Departement Mathematik

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Talks in financial and insurance mathematics

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Herbstsemester 2016

Datum / Zeit Referent:in Titel Ort
25. August 2016
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Talks in Financial and Insurance Mathematics

Titel No seminar
Referent:in, Affiliation
Datum, Zeit 25. August 2016,
Ort
No seminar
1. September 2016
17:15-18:15 		Marcel Nutz
Columbia University
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Talks in Financial and Insurance Mathematics

Titel A Mean Field Game of Optimal Stopping
Referent:in, Affiliation Marcel Nutz, Columbia University
Datum, Zeit 1. September 2016, 17:15-18:15
Ort HG G 43
Abstract We formulate a stochastic game of mean field type where the agents solve optimal stopping problems and interact through the proportion of players that have already stopped. Working with a continuum of agents, typical equilibria become functions of the common noise that all agents are exposed to, whereas idiosyncratic randomness can be eliminated by an Exact Law of Large Numbers. Under a structural monotonicity assumption, we can identify equilibria with solutions of a simple equation involving the distribution function of the idiosyncratic noise. Solvable examples allow us to gain insight into the uniqueness of equilibria and the dynamics in the population.
A Mean Field Game of Optimal Stoppingread_more
HG G 43
29. September 2016
17:15-18:15 		Yan Dolinsky
Hebrew University of Jerusalem
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Talks in Financial and Insurance Mathematics

Titel Super-Replication with Constant Transaction Costs
Referent:in, Affiliation Yan Dolinsky, Hebrew University of Jerusalem
Datum, Zeit 29. September 2016, 17:15-18:15
Ort HG G 43
Abstract We study super-replication of contingent claims in markets with fixed transaction costs. First we prove that in reasonable continuous time financial market the super-replication price is prohibitively costly and leads to trivial buy-and-hold strategies. Our second result is deriving non trivial scaling limits of super-replication prices in the binomial models. joint work with Peter Bank
Super-Replication with Constant Transaction Costsread_more
HG G 43
13. Oktober 2016
17:15-18:15 		Bruno Bouchard
Ceremade, Université Paris-Dauphine
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Talks in Financial and Insurance Mathematics

Titel Stochastic invariance of closed sets with non-Lipschitz coefficients
Referent:in, Affiliation Bruno Bouchard, Ceremade, Université Paris-Dauphine
Datum, Zeit 13. Oktober 2016, 17:15-18:15
Ort HG G 43
Abstract We provide a new characterization of the stochastic invariance of a closed subset with respect to a diffusion. We extend the well-known inward pointing Stratonovich drift condition to the case where the diffusion matrix can fail to be differentiable: we only assume that the covariance matrix is. In particular, our result can be directly applied to construct affine and polynomial diffusions on any arbitrary closed set.
Stochastic invariance of closed sets with non-Lipschitz coefficientsread_more
HG G 43
20. Oktober 2016
17:15-18:15 		Peter Tankov
Université Paris-Diderot
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Talks in Financial and Insurance Mathematics

Titel Optimal importance sampling for Lévy processes
Referent:in, Affiliation Peter Tankov, Université Paris-Diderot
Datum, Zeit 20. Oktober 2016, 17:15-18:15
Ort HG G 43
Abstract We develop importance sampling estimators for Monte Carlo pricing of European and path-dependent options in models driven by Lévy processes, extending earlier works focusing on the Black-Scholes and continuous stochastic volatility models. Using recent results from the theory of large deviations for processes with independent increments, we compute an explicit asymptotic approximation for the variance of the pay-off under an Esscher-style change of measure. Minimizing this asymptotic variance using convex duality, we then obtain an importance sampling estimator of the option price. Numerical tests in the variance gamma model show consistent variance reduction with a very small computational overhead. (Adrien Genin and Peter Tankov)
Optimal importance sampling for Lévy processesread_more
HG G 43
27. Oktober 2016
17:15-18:15 		Tim Boonen
Universiteit van Amsterdam
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Talks in Financial and Insurance Mathematics

Titel Capital allocation for portfolios with non-linear risk aggregation
Referent:in, Affiliation Tim Boonen, Universiteit van Amsterdam
Datum, Zeit 27. Oktober 2016, 17:15-18:15
Ort HG G 43
Abstract Existing risk capital allocation methods, such as the Euler rule, work under the explicit assumption that portfolios are formed as linear combinations of random loss/profit variables, with the firm being able to choose the portfolio weights. This assumption is unrealistic in an insurance context, where arbitrary scaling of risks is generally not possible. Here, we model risks as being partially generated by Lévy processes, capturing the non-linear aggregation of risk. The model leads to non-homogeneous fuzzy games, for which the Euler rule is not applicable. For such games, we seek capital allocations that are in the core, that is, do not provide incentives for splitting portfolios. We show that the Euler rule of an auxiliary linearized fuzzy game (non-uniquely) satisfies the core property and, thus, provides a plausible and easily implemented capital allocation. In contrast, the Aumann-Shapley allocation does not generally belong to the core. For the non-homogeneous fuzzy games studied, Tasche's (1999) criterion of suitability for performance measurement is adapted and it is shown that the proposed allocation method gives appropriate signals for improving the portfolio underwriting profit. This presentation is based on joint work with Andreas Tsanakas (Cass Business School) and Mario Wüthrich (ETH Zürich).
Capital allocation for portfolios with non-linear risk aggregationread_more
HG G 43
10. November 2016
17:15-18:15 		Michaela Szölgyenyi
Vienna University of Economics and Business
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Talks in Financial and Insurance Mathematics

