Title: Model-independent FTAP from American option prices
Abstract: We consider a model-independent setting where we observe the price of American put options. We provide necessary and sufficient conditions for the existence of market models consistent with the observed prices, and prove a Fundamental Theorem of Asset Pricing for a suitable concept of arbitrage. While in the case of European options NA corresponds to dominance in convex order of the resulting asset marginal distributions, in the case of American options NA is characterized via dominance in a 'biased convex order'.
Based on joint work with M. Beiglboeck, E. Kolosov, G. Pammer.
Title: When defaults cannot be hedged: XVA calculations via Local Risk-Minimization
Abstract: In this talk we consider pricing and hedging of counterparty credit risk and funding in absence of hedging possibilities against the default of the bank or the counterparty. We tackle the market incompleteness due to the presence of possible defaults with the well-known local risk-minimization approach extended to a multi-curve setting. We describe the optimal strategy via the solution of a BSDE and use this
result to derive a decomposition of the price in terms of value adjustments.
Title: TBA
Abstract: TBA
Title: TBA
Abstract: TBA
Title: Feynman Formula for Discrete-time Quantum Walks
Abstract: We explicitly connect (discrete-time) quantum walks on Z with a four-state Markov additive process via a Feynman-type formula. Using this representation, we derive a relation between the spectral decomposition of the Markov additive process and the limiting density of the homogeneous quantum walk. In addition, we consider a space-time rescaling of quantum walks, which leads to a system of quantum transport PDEs in continuous time and space with a phase interaction term. Our probabilistic representation of this type of PDE offers an efficient Monte Carlo computational technique.
Title: TBA
Abstract: TBA
Title: From Quantiles to Lambda-Quantiles: An Ordinal Covariance Approach
Abstract: Lambda-quantiles generalise classical quantiles and were introduced in the financial literature by Frittelli et al. (2014), who replaced the fixed probability level in the usual definition of a quantile with a functional parameter $\Lambda \colon \mathbb{R} \to [0,1]$. In recent years, these functionals have received substantial attention in the actuarial and risk management literature. Applications should, however, be informed by a proper understanding of their axiomatic properties: in particular, which conditions on a functional $\rho$ on random variables $X$ ensure that $\rho$ is a Lambda-quantile.
Bellini and Peri (2022) and Chambers et al. (2025) provide axiomatisations of Lambda-quantiles for decreasing $\Lambda$. Their approaches are unrelated though to the classical axiomatisations of quantiles by Chambers (2009) and Fadina et al. (2023), which rely on ordinal covariance properties. The latter identify large classes of measurable scale changes $g \colon \mathbb{R} \to \mathbb{R}$ under which input and output of the functional $\rho$ transform in the same way:
\[\rho(g(X)) = g(\rho(X)) \quad \text{for all random variables } X.\]
In this talk, we bridge this gap by developing ordinal covariance properties for general Lambda-quantiles and demonstrating that they lead to far-reaching axiomatic characterisations. Based on joint work with Fabio Bellini (Milan-Bicocca).
Title: Notions of risk aversion
Abstract: We propose a new approach to risk aversion based on insurance motives.
Title: TBA
Abstract: TBAA
Title: Hidden Dependence and Aggregate Tail Risk
Abstract: We study risk aggregation problems for arbitrary non-decreasing aggregation functions and tail risk measures under dependence uncertainty in a distributionally robust setting. To this end, we introduce the notion of hidden dependence for random vectors, which is built on the concepts of risk concentration and common tail events developed in Wang and Zitikis (2020). We show that, starting from a tail event A of the aggregate loss for an arbitrary random vector Y, one can construct a random vector with hidden dependence that dominates Y on the tail event A. We then focus on the case in which model uncertainty is described by small perturbations of the distribution of a random vector with respect to a suitable probability distance without changing the marginals. We show that these perturbations of the reference distribution are compatible with hidden dependence and thus lead to the same worst-case risk bounds as in the unconstrained case for arbitrary γ-tail risk measures with a suitable level γ. Finally, we apply our results in a credit risk context and quantify the potential underestimation of portfolio risk arising from uncertainty in the dependence structure. In particular, we show that even small deviations from a reference Gaussian dependence model can, in principle, justify dramatic increases in capital requirements.
