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.
Alfred Müller (Universität Siegen)
Titel: Decisions under uncertainty: sufficient conditions for almost stochastic dominance
Abstract: Decision making under risk involves a ranking of distributions, which is typically based on a method for assigning a real number to a distribution using a risk measure, a premium principle or a context of expected utility. As it is typically difficult to assess a concrete risk measure or utility function it is a well established idea to use stochastic dominance rules in form of stochastic orders to compare distributions. However, it is often equally difficult to completely specify a distribution. Therefore it is an interesting question whether one can derive unambiguous decisions under partial knowledge of the distributions. In this talk we in particular address this question under the condition that we only know the mean and variance of the involved distributions or that we know the marginal distributions but not the copulas in a multivariate context. Under such assumptions we derive sufficient conditions for concepts of almost stochastic dominance that are based on restrictions on marginal utilities. The talk is based on joint work with Marco Scarsini, Ilia Tsetlin and Robert L. Winkler.
Leonie Brinker (Universität zu Köln)
Titel: Waiting for better times: Dividend optimisation with a negative preference rate
Abstract: How and when to pay out dividends is a crucial question for many companies. In stochastic control theory, this question can be modelled as the problem of choosing a càdlàg, adapted process D (representing the accumulated dividend payments) which maximises the expected discounted value of dividends up to the time when the post-dividend surplus becomes negative. Often the discounting function is modelled in such a way that money `today' is preferred to money `tomorrow'. However, these preferences can change over time and are subject to various exogenous and endogenous factors, such as changes in management, the influence of (im-)patient investors, regulatory requirements and market crashes.
In this talk, we consider an extension of the dividend maximisation problem for an insurance company by allowing switches between a positive and a negative time preference rate. The negative preference reflects the `tendency to wait' many companies show in times of uncertainty. We model the surplus by a Brownian risk process and the preference rate by a two-state Markov chain. We solve the problem of finding the optimal dividend payout strategy for the setting with a classical ruin concept as well as for the case of Parisian ruin with an exponential delay.
The talk is based on joint work with Julia Eisenberg (TU Vienna).
Andrea Modena (University of Mannheim)
Titel: Dynamic Tax Evasion and Capital Misallocation in General Equilibrium
Abstract: We study tax evasion in a tractable macroeconomic model with productive public expenditure financed by a fixed-rate income tax. Taxpayers are heterogeneous in their productivity and subject to borrowing constraints. They can lower their fiscal burden by evading taxes at the risk of being audited (and fined) by the government. We solve the model for its competitive equilibrium and characterize entrepreneurs’ optimal policies contingent on their individual productivity and endogenous price levels. The model predicts that enforcing tax compliance stimulates the productivity of public expenditure, thus making less productive enterprises viable. At the same time, however, fewer evasion opportunities alleviate borrowing constraints by offsetting the advantage of low-productivity (and highly evasive) entrepreneurs, thereby reallocating capital to more productive users. On the demand side, decreasing tax evasion reduces consumption levels by curbing private capital accumulation. However, it fosters consumption rates by mitigating entrepreneurs’ precautionary motif against auditing risk.
Neofytos Rodosthenous (University College London)
Titel: Non-zero-sum optimal stopping game with continuous versus periodic observations
Abstract: We introduce a new non-zero-sum game of optimal stopping with asymmetric exercise opportunities. Given a stochastic process modelling the value of an asset, one player observes and can act on the process continuously, while the other player can act on it only periodically at independent Poisson arrival times. The first one to stop receives a reward, different for each player, while the other one gets nothing. We study how each player balances the maximisation of gains against the maximisation of the likelihood of stopping before the opponent. In such a setup, driven by a Lévy process with positive jumps, we not only prove the existence, but also explicitly construct a Nash equilibrium with values of the game written in terms of the scale function. Numerical illustrations with put-option payoffs are also provided to study the behaviour of the players' strategies as well as the quantification of the value of available exercise opportunities.
Dylan Possamai (ETH Zürich)
Title: Moral hazard for time-inconsistent agents and BSVIEs
Abstract: We address the problem of Moral Hazard in continuous time between a Principal and an Agent that has time-inconsistent preferences. Building upon previous results on non-Markovian time-inconsistent control for sophisticated agents, we are able to reduce the problem of the principal to a novel class of control problems, whose structure is intimately linked to the representation of the problem of the Agent via a so-called extended Backward Stochastic Volterra Integral equation. We will present some results on the characterization of the solution to problem for different specifications of preferences for both the Principal and the Agent.
Olivier Guéant (Université Paris 1)
Titel: Optimal market making in OTC markets: from optimal control on graphs to applications to FX
Abstract: The goal of this talk is to summarize the progress made over the last decade in the field of optimal market making modelling and to discuss new (open) problems. The talk will go through theoretical results about optimal control on graphs, closed-form approximations of solutions of Hamilton-Jacobi equations, and of course real world applications (to the foreign exchange markets).
Nizar Touzi (École Polytechnique)
Titel: Mean field game of mutual holding and systemic risk
Abstract: We provide an explicit solution for the mean field game of mutual holding with defaultable agents modeled by absorbtion at zero. The optimal dynamics are defined by a Mckean-Vlasov SDE with discontinuous diffusion coefficient and nonsmooth drift coefficient. We also provide an autonomous characterization of the distribution of defaults.
Christian Bender (Universität des Saarlandes)
Titel: Solving Optimal Stopping Problems via Randomization and Empirical Dual Optimization
Abstract: In this talk, we consider optimal stopping problems in their dual form. In this way, the optimal stopping problem can be reformulated as a problem of sample average approximation (SAA) that can be solved via linear programming. By randomizing the initial value of the underlying process, we enforce solutions with zero variance while preserving the linear programming structure of the problem. A careful analysis of the randomized SAA algorithm shows that it enjoys favorable properties such as faster convergence rates and reduced complexity compared to the nonrandomized procedure. We illustrate the performance of our algorithm on several benchmark examples.
The talk is based on joint work with D. Belomestny (U Duisburg-Essen) and John Schoenmakers (WIAS Berlin).
Ruonan Fu (Tilburg University)
Titel: Quantifying Ambiguity in the Stock Market Using Option Data
Abstract: tba
Lasse Mononen (University of Zürich)
Titel: State Dependent Utility and Ambiguity
Abstract: ls of choice under uncertainty study choice behavior when outcomes depend on the realized state of the world. The typical assumption is that utilities of outcomes do not depend on the realized state and are state independent. Without this simplifying assumption, it is difficult to separately identify utilities and beliefs. This paper provides novel general foundations for models with state dependent utilities: once we depart from expected utility, it is often possible to uniquely identify utilities and beliefs. Specifically, we show that with general models of non-expected utility under ambiguity we have complete identification of utilities and probabilities under full-dimensional uncertainty. Additionally, we offer novel axiomatizations for state dependent dual-self variational expected utility and dual-self expected utility. Finally, we consider applications of this identification to social choice theory for the identification of the fairness of a society and to intertemporal choice for the identification of evolving tastes.