Post/Doctoral Seminar in Mathematical Finance

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Spring Semester 2019

Date / Time

Speaker

Title

Location

19 February 2019
15:15-16:30

Dr. Anastasis Kratsios
ETH Zürich

Details

Post/Doctoral Seminar in Mathematical Finance

Title	Risk-Averse Conditional Expectation and Shortfall-Regression
Speaker, Affiliation	Dr. Anastasis Kratsios, ETH Zürich
Date, Time	19 February 2019, 15:15-16:30
Location	HG G 19.1
Abstract	The risk-averse conditional expectation is introduced. A characterization is obtained through in the form of a decomposition theorem, expressing the risk-averse conditional expectation as a corrected conditional expectation. As an application, the expected shortfall is considered in the linear Gaussian case and used to obtain closed form expressions. Its performance is evaluated through predictive analysis in the cryptocurrency market.

Risk-Averse Conditional Expectation and Shortfall-Regressionread_more

HG G 19.1

5 March 2019
15:15-16:30

Prof. Dr. Stephan Sturm
Worcester Polytechnic Institute

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Post/Doctoral Seminar in Mathematical Finance

Title	Portfolio Optimization Using the Distribution Builder - Intertemporal Consumption and Incomplete Markets
Speaker, Affiliation	Prof. Dr. Stephan Sturm, Worcester Polytechnic Institute
Date, Time	5 March 2019, 15:15-16:30
Location	HG G 19.2
Abstract	Portfolio optimization subject to personal preferences of an economic agent is a mainstay in financial mathematics. The common way this problem is set up is via a utility function representing the agent's preferences. This supposes in practice that agents behave rationally as well as that there is a practical and tangible way to determine their utility function. An alternative approach, known as Distribution Builder, has been proposed by Goldstein, Sharpe and Blythe: investors should determine directly the distribution of the terminal payoff given their budget constraint. In this talk we first review the concept of the distribution builder and the mathematical model behind it, and then propose extensions to optimization of intertemporal consumption and in incomplete markets. This is based on ongoing joint work with Carole Bernard and Mauricio Elizalde Mejía.

Portfolio Optimization Using the Distribution Builder - Intertemporal Consumption and Incomplete Marketsread_more

HG G 19.2

6 March 2019
15:15-16:30

Dr. Jameson Graber
Baylor University

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Post/Doctoral Seminar in Mathematical Finance

Title	Mean Field Games Models for Exhaustible Commodities Trade
Speaker, Affiliation	Dr. Jameson Graber, Baylor University
Date, Time	6 March 2019, 15:15-16:30
Location	HG G 19.1
Abstract	Mean field game theory allows us to model competitive situations with large numbers of actors using systems of PDE comprising a Hamilton-Jacobi equation coupled to a Fokker-Planck equation, where the coupling occurs via the drift term. Several models have been proposed recently to describe producers of an exhaustible commodity such as oil. Existence, uniqueness, and regularity of solutions is still an open question in many cases. In this talk I will give some recent results in this direction as well as an application to approximate Nash equilibria for N-player games.

Mean Field Games Models for Exhaustible Commodities Traderead_more

HG G 19.1

19 March 2019
15:15-16:30

Diyora Salimova
ETH Zürich

Details

Post/Doctoral Seminar in Mathematical Finance

Title	Deep Neural Networks in the Numerical Approximation of Kolmogorov PDEs
Speaker, Affiliation	Diyora Salimova, ETH Zürich
Date, Time	19 March 2019, 15:15-16:30
Location	HG G 19.1
Abstract	In recent years, deep artificial neural networks (DNNs) have very successfully been used in numerical simulations for numerous computational problems including object and face recognition, natural language processing, fraud detection, computational advertisement, and numerical approximations of partial differential equations (PDEs). Such numerical simulations indicate that DNNs seem to admit the fundamental flexibility to overcome the curse of dimensionality in the sense that the number of real parameters used to describe the DNN grows at most polynomially in both the reciprocal of the prescribed approximation accuracy and the dimension of the function which the DNN aims to approximate in such computational problems. In this talk I present our recent result which rigorously proves that DNNs do overcome the curse of dimensionality in the numerical approximation of Kolmogorov PDEs with constant diffusion and nonlinear drift coefficients.

