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)
Title: Mathematical Modelling for a Sustainable Energy Future
Abstract: The environmental transition is one of the defining challenges of our time, and a key pillar in achieving it is the energy transition—the shift toward a cleaner, more efficient, and more flexible energy system. Within this context, demand side management plays a central role, relying on two complementary approaches: energy efficiency, which aims to reduce overall energy consumption, and demand flexibility, which enables consumers to adjust their usage in response to system needs.
In this talk, I will present two mathematical models that explore these approaches through the lens of incentives and interactions among large populations of consumers. Both models are developed using the frameworks of mean-field games and principal–agent mean-field games, powerful tools for analysing systems with many interacting decision-makers.
The first model focuses on demand flexibility, studying a scenario where consumers participate in a Demand Side Management contract and agree to reduce their aggregated power consumption by a predefined amount at random times. Numerical results illustrate how such interactions influence consumption patterns and electricity prices.
The second model addresses energy efficiency, examining how an energy retailer can design innovative contracts based on a ranking system to encourage heterogeneous consumers to make lasting energy savings.
Together, these models shed light on how mathematical modelling can help design effective incentives and coordination mechanisms to support a sustainable energy future.
First Speaker: Christa Cuchiero (Universität Wien)
Title: Generative AI for finance: modeling with neural and signature stochastic differential equations
Abstract: Generative AI has recently transformed a wide range of fields by enabling the modeling of complex and high-dimensional datasets as well as the synthesis of new content. In finance, it offers a modern approach to scenario generation, for instance through market simulators and return generators. This talk explores the key characteristics of generative AI models, including autoencoders, GANs, diffusion models, as well as neural and signature stochastic differential equations (SDEs) - with a particular focus on the latter two.
We delve into the mathematical foundations of neural and signature SDEs, emphasizing especially their universal approximation capabilities. As financial applications we present a Bayesian calibration approach to neural SDEs, a data-driven version of the Heath–Jarrow–Morton framework for interest rate modeling, and signature-based asset price models calibrated jointly to VIX and SPX options.
Second Speaker: Eduardo Abi Jaber (Ecole Polytechnique)
Title: Efficient Simulation of Affine Volterra Processes: From Heston to Hawkes
Abstract: We propose simple and efficient schemes for Affine Volterra processes, using integrated kernel quantities and the Inverse Gaussian distribution. The schemes preserve positivity, and can be shown to converge weakly by recasting them as stochastic Volterra equations with a measure-valued kernel. Our method applies to two important examples: Volterra square-root/Heston and Hawkes processes. In the first case, when using a fractional kernel, the scheme with large time steps seems to be more performant as the Hurst index H decreases to -1/2. In the second case, our scheme has deterministic complexity, in contrast with exact methods based on sampling jump times that have random complexity, which opens the door to efficient Monte Carlo methods.
First Speaker: Eyal Neumann (Imperial College London)
Titel: Stochastic Graphon Games with Memory
Abstract: We study finite-player dynamic stochastic games with heterogeneous interactions and non-Markovian linear-quadratic objective functionals, that admit player-specific memory. We derive the Nash equilibrium explicitly by converting the first-order conditions into a coupled system of stochastic Fredholm equations, which we solve in terms of operator resolvents. When interactions are modeled by a weighted graph, we formulate the corresponding continuum-player graphon game, and derive its Nash equilibrium explicitly using a novel approach. This approach consists of converting the first-order conditions into an infinite-dimensional coupled system of stochastic Fredholm equations, reducing it to an uncoupled system using the spectral decomposition of the graphon operator, and solving it in in closed form. Moreover, we show that the Nash equilibria of finite-player games on graphs converge to those of the graphon game as the number of players increases. Finally, we apply our results to various network games, including systemic risk models with delayed controls.
Second Speaker: Martin Herdegen (Universität Stuttgart)
Titel: The Interplay between Utility and Risk in Portfolio Selection
Abstract: We revisit the problem of portfolio selection, where an investor maximizes utility subject to a risk constraint. Our framework is very general and accommodates a wide range of utility and risk functionals, including non-concave utilities such as S-shaped utilities from prospect theory and non-convex risk measures such as Value at Risk.
Our main contribution is a novel and complete characterization of well-posedness for utility-risk portfolio selection in one period that takes the interplay between the utility and the risk objectives fully into account. We show that under mild regularity conditions the minimal necessary and sufficient condition for well-posedness is given by a very simple either-or criterion: either the utility functional or the risk functional need to satisfy the axiom of sensitivity to large losses. This allows to easily describe well-posedness or ill-posedness for many utility/risk pairs, which we illustrate by a large number of examples. The talk is based on joint work with Leonardo Baggiani and Nazem Khan.
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.