Talks in Financial and Insurance Mathematics

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This is the regular weekly research seminar on Insurance Mathematics and Stochastic Finance.

Spring Semester 2016

Note: The highlighted event marks the next occurring event.

Date / Time Speaker Title Location
4 February 2016
17:15-18:15
Tolulope Fadina
Universität Freiburg
Credit risk with ambiguity on the default intensity  HG G 43 
Abstract: In this talk, we will introduce the concept of no-arbitrage in a credit risk market under ambiguity. We consider an intensity-based framework where we assume that the default intensity is strictly positive. This assumption is economically intuitive, as it is equivalent to an approach where at every time s credit risk is present and not negligible. However, we consider the realistic case where the intensity is not precisely known, but there is ambiguity on the intensity. By means of the Girsanov theorem, we start from the reference measure where the intensity is equal 1 and define the equivalent measures P^h where the intensity is h. Ambiguity is considered in the sense that h lies between an upper and lower bound. From this viewpoint, the credit risky case turns out to be similar to the case of drift uncertainty in the G-expectation framework.
25 February 2016
17:15-18:15
Thaleia Zariphopoulou
Universität of Texas at Austin
Turnpike portfolios under forward investment performance criteria  HG G 43 
Abstract: In this talk, I will discuss the behavior of optimal portfolios under time-monotone forward performance criteria for large horizons. Contrary to the classical case, the limiting behavior of the optimal policies for large wealth differs from the one for large time. I will discuss what determines these two limits and present examples. (joint work with T. Geng)
3 March 2016
17:15-18:15
Johannes Muhle-Karbe
University of Michigan
Risk-Tolerance Processes and the Sensitivity of Optimal Investment and Consumption  HG G 43 
Abstract: In this talk, we discuss the pivotal role of the (indirect) risk-tolerance process in the perturbation analysis of optimal investment/consumption problems. Existence and several dynamic characterizations are established in a general semimartingale setting, building on earlier results of Kramkov and Sirbu (2006, 2007). (Joint work with Christoph Czichowsky and Jan Kallsen)
17 March 2016
17:15-18:15
Carlo Acerbi
MSCI
L'ES est mort, vive l'ES!  HG G 43 
Abstract: We give a so far missing formal definition of backtestability that we believe correctly embodies the meaning of this term in the statistical prediction practice. We conclude that the Expected Shortfall is non backtestable, an issue that has raised controversy, in the absence of a formal definition. We show however how a number of statistics, notably the ES, can be subject to special backtesting procedures - jointly with another partner statistics - with two important properties. 1) The sensitivity to possible misspecification in the partner statistics vanishes “at first order” and 2) the possible error in the ES resulting backtest is in any case always of prudential type, in a risk theoretical sense of the word. This result opens the way to practical approaches to ES backtesting.
24 March 2016
17:15-18:15
Yan Dolinsky
Hebrew University
Super-Replication in Extremely Incomplete Markets  HG G 43 
Abstract: In this work we introduce the notion of extremely incomplete markets. We prove that for these markets the super-replication price coincide with the model free super-replication price. Namely, the knowledge of the model does not reduce the super-replication price. We provide two families of extremely incomplete models: stochastic volatility models and rough volatility models. Moreover, we give several computational examples. Our approach is purely probabilistic. This is joint work with Ariel Neufeld.
31 March 2016
17:15-18:15
Sidney Resnick
Cornell University
Multivariate Heavy Tails and Network Growth Models HG G 43 
7 April 2016
17:15-18:15
Tobias Fissler
Universität Bern
Higher Order Elicitability: Expected Shortfall is jointly elicitable with Value at Risk - Implications for Backtesting  HG G 43 
Abstract: A statistical functional, such as the mean or the median, is called elicitable if there is a scoring function or loss function such that the correct forecast of the functional is the unique minimizer of the expected score. Such scoring functions are called strictly consistent for the functional. The elicitability of a functional opens the possibility to compare competing forecasts and to rank them in terms of their realized scores. In the first part of this talk, we explore the notion of higher order elicitability, that is, we investigate the question of elicitability for higher-dimensional functionals. As a result of particular applied interest we show that the pair (Value at Risk, Expected Shortfall) ((VaR, ES)) is elicitable despite the fact that ES itself is not. More generally, we give a characterization of the class of strictly consistent scoring functions for this pair, making use of a higher dimensional version of Osband's principle. In the second part of the talk, we discuss the consequences of this result for backtesting ES-forecasts. We introduce comparative backtests of Diebold-Mariano type using a strictly consistent scoring function for the pair (VaR, ES). Comparative backtests open the possibility to choose a conservative null hypothesis in comparison to the current state of the art. Emphasizing our argument with a brief simulation study, we demonstrate that the change of the null hypothesis in comparative backtests amounts to a reversed onus of proof in backtesting decisions. This appears to be beneficial to all stakeholders, including banks, regulators, and society at large. References: T. Fissler and J. F. Ziegel (2016). Higher order elicitability and Osband's principle. To appear in The Annals of Statistics. Preprint. arxiv.org/abs/1503.08123 T. Fissler, J. F. Ziegel and T. Gneiting (2016). Expected Shortfall is jointly elicitable with Value at Risk -- Implications for backtesting. Risk, January 2016. Preprint. arxiv.org/abs/1507.00244
20 April 2016
16:15-17:15
Dylan Possamaï
Université Paris Dauphine
A tale of a Principal and many Agents  HG G 26.5 
Abstract: In this talk, I will present ongoing work on a problem of moral hazard involving a Principal and a system of interacting Agents whose actions are summed up in a mean-field game. This is a new problem in the literature, and our main current result is that the problem of the Principal can always be rewritten as stochastic control problem of a system of McKean-Vlasov SDEs, for which we can derive explicit solutions in specific instances. This is based on joint works with Romuald Elie and Thibaut Mastrolia.
