-linear context. In addition, capturing the quantile conditional dependence structure could prove of interest in order to measure financial contagion risk. We propose a 3-stage estimation copula-based method applied to non-linear quantile dependence analysis of time-series vectors. This method aims to analyse the serial and cross-section dependence of time-series given specified quantiles, reducing the computational complexity. To the best of our knowledge, this is the first approach that combines the conditional quantile dependence analysis of multiple time-series with non-linear modelling by means of copula functions. Finally, we examine the conditional quantile behaviour of financial time-series with a non-linear copula quantile VAR model.
The talk is based on joint work with Giovanni De Luca.

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### 08.05.2017 16:05 Philipp Harms: Markovian representations of fractional Brownian motion and some applications in mathematical finance

A wide class of Gaussian processes, including fractional
Brownian motion, can be represented as linear functions of an
infinite-dimensional affine process. This opens the door to analyzing
such processes using tools from Markov processes and SPDEs. Moreover,
the affine structure makes computations tractable, and the
representation lends itself to numerical implementation. We will look
into some of this theory and its applications in mathematical finance.

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### 08.05.2017 16:50 Jeannette Woerner: Inference for the driving Lévy process of continuous-time moving average processes

Continuous-time moving average processes, defined as integrals of a deterministic kernel
function integrated with respect to a two sided Lévy process, provide a unifying framework
to different types of processes, including the popular examples of fractional Brownian
motion and fractional Lévy processes on the one side and Ornstein-Uhlenbeck processes
on the other side. The whole class of processes especially allows for a combination of a
given correlation structure with an infinitely divisible marginal distribution as it is desirable
for applications in finance, physics and hydrology.
So far inference for these processes is mainly concerned with estimating parameters
entering the kernel function which is responsible for the correlation structure. We now
consider the estimating problem for the driving Lévy process. We will provide two methods
working on different sets of conditions, one is based on a suitable integral transform, the
other on the Mellin transform.

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### 23.01.2017 14:15 Cagin Ararat, Ph.D. (Bilkent University, Ankara): Multi-objective risk-averse stochastic optimization

Two-stage risk-averse stochastic optimization is concerned with the minimization of a risk measure of a random cost function over the feasible choices of a deterministic and a random decision variable. We study the multi-objective version of this problem in which case the cost function is vector-valued and its risk is quantified via a multivariate (set-valued) risk measure. We reformulate the resulting problem as a convex vector optimization problem with set-valued constraints and propose customized versions of Benson’s algorithm to solve it. In particular, by randomizing the deterministic decision variable, we develop convex duality-based decomposition methods to solve the scalar subproblems appearing in Benson’s algorithm. The algorithm is illustrated on examples including the multi-asset portfolio optimization problem with transaction costs.

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### 23.01.2017 15:00 Lorenz Schneider, Ph.D. (EM Lyon) : Seasonal Stochastic Volatility and Correlation together with the Samuelson Effect in Commodity Futures Markets

We introduce a multi-factor stochastic volatility model based on the CIR/Heston volatility process that incorporates seasonality and the Samuelson effect. First, we give conditions on the seasonal term under which the corresponding volatility factor is well-defined. These conditions appear to be rather mild. Second, we calculate the joint characteristic function of two futures prices for different maturities in the proposed model. This characteristic function is analytic. Finally, we provide numerical illustrations in terms of implied volatility and correlation produced by the proposed model with five different specifications of the seasonality pattern. The model is found to be able to produce volatility smiles at the same time as a volatility term-structure that exhibits the Samuelson effect with a seasonal component. Correlation, instantaneous or implied from calendar spread option prices via a Gaussian copula, is also found to be seasonal.

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### 23.01.2017 16:15 Christa Cuchiero, Ph.D. (University of Vienna): Cover's universal portfolio, stochastic portfolio theory and the numéraire portfolio

Cover's celebrated theorem states that the long run yield of a properly chosen "universal" constant rebalanced portfolio is as good as the long run yield of the best retrospectively chosen constant rebalanced portfolio. The "universality" pertains to the fact that this result is modelfree, i.e., not dependent on an underlying stochastic process. We extend Cover's theorem to the setting of stochastic portfolio theory as initiated by R. Fernholz: the rebalancing rule need not to be constant anymore but may depend on the present state of the stock market. This result is complimented by a comparison with the log-optimal numéraire portfolio when fixing a stochastic model of the stock market. Roughly speaking, under appropriate assumptions, the optimal long run yield coincides for the three approaches mentioned in the title. We present our results in discrete as well as in continuous time. The talk is based on joint work with Walter Schachermayer and Leonard Wong.

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