Deep Neural Networks in the Numerical Approximation of Kolmogorov PDEsread_more

HG G 19.1

7 May 2019
15:15-16:30

Andrea Gabrielli
ETH Zürich

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Post/Doctoral Seminar in Mathematical Finance

Title	A Neural Network Boosted Double Over-Dispersed Poisson Claims Reserving Model
Speaker, Affiliation	Andrea Gabrielli, ETH Zürich
Date, Time	7 May 2019, 15:15-16:30
Location	HG G 19.1
Abstract	We present an actuarial loss reserving technique that takes into account both claim counts and claim amounts. Separate (over-dispersed) Poisson models for the claim counts and the claim amounts are combined by a joint embedding into a neural network architecture. As a starting point of the neural network calibration we use exactly these two separate (over-dispersed) Poisson models. Such a nested model can be interpreted as a boosting machine. It allows for joint modeling and mutual learning of claim counts and claim amounts beyond the two individual (over-dispersed) Poisson models.

A Neural Network Boosted Double Over-Dispersed Poisson Claims Reserving Modelread_more

HG G 19.1

14 May 2019
15:15-16:30

Wahid Khosrawi-Sardroudi
ETH Zürich

Details

Post/Doctoral Seminar in Mathematical Finance

Title	A Neural Network Approach to Local Stochastic Volatility Calibration
Speaker, Affiliation	Wahid Khosrawi-Sardroudi, ETH Zürich
Date, Time	14 May 2019, 15:15-16:30
Location	HG G 19.1
Abstract	A central task in modeling, which has to be performed each day in banks and financial institutions, is to calibrate models to market and historical data. So far the choice which models should be used was not only driven by their capacity of capturing empirically the observed market features well, but rather by computational tractability considerations. Due to recent work in the context of machine learning, this notion of tractability has changed significantly. In this work, we show how a neural network approach can be applied to the calibration of (multivariate) local stochastic volatility models. We will see how an efficient calibration is possible without the need of interpolation methods for the financial data. Joint work with Christa Cuchiero and Josef Teichmann.

A Neural Network Approach to Local Stochastic Volatility Calibrationread_more

HG G 19.1

21 May 2019
15:15-16:30

Dr. Blanka Horváth
King's College London

Details

Post/Doctoral Seminar in Mathematical Finance

Title	Deep Learning Volatility
Speaker, Affiliation	Dr. Blanka Horváth, King's College London
Date, Time	21 May 2019, 15:15-16:30
Location	HG G 19.2
Abstract	We present a consistent neural network based calibration method for a number of volatility models-including the rough volatility family-that performs the calibration task within a few milliseconds for the full implied volatility surface. The aim of neural networks in this work is an off-line approximation of complex pricing functions, which are difficult to represent or time-consuming to evaluate by other means. We highlight how this perspective opens new horizons for quantitative modelling: The calibration bottleneck posed by a slow pricing of derivative contracts is lifted. This brings several model families (such as rough volatility models) within the scope of applicability in industry practice. As customary for machine learning, the form in which information from available data is extracted and stored is crucial for network performance. With this in mind we discuss how our approach addresses the usual challenges of machine learning solutions in a financial context (availability of training data, interpretability of results for regulators, control over generalisation errors). We present specific architectures for price approximation and calibration and optimize these with respect different objectives regarding accuracy, speed and robustness. We also find that including the intermediate step of learning pricing functions of (classical or rough) models before calibration significantly improves network performance compared to direct calibration to data.

Deep Learning Volatilityread_more

HG G 19.2

28 May 2019
15:15-16:30

Robert Crowell
ETH Zürich

Details

Post/Doctoral Seminar in Mathematical Finance

Title	Dynamic Programming Techniques for Principal-Agent Models
Speaker, Affiliation	Robert Crowell, ETH Zürich
Date, Time	28 May 2019, 15:15-16:30
Location	HG G 19.2
Abstract	We give an overview of modelling approaches for principal-agent models with moral hazard. This class of models is used in contracting theory to analyse strategic interactions with contracts that can be made contingent upon the state of a controlled system, but not the controls themselves. Recent results obtained by employing classical techniques from dynamic programming and BSDE, as well as more recent developments from 2BSDE theory are surveyed.

Dynamic Programming Techniques for Principal-Agent Modelsread_more

HG G 19.2

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