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.
First Speaker: Matthias Scherer (Technische Universität München )
Titel: Pricing Insurance Contracts with an Existing Portfolio as Background Risk.
Abstract: How should an insurer price a new contract when it wants to account for the dependence between the new risk and its existing portfolio? This talk introduces a new premium principle—the conditional indifference premium—which explicitly incorporates the insurer’s current portfolio as background risk. Unlike classical law-invariant pricing rules, this approach captures the dependence between the new risk and existing exposures, yielding prices that better reflect diversification and accumulation effects.
The talk will present the theoretical foundations of the conditional indifference premium, explore its axiomatic and stochastic dominance properties, and highlight its connection to risk measures and regulatory capital. Through examples with exchangeable portfolios, we illustrate how portfolio size and dependence structure influence the marginal price of additional risks, shedding new light on the limits of diversification in insurance pricing.
Second Speaker: Holger Kraft (Goethe Universität Frankfurt)
Titel: Sustainable Decisions.
Abstract: This paper rigorously defines sustainable decisions from first principles. A decision is sustainable if its performance (e.g., utility) constitutes at least a fair game. From a probabilistic point of view, this idea can be formalized by applying the concept of submartingales. Our approach allows us to establish the novel concept of sustainable optimization and leads to novel sustainable optimization and equilibrium problems. It requires an extension of the classical dynamic-programming paradigm including a formal derivation of a sustainable Bellman principle. Our approach can be applied to a huge number of decision problems where potentially heterogeneous decision makers optimize some form of "well-being" (e.g., utility or costs). We demonstrate its usefulness by studying various problems from economics, finance, marketing, or engineering. We derive sustainable consumption-investment strategies with habit formation or recursive utility, sustainable advertising strategies, sustainable compensation contracts in a principal-agent framework, or a sustainable equilibrium in a two-agent endowment economy.
Speaker: Roxana Dumitrescu (ENSAE-CREST, Institut Polytechnique de Paris)
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First Speaker: Christa Cuchiero (Universität Wien)
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Second Speaker: Eduardo Abi Jaber (Ecole Polytechnique)
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First Speaker: Eyal Neumann (Imperial College London)
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Second Speaker: Martin Herdegen (Universität Stuttgart)
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First Speaker: Peter Hieber (Université de Lausanne, Switzerland)
Title: Irrationality and exogeneous risk in optimal control problems
Abstract: For optimal control problems in finance and insurance, it is a common assumption to look at “rational” individuals. However, to understand human decision making, it is sometimes necessary to analyze and understand systematic irrational behavior. People tend to have systematic perceptions or biases that lead to “irrational” decisions. We discuss the example of over-confidence and subjective mortality beliefs and show how their presence can impact the relative attractiveness of different retirement products. This is one possible explanation of phenomena like the so-called annuity puzzle.
In the second part of the talk, we look at the impact of exogenous risks (taxes, tariffs) on optimal investment decisions. The focus is on tax risk, that is an uncertainty in the future taxation of investments. We use this setting to look at advance tax rulings (ATR), agreements with governments to mitigate tax uncertainty for multi-national companies.
Part of this talk is joint work with An Chen (University of Ulm), Manuel Rach (University of St. Gallen) and Caren Sureth-Sloane (University of Paderborn).
Second Speaker: Scott Robertson (Boston University)
Title: Equilibrium with Endogenous Insider Information Acquisition Time
Abstract: In this talk, we establish equilibrium in the presence of heterogeneous information. In particular, there is an insider who receives a private signal, an uninformed agent with no private signal, and a noise trader with semi price-inelastic demand. The novelty is that we allow the insider to decide (optimally) when to acquire the private signal. This endogenizes the entry time and stands in contrast to the existing literature which assumes the signal is received at the beginning of the period. Allowing for optimal entry also enables us to study what happens before the insider enters with private information, and how the possibility for future information acquisition both affects current asset prices and creates demand for information related derivatives. Results are valid in continuous time, when the private signal is a noisy version of the assets’ terminal payoff, and when the quality of the signal depends on the entry time. This is joint work with Jerome Detemple of Boston University.
First Speaker: Min Dai (Hong Kong Polytechnic University, Hong Kong)
Title: Some Differential Game Problems in Finance
Abstract: In this talk, I will discuss several differential game problems in finance, including: (i) a zero-sum Dynkin game related to portfolio selection with transaction costs; (ii) a non-zero-sum Dynkin game arising from the pricing of convertible bonds; (iii) a real-option entry (stopping-time) game featuring equilibrium second-mover advantages; and (iv) a repeated irreversible investment (singular-control) game. This talk is based on my collaborative work with Nan Chen, Zhaoli Jiang, Neng Wang, Xiangwei Wan, and Fahuai Yi.
Second Speaker: Gero Junike (Carl von Ossietzky Universität Oldenburg)
Title: Profit and Loss decompositions under model ambiguity
Abstract: Financial institutions and insurance companies analyzing the evolution and sources of profits and losses often look at risk factors only at discrete reporting dates, ignoring the detailed paths. Continuous-time decompositions avoid this weakness and also makes decompositions consistent across different reporting grids. In the first part of the talk, we construct a large class of continuous-time decompositions from a new extended version of Itô's formula and uniquely identify a preferred decomposition from the axioms of exactness, symmetry and normalization. This unique decomposition turns out to be a stochastic limit of recursive Shapley decompositions, but it suffers from a curse of dimensionality as the number of risk factors increases. We develop an approximation that breaks this curse when the risk factors almost surely have no simultaneous jumps. In the second part of the talk, we introduce model ambiguity. Why this? In practical applications, one usually observes only a single path of the risk factors. The stochastic behavior of the risk factors is often unknown. Therefore, we do not assume that the probability measure is known, but take a model-free approach. Our pathwise construction of the stochastic integral follows Bichteler (1981) and Karandikar (1995), but we make modifications to ensure non-anticipativity.