Insurance Mathematics and Stochastic Finance

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Talks in Financial and Insurance Mathematics

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

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Spring Semester 2016

Date / Time Speaker Title Location
4 February 2016
17:15-18:15 		Tolulope Fadina
Universität Freiburg
Event Details

Talks in Financial and Insurance Mathematics

Title Credit risk with ambiguity on the default intensity
Speaker, Affiliation Tolulope Fadina, Universität Freiburg
Date, Time 4 February 2016, 17:15-18:15
Location 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.
Credit risk with ambiguity on the default intensityread_more
HG G 43
25 February 2016
17:15-18:15 		Thaleia Zariphopoulou
Universität of Texas at Austin
Event Details

Talks in Financial and Insurance Mathematics

Title Turnpike portfolios under forward investment performance criteria
Speaker, Affiliation Thaleia Zariphopoulou, Universität of Texas at Austin
Date, Time 25 February 2016, 17:15-18:15
Location 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)
Turnpike portfolios under forward investment performance criteriaread_more
HG G 43
3 March 2016
17:15-18:15 		Johannes Muhle-Karbe
University of Michigan
Event Details

Talks in Financial and Insurance Mathematics

Title Risk-Tolerance Processes and the Sensitivity of Optimal Investment and Consumption
Speaker, Affiliation Johannes Muhle-Karbe, University of Michigan
Date, Time 3 March 2016, 17:15-18:15
Location 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)
Risk-Tolerance Processes and the Sensitivity of Optimal Investment and Consumptionread_more
HG G 43
17 March 2016
17:15-18:15 		Carlo Acerbi
MSCI
Event Details

Talks in Financial and Insurance Mathematics

Title L'ES est mort, vive l'ES!
Speaker, Affiliation Carlo Acerbi, MSCI
Date, Time 17 March 2016, 17:15-18:15
Location 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.
L'ES est mort, vive l'ES!read_more
HG G 43
24 March 2016
17:15-18:15 		Yan Dolinsky
Hebrew University
Event Details

Talks in Financial and Insurance Mathematics

Title Super-Replication in Extremely Incomplete Markets
Speaker, Affiliation Yan Dolinsky, Hebrew University
Date, Time 24 March 2016, 17:15-18:15
Location 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.
Super-Replication in Extremely Incomplete Marketsread_more
HG G 43
31 March 2016
17:15-18:15 		Sidney Resnick
Cornell University
Event Details

Talks in Financial and Insurance Mathematics

Title Multivariate Heavy Tails and Network Growth Models
Speaker, Affiliation Sidney Resnick, Cornell University
Date, Time 31 March 2016, 17:15-18:15
Location HG G 43
Multivariate Heavy Tails and Network Growth Models
HG G 43
7 April 2016
17:15-18:15 		Tobias Fissler
Universität Bern
Event Details

Talks in Financial and Insurance Mathematics

Title Higher Order Elicitability: Expected Shortfall is jointly elicitable with Value at Risk - Implications for Backtesting
Speaker, Affiliation Tobias Fissler, Universität Bern
Date, Time 7 April 2016, 17:15-18:15
Location 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
Higher Order Elicitability: Expected Shortfall is jointly elicitable with Value at Risk - Implications for Backtestingread_more
HG G 43
20 April 2016
16:15-17:15 		Dylan Possamaï
Université Paris Dauphine
Event Details

Talks in Financial and Insurance Mathematics

Title A tale of a Principal and many Agents
Speaker, Affiliation Dylan Possamaï, Université Paris Dauphine
Date, Time 20 April 2016, 16:15-17:15
Location 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.
A tale of a Principal and many Agentsread_more
HG G 26.5
28 April 2016
17:15-18:15 		Yaroslav Melnyk
EPF Lausanne
Event Details

Talks in Financial and Insurance Mathematics

Title Portfolio Optimization with Recursive Utility under Small Transaction Costs
Speaker, Affiliation Yaroslav Melnyk, EPF Lausanne
Date, Time 28 April 2016, 17:15-18:15
Location 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
Portfolio Optimization with Recursive Utility under Small Transaction Costsread_more
HG G 43
5 May 2016
17:15-18:15
Event Details

Talks in Financial and Insurance Mathematics

Title Ascension
Speaker, Affiliation
Date, Time 5 May 2016, 17:15-18:15
Location
Ascension
12 May 2016
17:15-18:15 		Agostino Capponi
Columbia University
Event Details

Talks in Financial and Insurance Mathematics

Title Collateral Levels and Centralized Trading
Speaker, Affiliation Agostino Capponi, Columbia University
Date, Time 12 May 2016, 17:15-18:15
Location 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.
Collateral Levels and Centralized Tradingread_more
HG G 43
19 May 2016
17:15-18:15 		Jérôme Lelong
ENSIMAG
Event Details

Talks in Financial and Insurance Mathematics

Title Pricing American options using martingale bases
Speaker, Affiliation Jérôme Lelong, ENSIMAG
Date, Time 19 May 2016, 17:15-18:15
Location 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.
Pricing American options using martingale basesread_more
HG G 43
26 May 2016
17:15-18:15 		Boris Choy
University of Sydney, Australia
Event Details

Talks in Financial and Insurance Mathematics

Title Stochastic loss reserving modelling in general insurance using non-elliptical probability distributions
Speaker, Affiliation Boris Choy, University of Sydney, Australia
Date, Time 26 May 2016, 17:15-18:15
Location 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.
Stochastic loss reserving modelling in general insurance using non-elliptical probability distributionsread_more
HG G 43
22 June 2016
17:15-18:15 		Marie Kratz
ESSEC Business School
Event Details

Talks in Financial and Insurance Mathematics

Title An implicit backtest for Expected Shortfall via a simple multinomial approach
Speaker, Affiliation Marie Kratz, ESSEC Business School
Date, Time 22 June 2016, 17:15-18:15
Location 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.
An implicit backtest for Expected Shortfall via a simple multinomial approachread_more
HG G 43
23 June 2016
17:15-18:15 		Gordan Zitkovic
University of Texas at Austin
Event Details

Talks in Financial and Insurance Mathematics

Title A class of globally solvable Markovian quadratic BSDE systems and applications
Speaker, Affiliation Gordan Zitkovic, University of Texas at Austin
Date, Time 23 June 2016, 17:15-18:15
Location 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).
A class of globally solvable Markovian quadratic BSDE systems and applicationsread_more
HG G 43

Organizers: Matteo Burzoni

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