Das Institut für Mathematische Wirtschaftsforschung veranstaltet im Rahmen des Bielefeld Stochastic Afternoon regelmäßig Seminare zum Thema Finanzmathematik. Das Programm des aktuellen Semesters finden Sie hier.
Michael Kupper (University of Konstanz)
Titel: Duality formulas for robust pricing and hedging in discrete time
Abstract: We focus on robust super- and subhedging dualities for contingent claims that can depend on several underlying assets. In addition to strict super- and subhedging, we also consider relaxed versions which, instead of eliminating the shortfall risk completely, aim to reduce it to an acceptable level. This yields robust price bounds with tighter spreads. As applications we study strict super- and subhedging with general convex transaction costs and trading constraints as well as risk based hedging with respect to robust versions of the average value at risk and entropic risk measure. As another application we discuss generalized Frechet-Hoeffding bounds. Our approach is based on representation results for increasing convex functionals. The talk is based on a joint work with Patrick Cheridito and Ludovic Tangpi.
Mathias Beiglboeck (TU Wien)
Titel: The Geometry of Model Uncertainty
Abstract: The over-confidence in mathematical models and the failure to account for model uncertainty have frequently been blamed for their infamous role in financial crises. Serious consideration of model ambiguity is vital not only in the financial industry and for proficient regulation but also for university level teaching. Remarkably, it remains an open challenge to quantify the effects of model uncertainty in a coherent way. From a mathematical perspective, this is a delicate issue which touches on deep classical problems of stochastic analysis. In recent work, we establish a new link to the field of optimal transport. This yields a powerful geometric approach to the problem of model uncertainty and, more generally, the theory of stochastic processes.
Huyen Pham (University Paris Diderot)
Titel: Robust Markowitz mean-variance portfolio selection under ambiguous volatility and correlation
Abstract: The Markowitz mean-variance portfolio selection problem is the cornerstone of modern portfolio allocation theory. In this talk, we study a robust continuous time version of the Markowitz criterion when the model uncertainty carries on the variance-covariance matrix of the risky assets. This problem is formulated into a min-max mean-variance problem over a set of non-dominated probability measures that is solved by a McKean-Vlasov dynamic programming approach, which allows us to characterize the solution in terms of a Bellman-Isaacs equation in the Wasserstein space of probability measures. We provide explicit solutions for the optimal robust portfolio strategies in the case of uncertain volatilities and ambiguous correlation between two risky assets, and then derive the robust efficient frontier in closed-form. We obtain a lower bound for the Sharpe ratio of any robust efficient portfolio strategy, and compare the performance of Sharpe ratios for a robust investor and for an investor with a misspecified model.
Jan Kallsen (University of Kiel)
Titel: On portfolio optimization under small fixed transaction costs
Abstract: While optimal investment under proportional transaction costs is quite well understood by now, less has been done in the presence of fixed fees for any single transaction. In this talk we consider the asymptotics ofthe no-trade region for small fixed costs. More specifically, we sketch the rigorous verification for a general univariate Ito process market under exponential utility. The talk is based on joint work with Mark Feodoria.
Frank Seifried (University of Trier)
Titel: Some Recent Results on Continuous-Time Recursive Utility
Abstract: This talk presents some recent work on the foundations of continuous-time recursive utility. The first part addresses the classical Epstein-Zin (EZ) parametrization of recursive utility. We establish existence, uniqueness, monotonicity, concavity, and a utility gradient inequality for continuous-time EZ utility in a fully general semimartingale setting. This generalizes existing results for Brown-ian filtrations as in Schroder and Skiadas (1999) and Xing (2015). In the second part, building on an abstract framework for nonlinear expectations that comprises g-, G- and random G-expectations, we develop a theory of backward nonlinear expectation equations (BNEEs) of the form
Xt = εt [ t ∫ T g(s,X)m(ds) + ξ ], t ∈ [0,T].
These can be thought of as BSDEs under nonlinear expectations. We provide existence, uniqueness, and stability results and establish convergence of the associated discrete-time nonlinear aggregations. BNEEs emerge naturally in the context of recursive preferences when ambiguity is taken into account. We apply our results to show that discrete-time recursive utility with ambiguity converges to the nonlinear stochastic differential utility of Chen and Epstein (2002) and Epstein and Ji (2014).
Mete Soner (ETH Zürich)
Titel: Trading with market impact
Abstract: It is well known that large trades cause unfavourable price impact resulting in trading losses. These losses are particularly high when the underlying instrument is not liquid enough or when the trade size is large. Other type of market frictions such as transaction costs also cause similar effects. The problem of optimal execution is a related problem which has been recently widely studied. In joint work with Peter Bank and Moritz Voss from TU Berlin we studied the tracking problem in such markets. The question we study is to efficiently construct a tracking portfolio once a desired portfolio process is given. Perfect tracking is not possible due to market frictions. The question is very much in analogy with image processing in which one is given a noisy image. We formulate the problem as quadratic optimization problem and provide an explicit solution using Riccati equations.