Mathematical Finance Seminar
Date
Time
17:15
Location:
RUD 25; 1.115
Stefan Weber (Hannover)

Robust Portfolio Selection Under Recovery Average Value at Risk

We study mean-risk optimal portfolio problems where risk is measured by Recovery Average Value at Risk, a prominent example in the class of recovery risk measures. We establish existence results in the situation where the joint distribution of portfolio assets is known as well as in the situation where it is uncertain and only assumed to belong to a set of mixtures of benchmark distributions (mixture uncertainty) or to a cloud around a benchmark distribution (box uncertainty). The comparison with the classical Average Value at Risk shows that portfolio selection under its recovery version allows financial institutions to better control the recovery of liabilities while still allowing for tractable computations. The talk is based on joint work with Cosimo Munari, Justin Plückebaum and Lutz Wilhelmy.

Mathematical Finance Seminar
Date
Time
16:15
Location:
RUB 25; 1.115
Alexandros Saplaouras (Athens)

The Itô Integral for Nonlinear Lévy Processes: Insights into the G-Lévy Framework

Nonlinear Lévy processes, as established within the general framework by A. Neufeld and M. Nutz, offer a versatile foundation without restrictions on the characteristic triplets. Building on this foundational work, we focus specifically on G-Lévy processes, a concept introduced by S. Peng. Adopting Peng's approach, we construct the Itô integral with respect to G-Lévy processes and examine its associated properties. Alongside, we delve into results concerning the uniqueness of fully nonlinear integro-partial differential equations and briefly discuss the technical challenges.

Mathematical Finance Seminar
Date
Time
17:15
Location:
HUB; RUD 25; 1.115
Patrick Cheridito (ETH)

Sentiment-based asset pricing

We propose a continuous-time equilibrium model with a representative agent that is subject to stochastically fluctuating sentiments. Sentiments dynamically respond to past price movements and exhibit jumps, which occur more frequently when sentiments are disconnected from underlying fundamentals. We model feedback effects between asset prices and sentiment in both directions. Our analysis shows that in equilibrium, sentiments affect prices even though they have no direct impact on the asset’s fundamentals. Empirically, the equilibrium risk premia and risk-free rate respond to measurable shifts in sentiment in the direction predicted by the model. 

Mathematical Finance Seminar
Date
Time
16:15
Location:
RUD 25; 1.115
Stefanos Theodorakopoulos (TU Berlin)

Topics on mean-field and McKean–Vlasov BSDEs, and the backward propagation of chaos

We shall present different versions of McKean-Vlasov and mean-field BSDEs of increasing generality, and the notion of backward propagation of chaos. We will then discuss some of the technical difficulties associated with the corresponding limit theorems and see some of their immediate corollaries and rates of convergence. Finally, we will introduce the concept of stability with respect to data sets for the backward propagation of chaos, and state the intermediate results that allowed us to prove its validity under a natural framework.

Probability Colloqium
Date
Time
16:15
Location:
HUB; RUD 25; 1.115
Patrick Cheridito (ETH)

Optimal transport and Wasserstein distances for causal models

We introduce a variant of optimal transport adapted to the causal structure given by an underlying directed graph G. Different graph structures lead to different specifications of the optimal transport problem. For instance, a fully connected graph yields standard optimal transport, a linear graph structure corresponds to causal optimal transport between the distributions of two discrete-time stochastic processes, and an empty graph leads to a notion of optimal transport related to CO-OT, Gromov–Wasserstein distances and factored OT. We derive different characterizations of G-causal transport plans and introduce Wasserstein distances between causal models that respect the underlying graph structure. We show that average treatment effects are continuous with respect to G-causal Wasserstein distances and small perturbations of structural causal models lead to small deviations in G-causal Wasserstein distance. We also introduce an interpolation between causal models based on G-causal Wasserstein distance and compare it to standard Wasserstein interpolation.

 

Probability Colloqium
Date
Time
16:15
Location:
RUD 25; 1.115
Günter Last (KIT)

The stationary marked random connection model: uniqueness of the infinite cluster and sharp phase transition

Mathematical Finance Seminar
Date
Time
17:15
Location:
RUD 25; 1.115
Filippo de Feo (Luiss Guido Carli University, Milano)

Optimal control of stochastic delay differential equations and applications to financial and economic models

Mathematical Finance Seminar
Date
Time
16:15
Location:
RUD 25; 1.115
Yonatan Shadmi (Imperial College London)

Fluid limits of fragmented limit order markets

Probability Colloqium
Date
Time
16:15
Location:
RUD 25; 1.115
Julia Komjathy (Delft)

Cluster-size decay for long range percolation

Mathematical Finance Seminar
Date
Time
17:15
Location:
HUB; RUD 25; 1.115
Johannes Muhle-Karbe (London)

Concave Cross Impact

The price impact of large orders si wel known ot be a concave function of trade size. We discuss how ot extend models consistent with this "square-root law" to multivariate setings with cross impact, where trading each asset also impacts the prices of the others. nI this context, we derive consistency conditions that rule out price manipulation. These minimal conditions make risk-neutral trading problems tractable and also naturally lead ot parsimonious specifications that can be calibrated ot historical data. We ilustrate this with a case study using proprietary CFM meta order data.
(Joint work ni progress with Natascha Hey and lacopo Mastromateo)