Titel A numerical method for SDEs appearing in insurance and financial mathematics
Referent:in, Affiliation Michaela Szölgyenyi, Vienna University of Economics and Business
Datum, Zeit 10. November 2016, 17:15-18:15
Ort HG G 43
Abstract When solving certain stochastic control problems in insurance- or financial mathematics, the optimal control policy sometimes turns out to be of threshold type, meaning that the control depends on the controlled process in a discontinuous way. The stochastic differential equations (SDEs) modeling the underlying process then typically have a discontinuous drift coefficient. This motivates the study of a more general class of such SDEs. We prove an existence and uniqueness result, based on a certain transformation of the state space by which the drift is “made continuous”. As a consequence the transform becomes useful for the construction of a numerical method. The resulting scheme is proven to converge with strong order 1/2. This is the first scheme for which strong convergence is proven for such a general class of SDEs with discontinuous drift. Joint work with G. Leobacher (JKU Linz)
A numerical method for SDEs appearing in insurance and financial mathematicsread_more
HG G 43
17. November 2016
17:15-18:15 		Pavel Shevchenko
Macquarie University
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Talks in Financial and Insurance Mathematics

Titel Crunching Mortality and Annuity Portfolios with extended CreditRisk+
Referent:in, Affiliation Pavel Shevchenko, Macquarie University
Datum, Zeit 17. November 2016, 17:15-18:15
Ort HG G 43
Abstract Using an extended version of the credit risk model CreditRisk+, we develop a flexible framework that provides a unified and stochastically sound approach to model mortality, allowing underlying stochastic risk factors on the one hand and risk aggregation in annuity portfolios on the other hand. Deaths are driven by common stochastic risk factors which may be interpreted as death causes like neoplasms, circulatory diseases or idiosyncratic components. These common factors introduce dependence between policyholders in the annuity portfolios or between death events in population. The approach provides an efficient and numerically stable algorithm for an exact calculation of the one-period loss distribution where various sources of risk are considered. As required by many regulators, we can then derive risk measures for the one-period loss distribution such as value-at-risk and expected shortfall. Using publicly available data, we provide estimation procedures for mortality model parameters including classical approaches, as well as Markov chain Monte Carlo methods. The model allows stress testing and offers insight into how certain health scenarios influence annuity payments of an insurer. Such scenarios may include outbreaks of epidemics, improvement in health treatment, or development of better medication. We conclude with a real world example using Australian death data and present long-term forecast for life expectancy and death probabilities due to different causes.The talk is based on recent papers: 1) J. Hirz, U. Schmock and P.V. Shevchenko and (2016). Crunching mortality and annuity portfolios with extended CreditRisk Plus. Preprint, http://ssrn.com/abstract=2717518. 2) J. Hirz, U. Schmock and P.V. Shevchenko (2016). Modelling Annuity Portfolios and Longevity Risk with Extended CreditRisk Plus. Preprint, http://arxiv.org/abs/1505.04757. 3) P.V. Shevchenko, J. Hirz and U. Schmock (2015). Forecasting Leading Death Causes in Australia using Extended CreditRisk+. In T. Weber, M. J. McPhee, and R. S. Anderssen (Eds.), MODSIM2015, 21st International Congress on Modelling and Simulation. Modelling and Simulation Society of Australia and New Zealand, pp. 966-972. ISBN: 978-0-9872143-5-5. http://www.mssanz.org.au/modsim2015/E1/shevchenko.pdf.
Crunching Mortality and Annuity Portfolios with extended CreditRisk+read_more
HG G 43
24. November 2016
17:15-18:15 		Johannes Muhle-Karbe
University of Michigan
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Talks in Financial and Insurance Mathematics

Titel Equilibrium Liquidity Premia
Referent:in, Affiliation Johannes Muhle-Karbe, University of Michigan
Datum, Zeit 24. November 2016, 17:15-18:15
Ort HG G 43
Abstract In a continuous-time model with mean-variance investors and quadratic transaction costs, we show that the equilibrium expected return can be characterized as the solution of a system of coupled but linear forward-backward stochastic differential equations. Explicit formulas obtain in the small-cost limit, which allow to assess the comparative statics of equilibrium liquidity premia. (Joint work with Masaaki Fukasawa and Martin Herdegen)
Equilibrium Liquidity Premiaread_more
HG G 43
8. Dezember 2016
17:15-18:15 		Marcus C Christiansen
Heriot Watt University
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Talks in Financial and Insurance Mathematics

Titel Backward stochastic differential equations in life insurance mathematics
Referent:in, Affiliation Marcus C Christiansen, Heriot Watt University
Datum, Zeit 8. Dezember 2016, 17:15-18:15
Ort HG G 43
Abstract The concept of BSDEs primarily entered the life insurance literature as a tool to deal with financial risk, based on the fact that financial risk plays a major role in life insurance. Only recently BSDEs are also discussed as useful tools for distinctive insurance problems that are not just adopted from finance. The talk gives an overview of recent developments in the life insurance literature and discusses several BSDE applications in detail. In particular the talk covers the following problems: decomposition of risk, non-Markovian biometrical modelling, and circularly defined benefit payments. The latter question leads to a class of mean-field BSDEs that seem to be new in the literature.
Backward stochastic differential equations in life insurance mathematicsread_more
HG G 43

Organisatoren:innen: Matteo Burzoni

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