Departement Mathematik

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Herbstsemester 2017

Datum / Zeit Referent:in Titel Ort
21. September 2017
17:15-18:15 		Marco Cirant
University of Padova
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Talks in Financial and Insurance Mathematics

Titel Some results on aggregation in Mean-Field Games
Referent:in, Affiliation Marco Cirant, University of Padova
Datum, Zeit 21. September 2017, 17:15-18:15
Ort HG G 43
Abstract In this talk we consider stationary and time-dependent viscous Mean-Field Games systems in the case of local, decreasing and unbounded coupling. These systems arise in mean field game theory, and describe Nash equilibria of games with a large number of agents aiming at aggregation, i.e. at converging to a common state. From the PDE viewpoint, several issues are intrinsic in this framework, mainly caused by the lack of regularizing effects induced by increasing monotonicity of the coupling. Non-existence, non-uniqueness of solutions, non-smoothness, and concentration are likely to arise. Even more than in the competitive case, the assumptions on the Hamiltonian, the growth of the coupling and the dimension of the state space affect the qualitative behavior of the system. We use a variational approach based on convex optimization methods to show the existence of solutions, and prove that such solutions are smooth by blow-up arguments.
Some results on aggregation in Mean-Field Gamesread_more
HG G 43
28. September 2017
17:15-18:15 		Marius Hofert
University of Waterloo
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Talks in Financial and Insurance Mathematics

Titel Visualizing high-dimensional data: zenplots and zenpaths
Referent:in, Affiliation Marius Hofert, University of Waterloo
Datum, Zeit 28. September 2017, 17:15-18:15
Ort HG G 43
Abstract This talk concerns Data Visualization as part of Data Science. It raises the question how high-dimensional data can be visualized. The notion of a zenpath and a zenplot is introduced to search and visualize high-dimensional data for model building and statistical inference. By using any measure of "interestingness", a zenpath can construct paths through pairs of variables in different ways, which can then be laid out and displayed by a zenplot. Zenpaths and zenplots are useful tools for exploring dependence in high-dimensional data, for example, from the realm of finance, insurance and quantitative risk management. All presented algorithms are implemented using the R package zenplots.
Visualizing high-dimensional data: zenplots and zenpathsread_more
HG G 43
12. Oktober 2017
17:15-18:15 		Sergio Pulido
ENSIIE
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Talks in Financial and Insurance Mathematics

Titel The characteristic function of affine Volterra processes
Referent:in, Affiliation Sergio Pulido, ENSIIE
Datum, Zeit 12. Oktober 2017, 17:15-18:15
Ort HG G 43
Abstract A growing body of empirical research indicates that volatility fluctuates more rapidly than Brownian motion, which is inconsistent with standard semimartingale models. Fractional volatility models and their relatives have emerged as compelling alternatives; however, their non-Markovian structure makes computations more difficult. We show that, for a large class of such models, it is nonetheless possible to compute the characteristic function by solving an integral equation similar to the Riccati equations associated with standard affine processes.
The characteristic function of affine Volterra processesread_more
HG G 43
19. Oktober 2017
17:15-18:15 		Sebastian Engelke
EPF Lausanne
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Talks in Financial and Insurance Mathematics

Titel Extremal (in)dependence structures of copulas with multiplicative constructions
Referent:in, Affiliation Sebastian Engelke, EPF Lausanne
Datum, Zeit 19. Oktober 2017, 17:15-18:15
Ort HG G 43
Abstract A main construction principle for bivariate copulas with desirable tail properties uses the multiplicative representation $R(W_1, W_2)$, where $R$ is a univariate scaling variable, and $W = (W_1, W_2)$ is a bivariate random vector. Numerous models in extreme value statistics are particular cases of this construction, and, depending on the distributions of $R$ and $W$, they can result in either asymptotic dependence or asymptotic independence. We systematically characterize the extremal dependence structures arising from such multiplicative constructions. It turns out to be crucial how the tail decay rate in $R$ impacts the tail dependence of $(W_1, W_2)$. The results allow to recover the extremal properties of existing models in a unified way, and, on the other hand, they can be used to construct new statistical models with flexible tail (in)dependence structures. The theory can also be applied to understand tail properties of spatial models. This is joint work with Thomas Opitz and Jennifer Wadsworth.
Extremal (in)dependence structures of copulas with multiplicative constructionsread_more
HG G 43
26. Oktober 2017
17:15-18:15 		Claudio Fontana
Université Paris-Diderot
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Talks in Financial and Insurance Mathematics

Titel The Value of Informational Arbitrage
Referent:in, Affiliation Claudio Fontana, Université Paris-Diderot
Datum, Zeit 26. Oktober 2017, 17:15-18:15
Ort HG G 43
Abstract In the context of a general complete semimartingale financial model, we aim at answering the following question: How much are you willing to pay for learning some private information that will allow you to make arbitrage profits? In particular, we are interested in the case where the private information can yield arbitrage opportunities but not arbitrages of the first kind. In the spirit of Amendinger, Becherer & Schweizer (2003, Financ. Stoch.), we adopt an indifference pricing approach for general preferences over consumption and terminal wealth, relying on recent results on initial enlargement of filtrations. This is based on joint work with H.N. Chau and A. Cosso.
The Value of Informational Arbitrageread_more
HG G 43
2. November 2017
17:15-18:15 		Sigrid Källblad
TU Wien
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Talks in Financial and Insurance Mathematics

