Stochastics and Finance Workshop

Date and Time

• Friday, 14 November 2025

Venue

• Mathematical Insitute LMU, Theresienstr. 39, Room B 251

Schedule

Speakers

Talks and Abstracts

Johannes Wiesel - Bounding adapted Wasserstein metrics

The Wasserstein distance W is an important instance of an optimal transport cost. Its numerous mathematical properties as well as applications to various fields such as mathematical finance and statistics have been well studied in recent years. The adapted Wasserstein AW distance extends this theory to laws of discrete time stochastic processes in their natural filtrations, making it particularly well suited for analyzing time-dependent stochastic optimization problems.
While the topological differences between AW and W are well understood, their differences as metrics remain largely unexplored beyond the trivial bound W<AW . This talk closes this gap by providing upper bounds of AW in terms of W through investigation of the smooth adapted Wasserstein distance. Our upper bounds are explicit and are given by a sum of W, Eder's modulus of continuity and a term characterizing the tail behavior of measures. As a consequence, upper bounds on W automatically hold for AW under mild regularity assumptions on the measures considered. A particular instance of our findings is the inequality AW < CW^(1/2) on the set of measures that have Lipschitz kernels.

Our work also reveals how smoothing of measures affects the adapted weak topology. In fact, we find that the topology induced by the smooth adapted Wasserstein distance exhibits a non-trivial interpolation property, which we characterize explicitly: it lies in between the adapted weak topology and the weak topology, and the inclusion is governed by the decay of the smoothing parameter.

This talk is based on joint work with Jose Blanchet, Martin Larsson and Jonghwa Park.

David Criens - Stochastic control problems with irregular coefficients and L_d-drift

Stochastic optimal control problems naturally arise in contexts such as optimal investment, optimal consumption, and economic growth. Moreover, many fundamental models in robust finance - such as G-Brownian motion, G-diffusions, or G-semimartingales - can be translated to frameworks of stochastic control. A central aspect of these problems is the connection between value functions and Hamilton-Jacobi-Bellman (HJB) equations. For controlled diffusions with sufficiently regular coefficients, this link is typically established either through the comparison method, relying on a comparison principle for discontinuous viscosity solutions, or via the verification approach, which requires the existence of classical or Sobolev solutions.
In this talk, we consider a general class of controlled diffusions for which these traditional methods break down. We present a new approach that connects stochastic control problems and HJB equations by combining probabilistic and analytic techniques. Furthermore, we discuss uniqueness results, leading to stochastic representations of HJB equations in terms of control problems, and provide stability results for associated value functions.

Max Nendel - Upper Comonotonicity and Risk Aggregation Under Dependence Uncertainty

In this talk, we study dependence uncertainty and the resulting effects on tail risk measures, which play a fundamental role in modern risk management. We introduce the notion of a regular dependence measure, defined on multimarginal couplings, as a generalization of well-known correlation statistics such as the Pearson correlation. The first main result states that even an arbitrarily small positive dependence between losses can result in perfectly correlated tails beyond a certain threshold and seemingly complete independence before this threshold. In a second step, we focus on the aggregation of individual risks with known marginal distributions by means of arbitrary nondecreasing left-continuous aggregation functions. In this context, we show that under an arbitrarily small positive dependence, the tail risk of the aggregate loss might coincide with the one of perfectly correlated losses. A similar result is derived for expectiles under mild conditions. In a last step, we discuss our results in the context of credit risk, analyzing the potential effects on the value at risk for weighted sums of Bernoulli distributed losses.

Michael Kupper - Martingales and Path-Dependent PDEs via Evolutionary Semigroups on Path Space

Martingales associated with path-dependent payoff functions are intrinsically linked to path-dependent PDEs. While this connection is typically established via a functional Itô formula, in this talk we present a semigroup-theoretic framework for the analytic characterization of martingales with path-dependent terminal conditions. Specifically, we show that a measurable adapted process of the form V(t) - ∫_0^t Ψ(s)ds is a martingale if and only if a time-shifted version of V is a mild solution to a final value problem (FVP) involving a path-dependent differential operator. We establish existence and uniqueness of solutions to such FVPs using the concept of evolutionary semigroups on path space. We also discuss the relationship between semigroups on path space, nonlinear expectations and their penalty functions. The talk is based on joint work with David Criens, Robert Denk and Markus Kunze.