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 2017

Note: The highlighted event marks the next occurring event.

Date / Time Speaker Title Location
23 February 2017
Mathias Beiglböck 
TU Wien
Brenier-type results in Martingale Optimal Transport  HG G 43 
Abstract: A seminal result in optimal transport is Brenier's theorem on the structure of the optimal plan for squared distance costs. We briefly review related results on the martingale version of the transport problem and connections with robust finance and the Skorokhod embedding problem. We then introduce a continuous time Brenier-type theorem for the martingale transport problem which exhibits a particularly simple functional form. Finally, we explain a link of this result with the local vol model.
2 March 2017
Anthony Réveillac 
INSA de Toulouse
A Black-Scholes type formula for the pricing of some reinsurance contract  HG G 43 
Abstract: In this talk we will derive, using the Malliavin calculus, a new formula which can be thought as a counterpart for some reinsurance contracts of the celebrated Black-Scholes formula in Finance. Our approach allows one for instance to consider claims that may depend on the intensity of the underlying counting process defining the risk process. This constitutes a joint work with Caroline Hillairet (ENSAE - Paris) and Ying Jiao (ISFA - Lyon).
9 March 2017
Juan-Pablo Ortega 
Universität St. Gallen
Time-delay reservoir computers: nonlinear stability of functional differential systems and optimal nonlinear information processing capacity. Applications to stochastic nonlinear time series forecasting  HG G 43 
Abstract: Reservoir computing is a recently introduced brain-inspired machine learning paradigm capable of excellent performances in the processing of empirical data. We focus on a particular kind of time-delay based reservoir computers that have been physically implemented using optical and electronic systems and have shown unprecedented data processing rates. Reservoir computing is well-known for the ease of the associated training scheme but also for the problematic sensitivity of its performance to architecture parameters. This talk addresses the reservoir design problem, which remains the biggest challenge in the applicability of this information processing scheme. More specifically, we use the information available regarding the optimal reservoir working regimes to construct a functional link between the reservoir parameters and its performance. This function is used to explore various properties of the device and to choose the optimal reservoir architecture, thus replacing the tedious and time consuming parameter scannings used so far in the literature.
16 March 2017
Practitioner Seminar
23 March 2017
Walter Schachermayer 
Universität Wien
The amazing power of dimensional analysis: Quantifying market impact  HG G 43 
Abstract: A basic problem when trading in financial markets is to analyze the price movement caused by placing an order. Clearly we expect - ceteris paribus - that placing an order will move the price to the disadvantage of the agent. This price movement is called market impact. Following Kyle and Obizhaeva we apply dimensional analysis - a line of arguments wellknown in classical physics - to analyze to which extent the square root law applies. This universal law claims that the market impact is proportional to the square root of the size of the order. The mathematical tools of this analysis reside on elementary linear algebra. Joint work with Mathias Pohl, Alexander Ristig and Ludovic Tangpi.
30 March 2017
Fred Espen Benth 
University of Oslo
Cointegration in continuous-time for factor models  HG G 43 
Abstract: Based on some empirical evidence and stochastic models from the freight market, we propose a framework for cointegration in continuous-time. We study forward pricing, relevant in commodity markets, and how cointegration in the spot market affects the forward markets. We share some thoughts on particular cases like CARMA, polynomial and Levy stationary processes. Finally, we propose a notion of cointegration for infinite dimensional processes. The presentation is based on joint work with Andre Suess (Barcelona and Zuerich).
6 April 2017
Lisa R. Goldberg 
University of Berkeley
Identifying Financial Risk Factor with Sparse and Low-Rank Decompositions  HG G 43 
Abstract: We show how to use sparse and low-rank (SLR) matrix decompositions based on convex optimization to extract financial risk factors from a sample return covariance matrix. We provide an example that highlights the difference between this approach and the academic standard for financial factor identification, principal component analysis (PCA), which makes systematic errors. Using finance-oriented metrics, we analyze the accuracy of SLR and PCA on equally weighted portfolios and minimum variance portfolios in a simulated global equity market. Finally, we discuss non-convex programming formulations that show promise in identifying numerous sparse factors (industries, counties, etc) at various scales. A preprint that gives some background on what we’re up to is linked here: and more information can be found ion this page:
13 April 2017
Nabil Kazi-Tani 
ISFA and Université Lyon 1
Three points suffice  HG G 43 
Abstract: We consider the problem of optimally stopping a continuous-time Markov process with a stopping time satisfying a given expectation constraint. We first reformulate the problem as a linear optimization problem, over a set of probability measures satisfying some moment constraints. To do so, we extend the balayage approach of Chacon and Walsh to the Skorokhod embedding problem for general Markov processes. This also allows us to reduce the optimization over a set of atomic measures. Our main result is the following: it is sufficient to consider stopping times such that the stopped process has a law that is a weighted sum of 3 Dirac measures. In other words: stopping at three points is enough. Several examples will illustrate that result. This is a joint work with Stefan Ankirchner (University of Jena), Maike Klein (University of Jena) and Thomas Kruse (University of Duisburg-Essen).