Titel Measure-valued martingales and optimality solutions to the Skorohod Embedding Problem
Referent:in, Affiliation Sigrid Källblad, TU Wien
Datum, Zeit 2. November 2017, 17:15-18:15
Ort HG G 43
Abstract We consider (probability) measure valued processes, which we call MVMs, which have a natural martingale structure. Following previous work such processes are known to have a close connection to solutions to the Skorokhod Embedding Problem. Here, we consider two key properties of these processes, and in particular, we are able to show that the MVMs connected to the Bass and Root embeddings possess natural optimality properties. Based on joint work with M. Beiglböck, A. Cox and M. Huesmann. ​
Measure-valued martingales and optimality solutions to the Skorohod Embedding Problemread_more
HG G 43
9. November 2017
17:15-18:15 		Gareth Peters
Heriot-Watt University
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Talks in Financial and Insurance Mathematics

Titel Attempts to Characterise Families of Symmetric Non-Independent Increment Alpha-Stable Processes
Referent:in, Affiliation Gareth Peters, Heriot-Watt University
Datum, Zeit 9. November 2017, 17:15-18:15
Ort HG G 43
Abstract The characterization of spatial or temporal processes by a family of sufficient functions such as via a unique spectral representation and a mean functionforms the basis of a large number of statistical modelling approaches. For instance, recently in the active area of Gaussian process regression modelling, the mean and covariance function specify uniquely the properties of the resulting statistical model. One can therefore parameterize such regression models and understand their structure and attributes generally via a specification of the covariance kernel. In this work we attempt to generalize significantly the class of available spatial and temporal processes that may be used in statistical applications like regressions to allow for non-stationarity, non-independent increments and heavy-tailedness. To achieve this in a manner akin to the covariance kernel specification in a Gaussian process model, we develop a novel covariation spectral representation of some non-stationary and nonindependent increments symmetric Alpha-stable processes (SalphaS). Such a representation is based on a weaker covariation pseudo additivity condition which is more general than the condition of independence and should allow a very wide class of statistical regression models to be subsequently developed. We present a general framework for sufficient conditions to characterize such processes and develop general constructive approaches to building models satisfying these conditions. This is based on the preprint paper: Azzaoui, Nourddine and Peters, Gareth William and Guillin, Arnaud and Egan, Malcolm, Spectral Characterization of the Non-Independent Increment Family of Alpha-Stable Processes that Generalize Gaussian Process Models. (January 2, 2017). Available at SSRN: https://ssrn.com/abstract=2892547.
Attempts to Characterise Families of Symmetric Non-Independent Increment Alpha-Stable Processesread_more
HG G 43
21. November 2017
15:15-16:15 		Alexander Lipton
EPF Lausanne
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Talks in Financial and Insurance Mathematics

Titel Modern Monetary Circuit Theory and Stability of Financial Ecosystem
Referent:in, Affiliation Alexander Lipton, EPF Lausanne
Datum, Zeit 21. November 2017, 15:15-16:15
Ort HG G 19.1
Abstract A modern version of Monetary Circuit Theory with a particular emphasis on stochastic underpinning mechanisms is developed.
Existing theories of money creation are compared and contrasted. It is explained how money is created by the banking system as a whole and by individual banks.
The role of central banks as system stabilizers and liquidity providers is elucidated. It is shown that in the process of money creation banks become naturally interconnected.
A novel Extended Structural Default Model describing the stability of the Interconnected Banking Network is proposed.
The purpose of banks' capital and liquidity is explained.
Multi-period constrained optimization problem for banks's balance sheet is formulated and solved in a simple case.
Both theoretical and practical aspects are covered.
Modern Monetary Circuit Theory and Stability of Financial Ecosystemread_more
HG G 19.1
7. Dezember 2017
17:15-18:15 		Huyên Pham
Universitè Paris-Diderot
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Talks in Financial and Insurance Mathematics