The talk is based on joint work with Corrado De Vecchi and Steven Vanduffel.
Title: Graph causal optimal transport
Abstract: We study the graph causal optimal transport problem, a generalisation of the classical optimal transport problem in which the allowed couplings satisfy causal restrictions prescribed by a directed graph. We characterise fully the directed acyclic graphs for which the associated graph causal Wasserstein discrepancy is a metric and show that the induced topology agrees with other natural adapted topologies. We characterise the gluing properties of graph causal couplings, prove denseness of Monge couplings, and obtain a dynamic programming principle which allows us to deduce when the graph causal Wasserstein and the adapted Wasserstein distances are equal. Our results link fundamental properties of graph causal optimal transport to structural properties of its underlying graph. Complementing Cheridito and Eckstein (2025), who first introduced such distances and established Lipschitz continuity for the average treatment effect in structural causal models, we obtain Lipschitz continuity of the value function in stochastic team problems.
Joint work with Vlad Tuchilus
Title: Knightian Uncertainty under Identifiability: Uncertainty Sharing, Insurance, and Portfolio Choice
Abstract: Knightian uncertainty arises when the decision maker lacks precise probabilistic information about the relevant model. This talk focuses on the important case in which the uncertainty is identifiable: although the correct probabilistic model is unknown ex ante, it can be perfectly learned from sufficiently rich observations ex post. This setting is relevant, for example, to uncertainty about volatility in financial markets.
Using smooth ambiguity preferences, the talk explores the implications of identifiability for the sharing and management of model uncertainty. First, it characterizes efficient uncertainty sharing and shows that, because contracts can be made contingent on the model that is eventually revealed, efficiency separates across models and coincides with conditional efficiency under each model. Second, it studies optimal insurance when the true model can be identified ex post. Remarkably, Arrow's classical result is restored: optimal insurance consists of a straight deductible in each model, although the optimal deductible varies with the model. The talk concludes with portfolio choice under identifiable uncertainty, including an application to uncertain volatility in the Variance-Gamma model.
Title: Linking risk-sensitivity and entropic regularization via free energy-entropy duality
Abstract: Via the free energy-entropy duality we reduce a risk sensitive stochastic control problem to a risk neutral game with an entropic regularization. For a linear-quadratic Gaussian setting we explicitly solve the implied regularized game assuming the model parameters to be known. The resulting solution structure then guides a policy gradient actor-critic approach for the case when the model parameters are unknown. We also discuss some implications of the results. (Based on a joint project with Sebastien Lleo).
Title: Bass martingales versus martingale Schr¨odinger bridges
Abstract: TBA
Title: Absence of arbitrage and changes of numeraire
Abstract: From an economic perspective, it seems reasonable that absence of arbitrage should be largely independent of the units of account one uses to denominate assets (this is often called numeraire-independence). In finite discrete time, this property is easily checked to be true. With an infinite number of trading dates (and in particular in continuous time), things become more subtle. We revisit this question and present a new variant of the concept of NUPBR (no unbounded profit with bounded risk) that is as numeraire-independent as possible, in a general semimartingale model on a right-open time interval.
The results are based on joint work with Jonas Gebele.
Title: Path-Dependent Ergodic Optimal Control and Backward Stochastic Differential Equations
Abstract: We investigate a new class of infinite-horizon backward stochastic differential equations for ergodic optimal control where the cost and state dynamics are time and path-dependent. The state process is defined on an unbounded underlying domain and satisfies an extended dissipativity condition. In contrast with the time-homogeneous Markovian setting, the optimal ergodic cost in our framework is characterized by the asymptotic behavior of a deterministic function, rather than by a single real constant. We obtain wellposedness, verification and stability properties, which extend the previous results in the literature on the Markov case.