Insurance Mathematics and Stochastic Finance

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Post/Doctoral Seminar in Mathematical Finance

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Autumn Semester 2019

Date / Time Speaker Title Location
1 October 2019
15:15-16:15 		Dr. Wahid Khosrawi
ETH Zurich
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Post/Doctoral Seminar in Mathematical Finance

Title Polynomial semimartingales
Speaker, Affiliation Dr. Wahid Khosrawi, ETH Zurich
Date, Time 1 October 2019, 15:15-16:15
Location HG G 19.2
Abstract We extend the class of polynomial processes to incorporate examples beyond stochastic continuity. Such an extension has been recently provided in the affine case and we show how similar results can be obtained by developing a suitable two-parameter analogon to the theory of finite dimensional one-parameter semigroups. In particular we show how this new class of processes can be characterized by the polynomial structure of their semimartingale characteristics. Joint work with Thorsten Schmidt (University of Freiburg).
Polynomial semimartingalesread_more
HG G 19.2
8 October 2019
15:15-16:15 		Dr. Andrew Allan
ETH Zürich
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Post/Doctoral Seminar in Mathematical Finance

Title Parameter Uncertainty in Stochastic Filtering
Speaker, Affiliation Dr. Andrew Allan, ETH Zürich
Date, Time 8 October 2019, 15:15-16:15
Location HG G 19.2
Abstract We consider the problem of filtering - that is, estimating the current state of a stochastic 'signal' process from noisy observations - under uncertainty of both the dynamics of the signal and of its relationship with our observations. We take a nonlinear expectations approach, which leads naturally to a pathwise stochastic optimal control problem, the solution of which provides a new way of 'learning' unknown parameter values dynamically through time.
Parameter Uncertainty in Stochastic Filteringread_more
HG G 19.2
22 October 2019
15:15-16:15 		Dr. Anastasis Kratsios
ETH Zurich, Switzerland
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Post/Doctoral Seminar in Mathematical Finance

Title NEU Meta-Learning, Universal Approximation Properties, and Learning Model-Free Loss-Functions
Speaker, Affiliation Dr. Anastasis Kratsios, ETH Zurich, Switzerland
Date, Time 22 October 2019, 15:15-16:15
Location HG G 19.2
Abstract We introduce a new meta-learning procedure, called non-Euclidean upgrading (NEU), which learns algorithm-specific geometries by deforming the ambient space until the algorithm can achieve optimal performance. We prove that these deformations have several novel and semi-classical universal approximation properties. These deformations can be used to approximate any continuous, Borel, or modular-Lebesgue integrable functions to arbitrary precision. Further, these deformations can transport any data-set into any other data-set in a finite number of iterations while leaving most of the space fixed. The NEU meta-algorithm embeds these deformations into a wide range of learning algorithms. We prove that the NEU version of the original algorithm must perform better than the original learning algorithm. Moreover, by quantifying model-free learning algorithms as specific unconstrained optimization problems, we find that the NEU version of a learning algorithm must perform better than the model-free extension of the original algorithm. The properties and performance of the NEU meta-algorithm are examined in various simulation studies and applications to financial data. arXiv:1809.00082
NEU Meta-Learning, Universal Approximation Properties, and Learning Model-Free Loss-Functionsread_more
HG G 19.2
29 October 2019
15:15-16:15 		Prof. Dr. Eduardo Abi Jaber
Université Paris 1 Panthéon-Sorbonne
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Post/Doctoral Seminar in Mathematical Finance

Title Linear Quadratic optimal control for a class of stochastic Volterra equations
Speaker, Affiliation Prof. Dr. Eduardo Abi Jaber, Université Paris 1 Panthéon-Sorbonne
Date, Time 29 October 2019, 15:15-16:15
Location HG G 19.2
Abstract We treat Linear Quadratic optimal control problems for a class of stochastic Volterra equations of convolution type. These equations are in general neither Markovian nor semimartingales, and include the fractional Brownian motion with Hurst index smaller than 1=2 as a special case. We prove that the value function is of linear quadratic form with a linear optimal feedback control, depending on infinite dimensional Riccati equations. Furthermore, we show that the stochastic Volterra optimization problem can be approximated by conventional fi nite dimensional Markovian Linear Quadratic problems, which is of crucial importance for numerical implementation.
Linear Quadratic optimal control for a class of stochastic Volterra equationsread_more
HG G 19.2
5 November 2019
15:15-16:15 		Thuan Nguyen
Jyväskylä University
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Post/Doctoral Seminar in Mathematical Finance

