Departement Mathematik

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Talks in financial and insurance mathematics

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Herbstsemester 2018

Datum / Zeit Referent:in Titel Ort
5. September 2018
17:15-18:15 		Claudia Klüppelberg
TU München
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Talks in Financial and Insurance Mathematics

Titel Modelling system risk by a random bipartite graph structure
Referent:in, Affiliation Claudia Klüppelberg, TU München
Datum, Zeit 5. September 2018, 17:15-18:15
Ort HG G 43
Abstract We introduce a random network model for business relationships as for instance an insurance market or operational risk. Using Pareto-tailed losses and multivariate regular variation we obtain results for system risk measures, which are based on the Value-at-Risk, the Expected Shortfall, or the ruin probability. We show that the dependence on the network structure plays a fundamental role for their asymptotic behaviour. The focus of our analysis lies in the study of the influence of the random graph on risk measures, where we consider the Bernoulli graph and a Rasch-type graph as examples. In particular, we contrast the influence of the network on single components and on multivariate vectors. This is joint work with Anita Behme, Oliver Kley and Gesine Reinert. References: [1] Behme, A. and Klüppelberg, C., and Reinert, G. (2018) Hitting probabilities for compound Poisson processes in a bipartite network. arXiv: 1805.12459. [2] Kley, O., Klüppelberg, C., and Reinert, G. (2017) Conditional risk measures in a bipartite market structure. Scandinavian Actuarial Journal 2018 (4), 328-355. [3] Kley, O., Klüppelberg, C., and Reinert G. (2016) Risk in a large claims insurance market with bipartite graph structure. Operations Research 64 (5), 1159-1176.
Modelling system risk by a random bipartite graph structureread_more
HG G 43
20. September 2018
17:15-18:15 		Felix Matthys
ITAM Businees School
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Talks in Financial and Insurance Mathematics

Titel Stochastic Volatility and Model Uncertainty: Implications for Asset Prices and Optimal Portfolio Policies
Referent:in, Affiliation Felix Matthys, ITAM Businees School
Datum, Zeit 20. September 2018, 17:15-18:15
Ort HG G 43
Abstract This paper presents a framework in which stochastic volatility endogenously drives model uncertainty and shows how an investor derives optimal robust consumption and portfolio policies in fully closed-form. In turbulent times, characterized by elevated volatility levels, the amount of model uncertainty the investor is facing increases and thereby rendering the estimation of his reference model more difficult. Our jump diffusive stochastic volatility model accounts for the well-known stylized facts of asset price volatility, such as volatility clustering and occasional large jumps, which has direct implications on, first, how much model uncertainty there is and second, how the investor optimally guards himself against model miss-specification. Our quantitative analysis shows that the naive investor, who has full trust in his reference model and believes volatility is constant, incurs significant wealth losses as compared to a robust investor that accounts for the time series properties of empirical volatility. We derive a semi-closed form expression for the detection-error probability which allows us to efficiently quantify the amount of model uncertainty. Moreover, we also solve the model in general equilibrium in order to determine how the equity risk premia and the risk free are affected by both, stochastic volatility and model model uncertainty. Finally, we implement a quasi-maximum likelihood estimator to fit the model to the data and find that our jump-diffusive volatility model is able to reproduce key moments of asset prices. This is joint work with Yacine Ait-Sahalia (Princeton University) and Emilio Osambela (Federal Reserve Board).
Stochastic Volatility and Model Uncertainty: Implications for Asset Prices and Optimal Portfolio Policiesread_more
HG G 43
27. September 2018
17:15-18:15 		Mitja Stadje
Universität Ulm
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Talks in Financial and Insurance Mathematics

