Andreas Celary - Reproducing kernel based methods for modelling the discount curve
In analogy to the HJM setting, we formulate an arbitrage-free dynamic framework for modeling the discount curve. In the proposed setting, we derive no-arbitrage conditions to determine the set of admissible discount curves. We introduce reproducing kernels as a possible basis for the corresponding estimation problem. Finally, we provide specific examples
Theresa Traxler - Regulatory Capital Constraints and Procyclicality of Bank Behaviour - A Mean Field Control Approach
We consider a Mean Field Control model for the behaviour of large banking systems under regulatory capital constraints. It is described mathematically as a system of coupled forward and backward PDEs. First we study a simple test case without constraints, for which an explicit solution can be found. Then we implement a finite difference scheme for solving the PDE system numerically and test it on the simple case. In a second step, we apply the scheme to the case with capital constraints, where no explicit solution is available.
Andrea Panarotto - Exploiting mobile phone data for the analysis of urban mobility
Investigating the current people's moving choices is the starting point for a conscious transition towards a more sustainable mobility situation. Mobile phone data provides a powerful, yet tricky tool to explore the ways people move. In this presentation, we underline some relevant results obtained by the analysis of telephonic data for mobility in an urban framework, looking forward to future applications on modality detection and privacy-preserving techniques.
Nurtai Meimanjan - A mixed-integer programming approach for computing systemic risk measures
Systemic risk is concerned with the instability of a financial system whose members are interdependent in the sense that the failure of a few institutions may trigger a chain of defaults throughout the system. Recently, several systemic risk measures have been proposed in the literature that are used to determine capital requirements for the members subject to joint risk considerations. We address the problem of computing systemic risk measures for systems with sophisticated clearing mechanisms. In particular, we consider an extension of Rogers-Veraart network model where the operating cash flows are unrestricted in sign. We propose a mixed-integer programming problem that can be used to compute clearing vectors in this model. Due to the binary variables in this problem, the corresponding (set-valued) systemic risk measure fails to have convex values in general. We associate nonconvex vector optimization problems to the systemic risk measure and provide theoretical results related to the weighted-sum and Pascoletti-Serafini scalarizations of this problem. Finally, we test the proposed formulations on computational examples and perform sensitivity analyses with respect to some model-specific and structural parameters.
Natalie Frantsits - Computation of Nash Equilbria in dynamic Games via Vector Optimization
In the field of Game Theory, the Nash Equilibrium (NE) is widely recognized as the most common solution technique. A recent breakthrough has introduced a new mechanism for obtaining the set of all Nash Equilibria in non-cooperative, static games. This approach involves reformulating the problem as a Vector Optimization problem and computing the NEs as corresponding Pareto-efficient points with respect to a non-convex ordering cone. In order to extend the applicability of this method to an even larger class of games, specifically dynamic games, we propose an approach based on the dynamic programming principle that has been shown to hold for certain dynamic Nash games. In this dynamic setting, we focus on solving subgames by iteratively computing so-called subgame-perfect-equilibria (SPE), which are a refinement of the NE, and we aim to find conditions under which these SPEs correspond to the complete set of NEs for the whole game.
Giacomo Bressan - Climate risks, catastrophe bonds and financial instability
Climate change is increasingly relevant for the global economy and financial markets. Consequently, the frequency and intensity of natural catastrophes such as hurricanes and floods are increasing.
Catastrophe bonds have been introduced to transfer catastrophic risk from the institutions originally bearing it to the wider financial market but the effects of this innovation on systemic risk have received little attention.
We investigate the financial stability implications of catastrophe bonds in light of the impacts of climate change, studying a network of financial institutions originating and trading catastrophe bonds. We use copula functions to model the dependence structure between catastrophes and financial markets' shocks, and to introduce ambiguity in catastrophe bonds' pricing stemming from climate change.
We find that the compounding of catastrophes and financial shocks increases the probability of default of participants in the financial network. Similarly, the probability of default increases if investors require too little premiums for catastrophe bonds.
Thus, we show that catastrophe bonds can contribute to financial instability if incorrectly priced.
Robert Bajons - Curve Clustering Methods and their Applications to Sports Analytics
In team sports, such as American football or European football (Soccer), players naturally move on the pitch in specific trajectories. Usually the paths of players on the pitch are determined by specific team tactics, thus interesting analyses can be derived from studying common pattern in these movements. We discuss several approaches for clustering weighted curves, i.e. curves which may be assigned weights at each observation of the curve, in the context of sports analytics. First we present a weighted K-means approach for clustering curves, which is simple to implement but relies on substantial preprocessing to be applied to curves. A more elaborate approach, which is also able to handle most of the idiosyncrasies of curve data, is to employ model-based clustering using regression mixture models. Finally, we analyze the clustering methods by applying them to a dataset of NFL pass rushing routes obtained from Kaggle.