Titel Stochastic control under partial observation revisited
Referent:in, Affiliation Huyên Pham, Universitè Paris-Diderot
Datum, Zeit 7. Dezember 2017, 17:15-18:15
Ort HG G 43
Abstract We study and revisit the optimal control problem of partially observed stochastic systems. By using a control randomization method, we provide a nonlinear Feynman-Kac formula for the value function in a general framework including path-dependence in the coefficients (both on the state and control) and without any non degeneracy condition on the diffusion coefficient. In the standard Markovian case, this representation has important implications: it allows us to obtain a corresponding randomized dynamic programming principle (DPP) for the value function, which is obtained from a flow property of an associated filter process. This DPP is the key step towards our main result: a characterization of the value function of the partial observation control problem as the unique viscosity solution to the corresponding dynamic programming Hamilton-Jacobi-Bellman (HJB) equation. The latter is formulated as a new, fully non linear partial differential equation on the Wasserstein space of probability measures, and is derived by means of the recent notion of differentiability with respect to probability measures introduced by P.L. Lions in his lectures on mean-field games at the Collège de France. An important feature of our approach is that it does not require any condition to guarantee existence of a density for the filter process solution to the controlled Zakai equation, as usually done for the separated problem. We give an explicit solution to our HJB equation in the case of a partially observed non Gaussian linear quadratic model. Finally, we discuss the issue of numerical treatment of the proposed randomized Feynman-Kac formula for solving partial observation control problem. Based on joint works with E. Bandini (University of Milano-Biccoca), A. Cosso (University of Bologna), and M. Fuhrman (University of Milano).
Stochastic control under partial observation revisitedread_more
HG G 43
12. Dezember 2017
15:15-16:15 		Vladimir Vovk
Royal Holloway University of London
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Talks in Financial and Insurance Mathematics

Titel A probability-free theory of continuous martingales with applications to equity premium and CAPM
Referent:in, Affiliation Vladimir Vovk, Royal Holloway University of London
Datum, Zeit 12. Dezember 2017, 15:15-16:15
Ort HG G 19.2
Abstract In this talk, I will consider idealized financial markets with continuous price paths and give probability-free versions of some standard results of the theory of martingales concerning the Ito integral, the Dubins-Schwarz theorem, and the Girsanov theorem. These results shed new light on the equity premium puzzle and CAPM, which cease to depend on statistical assumptions and only depend on a natural economic assumption. The talk is based on joint work with Glenn Shafer.
A probability-free theory of continuous martingales with applications to equity premium and CAPMread_more
HG G 19.2
14. Dezember 2017
17:15-18:15 		Tim Verdonck
KU Leuven
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Talks in Financial and Insurance Mathematics

Titel Efficient estimation of higher order comoments
Referent:in, Affiliation Tim Verdonck, KU Leuven
Datum, Zeit 14. Dezember 2017, 17:15-18:15
Ort HG G 43
Abstract Optimal decision making often requires to take into account the higher order comoments of dependent random variables. The classical sample estimators performs poorly in terms of mean squared error (MSE) when the dimension increases. Therefore, we propose two approaches to increase the efficiency of the sample estimator by adding regularisation or structure to the comoment estimates. The first contribution is in terms of the coskewness matrix where we propose unbiased estimates for the MSE loss function determining the shrinkage intensity of the multi-target shrinkage estimator. The second contribution is the nearest comoment estimator for the comoments of a multidimensional process that exhibits a lower dimensional latent factor structure. Based on the influence function, we prove consistency and asymptotic normality. In both cases, extensive simulation studies validate all aspects of the proposed estimation framework, including data-driven selection of the number of latent factors and a bootstrap procedure to determine a regularization constant to increase the efficiency of the nearest comoment estimator. Applications in asset allocation, risk measurement and questionnaire analysis show the usefulness of the proposed estimators. This is based on joint work with K. Boudt and D. Cornilly.
Efficient estimation of higher order comomentsread_more
HG G 43
19. Dezember 2017
15:15-16:15 		Zinoviy Landsman
University of Haifa
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Talks in Financial and Insurance Mathematics

Titel Explicit solution of a portfolio optimization problem by a general bivariate functional of the mean and variance
Referent:in, Affiliation Zinoviy Landsman, University of Haifa
Datum, Zeit 19. Dezember 2017, 15:15-16:15
Ort HG G 19.1
Abstract We consider the problem of maximization of functional of expected portfolio return and variance portfolio return in it's most general form and present an explicit closed form solution of the optimal portfolio selection. This problem is closely related with the expected utility maximization and two-moments decision models. We observe that all the optimization problems corresponding to the considered general functional reduce to the same efficient frontier. We show that most of the known risk measures: mean-variance, expected short-fall, Sharpe ratio and the recently introduced tail-mean-variance are special cases of this functional. The new results essentially generalize previous results by the first two authors concerning the maximization of a combination of the expected portfolio return and a function of the variance portfolio return. (Based on joint work of Z. Landsman, U. Makov and T. Shushi)
Explicit solution of a portfolio optimization problem by a general bivariate functional of the mean and varianceread_more
HG G 19.1
21. Dezember 2017
17:15-18:15 		Johannes Muhle-Karbe
Carnegie Mellon University
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Talks in Financial and Insurance Mathematics

Titel A dynamic equilibrium model for brokerage fees
Referent:in, Affiliation Johannes Muhle-Karbe, Carnegie Mellon University
Datum, Zeit 21. Dezember 2017, 17:15-18:15
Ort HG G 43
Abstract We develop a dynamic equilibrium model for market liquidity. To wit, we solve for the equilibrium prices at which liquidity takers' demands are absorbed by liquidity providers, who can in turn gradually transfer these positions to a group of end users. (joint work in progress with Peter Bank and Ibrahim Ekren)
A dynamic equilibrium model for brokerage feesread_more
HG G 43

Organisatoren:innen: Matteo Burzoni

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