Titel Perfect Hedging under Endogenous Permanent Market Impacts
Referent:in, Affiliation Mitja Stadje, Universität Ulm
Datum, Zeit 27. September 2018, 17:15-18:15
Ort HG G 43
Abstract We model a nonlinear price curve quoted in a market as the utility indifference curve of a representative liquidity supplier. As the utility function, we adopt a g-expectation. In contrast to the standard framework of financial engineering, a trader is no longer a price taker as any trade has a permanent market impact via an effect on the supplier’s inventory. The P&L of a trading strategy is written as a nonlinear stochastic integral. Under this market impact model, we introduce a completeness condition under which any derivative can be perfectly replicated by a dynamic trading strategy. In the special case of a Markovian setting, the corresponding pricing and hedging can be done by solving a semilinear PDE.
Perfect Hedging under Endogenous Permanent Market Impacts read_more
HG G 43
4. Oktober 2018
17:15-18:15 		Samuel Cohen
University of Oxford
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Talks in Financial and Insurance Mathematics

Titel Uncertainty in Kalman-Bucy Filtering
Referent:in, Affiliation Samuel Cohen, University of Oxford
Datum, Zeit 4. Oktober 2018, 17:15-18:15
Ort HG G 43
Abstract The classical Kalman-Bucy filter is a beautiful result of practical significance. Using it, within a model for the dynamics of a signal and observation process, we can recursively find the posterior distribution of the signal given observations. In practice however, we also need to estimate the dynamics, and this introduces an additional source of uncertainty into our assessments. In this talk, we will consider a model for this uncertainty, and how it quickly leads to interesting problems in optimal stochastic control.
Uncertainty in Kalman-Bucy Filteringread_more
HG G 43
25. Oktober 2018
17:15-18:15 		Steven Vanduffel
Vrije Universiteit Brussel
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Talks in Financial and Insurance Mathematics

Titel Upper Bounds for Strictly Concave Distortion Risk Measures on Moment Spaces
Referent:in, Affiliation Steven Vanduffel, Vrije Universiteit Brussel
Datum, Zeit 25. Oktober 2018, 17:15-18:15
Ort HG G 43
Abstract The study of worst-case scenarios for risk measures (e.g., Value-at-Risk) when the underlying risk (or portfolio of risks) is not completely specified is a central topic in the literature on robust risk measurement. In this paper, we tackle the open problem of deriving upper bounds for strictly concave distortion risk measures on moment spaces. Building on early results of Rustagi (1957,1976), we show that in general this problem can be reduced to a parametric optimization problem. We completely specify the sharp upper bound (and corresponding maximizing distribution function) when the first moment and any other higher moment are xed. Specifically, in the case of a fixed mean and variance, we generalize the Cantelli bound for (Tail) Value-at-Risk in that we express the sharp upper bound for a strictly concave distorted expectation as a weighted sum of the mean and standard deviation.
Upper Bounds for Strictly Concave Distortion Risk Measures on Moment Spacesread_more
HG G 43
8. November 2018
17:15-18:15 		Lukasz Delong
Warsaw School of Economics
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Talks in Financial and Insurance Mathematics

Titel Fair valuation of insurance liability cash-flow streams in continuous time
Referent:in, Affiliation Lukasz Delong, Warsaw School of Economics
Datum, Zeit 8. November 2018, 17:15-18:15
Ort HG G 43
Abstract We investigate fair (market-consistent and actuarial) valuation of insurance liability cash-flow streams in continuous time. We first consider one-period hedge-based valuations, where in the first step, an optimal dynamic hedge for the liability is set up, based on the assets traded in the market and a quadratic hedging objective, while in the second step, the remaining part of the claim is valuated via an actuarial valuation. Then, we extend this approach to a multi-period setting by backward iterations for a given discrete-time step h, and consider the continuous-time limit for h converging to 0. We formally derive a partial differential equation for the valuation operator which satisfies the continuous-time limit of the multi-period, discrete-time iterations and prove that this valuation operator is actuarial and market-consistent. We show that our continuous-time fair valuation operator has a natural decomposition into the best estimate of the liability and a risk margin. The dynamic hedging strategy associated with the continuous-time fair valuation operator is also established. Finally, the valuation operator and the hedging strategy allow us to study the dynamics of the net asset value of the insurer.
Fair valuation of insurance liability cash-flow streams in continuous timeread_more
HG G 43
15. November 2018
17:15-18:15 		Kathrin Glau
Queen Mary Universtiy of London
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Talks in Financial and Insurance Mathematics