Title About an explicit mean-variance hedging strategy, discretization error and bounded mean oscillation
Speaker, Affiliation Thuan Nguyen, Jyväskylä University
Date, Time 5 November 2019, 15:15-16:15
Location HG G 19.2
Abstract Assume that the stock price is modelled by an exponential Lévy process S. We begin with an explicit form for the mean-variance hedging strategy of a European type option under an arbitrary equivalent martingale measure. That formula is established by exploiting Malliavin calculus without requiring any regularity from the payoff function nor any specific structure of the underlying Lévy process. We continue by discussing the error process resulting from the discretization of a stochastic integral driven by S using a deterministic time net. Our aim is to measure that error ``locally'' in L_2, and it turns out that the weighted bounded mean oscillation spaces naturally arise for such a purpose. If time permits, we also propose an approximation scheme for stochastic integrals where the jump sizes of S are taken into account which enables L_p estimates (p>2) for the corresponding global error.
About an explicit mean-variance hedging strategy, discretization error and bounded mean oscillationread_more
HG G 19.2
26 November 2019
15:15-16:15 		Dr. Nikolay Gudkov
ETH Zurich, Switzerland
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Post/Doctoral Seminar in Mathematical Finance

Title Application of Power Series Approximation Techniques to the pricing and hedging of European Style Options
Speaker, Affiliation Dr. Nikolay Gudkov, ETH Zurich, Switzerland
Date, Time 26 November 2019, 15:15-16:15
Location HG G 19.2
Abstract Fourier transforms provide versatile techniques for the pricing of financial derivative securities. In applying such techniques, a typical derivative valuation expression is often written as an inner product of the Fourier transform of the payoff and the characteristic function of the underlying asset dynamics. Some modelling specifications imply that it might be challenging to find a closed-form expression for the characteristic function. In such situations, numerical approximations have to be employed. This paper utilises the power series approximation technique in finding explicit expressions of the characteristic function for the underlying stochastic variables. We analyse the convergence and accuracy of the method in the context of valuing European style options written on underlying securities whose dynamics evolve under the influence of multiple Heston-type stochastic volatilities Heston (1993) and Cox-Ingersoll-Ross stochastic interest rates Cox (1985). The paper contributes to the existing literature four-folds by (i) adapting the valuation technique to long-dated instruments; (ii) providing an adjustment to the series of the points around which the power series expansion is performed; (iii) analysing the performance of different strategies for hedging European call options; (iv) applying the power series approach to the valuation of guaranteed minimum accumulation benefit riders embedded in variable annuity contracts. Our results demonstrate the high computational efficiency of the series approximation method for the computation of derivative prices and hedge ratios.
Application of Power Series Approximation Techniques to the pricing and hedging of European Style Optionsread_more
HG G 19.2
3 December 2019
15:15-16:15 		Xi Kleisinger-Yu
ETH Zurich, Switzerland
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Post/Doctoral Seminar in Mathematical Finance

Title A multi-factor polynomial framework for long-term electricity forwards with delivery period
Speaker, Affiliation Xi Kleisinger-Yu, ETH Zurich, Switzerland
Date, Time 3 December 2019, 15:15-16:15
Location HG G 19.2
Abstract We propose a multi-factor polynomial framework to model and hedge long-term electricity contracts with delivery period. This framework has various advantages: the computation of forwards and correlation between different forwards are fully explicit, and the model can be calibrated to observed electricity forward curves easily and well. Electricity markets suffer from non-storability and poor medium- to long-term liquidity. Therefore, we suggest a rolling hedge which only uses liquid forward contracts and is risk-minimizing in the sense of Föllmer and Schweizer. We calibrate the model to over eight years of German power calendar year forward curves and investigate the quality of the risk-minimizing hedge over various time horizons.
A multi-factor polynomial framework for long-term electricity forwards with delivery periodread_more
HG G 19.2
10 December 2019
15:15-16:15 		Dr. Fenghui Yu
ETH Zurich, Switzerland
Details

Post/Doctoral Seminar in Mathematical Finance

Title Credit Risk Modelling with Hidden Markovian Regime-Switching Process
Speaker, Affiliation Dr. Fenghui Yu, ETH Zurich, Switzerland
Date, Time 10 December 2019, 15:15-16:15
Location HG G 19.2
Abstract A generalized reduced-form intensity-based credit model with a hidden Markovian regime-switching process is developed for credit risk management. The intensities of defaults are determined by the hidden economic states which are governed by a Markov chain, as well as the past defaults. The model is applicable to a wide class of default intensities with various forms of dependent structures. For the hidden Markov process, a filtering method is proposed for extracting the underlying state given the observation processes. Closed-form formulas for the joint distribution of multiple default times are derived without imposing stringent assumptions on the form of default intensities. In addition, applications in credit risk management are also discussed.
Credit Risk Modelling with Hidden Markovian Regime-Switching Processread_more
HG G 19.2

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