20 April 2017
Tom Hurd 
McMaster University
Symmetric Modelling of Contagion in Banking Networks HG G 43 
27 April 2017
Scott Robertson 
Boston University
The pricing of contingent claims and optimal positions in asymptotically complete markets  HG G 43 
Abstract: We study utility indifference prices and optimal purchasing quantities for a contingent claim, in an incomplete semi-martingale market, in the presence of vanishing hedging errors and/or risk aversion. Assuming that the average indifference price converges to a well defined limit, we prove that optimally taken positions become large in absolute value at a specific rate. We draw motivation from and make connections to Large Deviations theory, and in particular, the celebrated Garrtner-Ellis theorem. To highlight the robustness of our main price convergence assumption, we analyze a number of well studied examples where this limiting behavior occurs, such as fixed markets with vanishing risk aversion, the basis risk model with high correlation, the Black-Scholes-Merton model with vanishing transaction costs, and the price impact recently introduced by Bank and Kramkov in the limit of vanishing market maker risk aversion. Lastly, we show that the large claim regime could naturally arise in partial equilibrium models. This is joint work with Constantinos Spilioupoulos (Boston Unviersity) and Michalis Anthropelos (University of Pireaus).
4 May 2017
Ari-Pekka Perkkiö 
Regular processes and duality  HG G 43 
Abstract: We study the optional projection on spaces of cadlag and continuous processes. Our main results sharpen those of Bismut in cases where the projected process has additional integrability properties. Moreover, we characterize the topological duals of optional cadlag processes and of regular processes with the given integrability properties. Our main results are derived by purely functional analytic arguments simplifying Bismut's original proofs. We also present results on dual representations for convex integral functionals on regular processes. These yield a maximum principle for a general class of singular stochastic control problems. In currency markets, we get dual representations for "regular" solvency cones. The talk is based on a joint work with Teemu Pennanen.
11 May 2017
Chris Rogers 
University of Cambridge
Combining different models  HG G 43 
Abstract: Portfolio selection is one of the most important areas of modern finance, both theoretically and practically. Reliance on a single model is fraught with difficulties, so attempting to combine the strengths of different models is attractive. This talk discusses model combination, but with a difference: the models we consider here are making statements about different sets of assets. There appear to be no studies making this structural assumption, which completely changes the nature of the problem. This paper offers suggestions for principles of model combination in this situation, characterizes the solution in the case of multivariate Gaussian distributions, and shows how a practical implementation can be done.
18 May 2017
Felix Kübler 
Universität Zürich
Markov equilibria in models with financial frictions  HG G 43 
Abstract: Dynamic general equilibrium models with heterogeneous agents and financial frictions are difficult to analyze because stationary Markov equilibria may fail to exist. I give a serious of sufficient conditions that guarantee existence in models with incomplete markets, and/or borrowing constraints.
22 May 2017
Paolo Guasoni 
Dublin City University
Optimal Consumption and Investment with Healthcare Spending  HG G 19.2 
Abstract: Health-care slows the natural growth of mortality, indirectly increasing utility from consumption through longer lifetimes. We solve the problem of optimal dynamic investment, consumption, and healthcare spending with isoelastic utility, when natural mortality grows exponentially to reflect the Gompertz' law and investment opportunities are constant. Optimal consumption and healthcare imply an endogenous mortality law that is asymptotically exponential in the old-age limit, with lower growth rate than natural mortality. Health spending steadily increases with age, both in absolute terms and relative to total spending. The optimal stochastic control problem reduces to a nonlinear ordinary differential equation with a unique solution, which has an explicit expression in the old-age limit. Differential access to healthcare can account for observed longevity gains across cohorts.
25 May 2017
Ascension day
1 June 2017
Hanspeter Schmidli 
Universität Köln
Dividends with Tax and Capital Injection in a Spectrally Negative Levy Risk Model  HG G 43 
Abstract: We consider a risk model driven by a spectrally negative L\'evy process. From the surplus dividends are paid and capital injections have to be made in order to keep the surplus positive. In addition, tax has to be paid for dividends, but injections lead to an exemption from tax. We generalise the results for the diffusion approximation and for the classical model, and show that the optimal dividend strategy is a two barrier strategy. The barrier depends on whether an immediate dividend would be taxed or not. For a risk process perturbed by diffusion with exponentially distributed claim sizes we show how the value function and the barriers can be determined.

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