Titel Magic Point Integration: A Numerical Learning Algorithm for Parametric Option Pricing
Referent:in, Affiliation Kathrin Glau, Queen Mary Universtiy of London
Datum, Zeit 15. November 2018, 17:15-18:15
Ort HG G 43
Abstract We propose an offline-online procedure for pricing parametric options with Fourier methods. In the offline phase a quadrature rule adapted to the parametric family is produced. We derive analyticity criteria for explicit error bounds and an exponential rate of convergence of the magic point empirical interpolation method introduced by Barrault et al. (2004). We find that the method is well suited to Fourier transforms and has a wide range of applications in such diverse fields as probability and statistics, signal and image processing, physics, chemistry and mathematical finance. To illustrate the method, we apply it to the evaluation to recurrent option pricing problems in finance. Our numerical experiments display convergence of exponential order, even in cases where the theoretical results do not apply. We also discuss some first results for the bivariate case.
Magic Point Integration: A Numerical Learning Algorithm for Parametric Option Pricingread_more
HG G 43
22. November 2018
15:15-16:15 		Adam Jakubowski
Nicolaus Copernicus University
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Talks in Financial and Insurance Mathematics

Titel Recent advances on the S topology
Referent:in, Affiliation Adam Jakubowski, Nicolaus Copernicus University
Datum, Zeit 22. November 2018, 15:15-16:15
Ort HG G 19.1
Abstract The S topology on the Skorokhod space was introduced by the author in 1997 and since then it has proved to be a useful tool in several areas of the theory of stochastic processes. We shall provide an overview of basic facts on the S topology, including historical motivations, the position in the hierarchy of topologies on the Skorokhod space and references to the most interesting applications. Special attention will be paid to locally convex structures related to the S topology.
Recent advances on the S topologyread_more
HG G 19.1
29. November 2018
17:15-18:15 		Marco Frittelli
Università degli studi di Milano
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Talks in Financial and Insurance Mathematics

Titel On systemic risk measures
Referent:in, Affiliation Marco Frittelli, Università degli studi di Milano
Datum, Zeit 29. November 2018, 17:15-18:15
Ort HG G 43
Abstract In our previous paper "A Unified Approach to Systemic Risk Measures via Acceptance Set" we have introduced a general class of systemic risk measures that allow random allocations to individual banks before aggregation of their risks.
In the present paper, we address the question of fairness of these allocations and propose a fair allocation of the total risk to individual banks. We show that the dual formulation of the minimization problem identifying the systemic risk measure provides a valuation of the random allocations, which is fair both from the point of view of the society/regulator and from the individual financial institutions. The case with exponential utilities which allows for explicit computation is treated in details.
On systemic risk measuresread_more
HG G 43
13. Dezember 2018
17:15-18:15 		Roger Cooke
University of Strathclyde
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Talks in Financial and Insurance Mathematics

Titel Vines and the Epicycles of Regression
Referent:in, Affiliation Roger Cooke, University of Strathclyde
Datum, Zeit 13. Dezember 2018, 17:15-18:15
Ort HG G 43
Abstract Regular vines are a tool for building joint densities with arbitrary one dimensional margins and conditional bivariate copula. They leverage the rich theory of bivariate copula to yield greater modeling flexibility for high dimensions. Although most applications have been in financial mathematics, this talk presents an application to predict the effect of breast feeding on IQ. Given a regular vine density, the well-known epicycles of regression modeling, to wit: including/excluding covariates, interactions, higher order terms, multicollinearity, transformations, heteroscedasticity, bias, convergence, efficiency, simply do not arise. This talk gives an intuitive introduction to regular vines and their application to regression with continuous covariates.
Vines and the Epicycles of Regressionread_more
HG G 43

Organisatoren:innen: Matteo Burzoni

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