28 April 2016
17:15-18:15
Yaroslav Melnyk
EPF Lausanne
Portfolio Optimization with Recursive Utility under Small Transaction Costs  HG G 43 
Abstract: We investigate the portfolio problem of an investor with Epstein-Zin recursive utility under proportional transaction costs. We characterize the solution via variational inequalities and prove existence of classical solutions for small cost parameters. We also provide a suitable verification theorem. This allows us to derive rigorous asymptotic expansions for optimal no-trade regions and consumption strategies and to investigate the effects of the investor's relative risk aversion and the elasticity of intertemporal substitution (EIS) \psi on the optimal strategies. Our main findings are: (a) At the leading order, the no-trade region is the same as with additive expected utility; in particular, it is determined solely by the relative risk aversion. The no-trade region depends on the investor's EIS only at the next-to-leading order, and only indirectly thought the frictionless optimal consumption rate. (b) The investor's optimal consumption depends on his EIS also at the leading order. The consumption-wealth ratio is higher than in the frictionless case if and only if \psi > 1. Based on joint work with Johannes Muhle-Karbe and Frank Thomas Seifried
5 May 2016
17:15-18:15
Ascension
12 May 2016
17:15-18:15
Agostino Capponi
Columbia University
Collateral Levels and Centralized Trading  HG G 43 
Abstract: We introduce a framework that relates optimal collateral levels to market fundamentals in a centralized trading setting. A profit maximizing clearinghouse chooses the fee and collateral level per traded contract. Collateral is then posted by heterogeneous traders who can strategically default. We derive an explicit characterization of the equilibrium collateral levels and show their relation to market fundamentals such as contract riskiness, fundamental value of trade, funding cost, and the trading venue’s operational cost. Increasing collateral levels introduces a trade off between higher protection from defaults and reduced trading activity due to lower default option values. Our model predicts that these levels may exhibit large swings when market fundamentals change.
19 May 2016
17:15-18:15
Jérôme Lelong
ENSIMAG
Pricing American options using martingale bases  HG G 43 
Abstract: In this work, we propose an algorithm to price American options by directly solving the dual minimization problem introduced by Rogers [2002]. Our approach relies on approximating the set of uniformly square integrable martingales by a finite dimensional Wiener chaos expansion. Then, we use a sample average approximation technique to efficiently solve the optimization problem. Unlike all the regression based methods, our method can transparently deal with path dependent options without extra computations and a parallel implementation writes easily with very little communication and no centralized work. We test our approach on several multi–dimensional options with up to 40 assets and show the impressive scalability of the parallel implementation. The corresponding paper is available on http://arxiv.org/pdf/1604.03317v1.
26 May 2016
17:15-18:15
Boris Choy
University of Sydney, Australia
Stochastic loss reserving modelling in general insurance using non-elliptical probability distributions  HG G 43 
Abstract: According to its 2008 study on the insolvency of insurance companies during the period from 1969 to 2007, rating agency A.M. Best identified under-reserving to be the most popular cause of the failure. Stochastic models based on the normality assumption are unable to capture the irregular claims. Various heavy-tailed distributions have been proposed to model the claim amount data and hence obtain more accurate loss reserves to avoid insolvency. This paper proposes new non-elliptical multivariate probability distributions to model claim amount data in general insurance. Unlike elliptical distributions, these distributions allow their marginal distributions to have different shape parameters. In modelling claim amount data from many lines of business, this is more realistic to assume that different lines of business have different shapes for their claim amount distributions. Since these non-elliptical distributions belong to the class of scale mixtures of normal distributions, we adopt the Bayesian approach for statistical inference and the forecast of the loss reserves. Real data are analysed using a state-space model with both elliptical and non-elliptical probability distributions and their performance is compared. Keywords: Scale mixture of normal, State space model, Markov chain Monte Carlo, Deviance Information Criterion, Risk Management.
22 June 2016
17:15-18:15
Marie Kratz
ESSEC Business School
An implicit backtest for Expected Shortfall via a simple multinomial approach  HG G 43 
Abstract: Replacing Value-at-Risk (VaR) by Expected Shortfall (ES) in Basel 3 is under current discussion, as ES is in general a better risk measure than VaR, more reliable tool for risk management. Hence the question of providing a backtest for ES, as handy in practice as the popular binomial backtest based on a violation process, used for the VaR. It is what we propose in this study. Following the idea by Emmer et al. of considering an empirical approach that consists in replacing ES by a set of a small number of quantiles for the backtesting, comes the natural proposition of a simple multinomial approach to backtest ES. It turns out to give reasonable results, certainly much better than with the binomial backtest, helping to distinguish between models. This is a joint work with Yen Lok and Alexander McNeil.
23 June 2016
17:15-18:15
Gordan Zitkovic
University of Texas at Austin
A class of globally solvable Markovian quadratic BSDE systems and applications  HG G 43 
Abstract: We establish existence and uniqueness for a wide class of Markovian systems of backward stochastic differential equations (BSDE) with quadratic nonlinearities. This class is characterized by an abstract structural assumption on the generator, an a-priori local-boundedness property, and a locally-Hölder-continuous terminal condition. We present easily verifiable sufficient conditions for these assumptions and treat several applications, including stochastic equilibria in incomplete financial markets, stochastic differential games, and martingales on Riemannian manifolds. Joint work with Hao Xing (London School of Economics).

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