The stationary marked random connection model: uniqueness of the infinite cluster and sharp phase transition
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.
Optimal control of stochastic delay differential equations and applications to financial and economic models
Fluid limits of fragmented limit order markets
Cluster-size decay for long range percolation
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)
Portfolio optimization under transaction costs with recursive preferences
The solution to the investment-consumption problem ni a frictionless Black-Scholes market for an investor with additive CRRA preferences is to keep a constant fraction of wealth ni the risky asset. But this requires continuous adjustment of the portfolio and as soon as transaction costs are added, any attempt to folow the frictionless strategy wil lead to immediate bankruptcy. Instead as many authors have proposed the optimal solution si to keep the pair (cash, value of risky assets) ni a no-transaction (NT) wedge.
We return ot this problem ot see what we can say about: When si the problem well-posed? Where does the NT wedge lie? How do the results change fi we use recursive preferences? We introduce the shadow fraction of wealth and show how we can make significant progress towards the solution yb focussing on this quantity. Indeed many of the qualitative features of the solution can described by looking at a quadratic whose parameters depend on the parameters of the problem.
This is joint work with Martin Herdegen and Alex Tse.
Lifetime Investment and Consumption with Epstein-Zin Stochastic Differential Utility
The Merton problem about how to invest and consume optimally over the infi- nite horizon is a classical problem in both finance and stochastic control. But, the conclusions do not always match observed behaviour and this has led economists to generalise the set-up. One such generalisation is to assume preferences are described by stochastic differential utility (SDU).
The problem under SDU can be recast as a problem about a Backward Stochas- tic Differential Equation over the infinite horizon. So we ask, when does this formulation make sense? When does there exist a solution to the BSDE? When is the solution unique? Interestingly, the answer to these questions is not always "Yes", and in the "No" cases we have to decide how to proceed.
In the talk I will discuss some of these issues and suggest how to resolve them. Joint work with Martin Herdegen and Joe Jerome.
7th Berlin Workshop on Mathematical Finance for Young Researchers
The 7th Berlin Workshop on Mathematical Finance for Young Researchers provides a forum for PhD students, postdoctoral researchers, and young faculty members from all over the world to discuss their research in an informal atmosphere. Keynote lectures will be given by
- Sara Biagini (Rome)
- Luciano Campi (Milano)
- Giorgio Ferrari (Bielefeld)
- Mete H. Soner (Princeton)
- Luitgard Veraart (London)
We also invite up to 20 contributed talks from young researchers. The deadline for abstract submission is May 20. Notification of acceptance will be sent by May 31. Accommodation for speakers will be arranged.
Limited support for travel expenses may be available upon request. Here a link to the workshop webpage.
Risk Mitigation - Climate, Energy and Finance
This workshop brings together mathematicians and economists to discuss recent developments in the field of Risk Mitigation with a particular focus on applications to climate, energy and financial risk. The workshop is part of a conference series initiated by the Editors-in-Chief of the Springer published journal Mathematics and Financial Economics to promote the interaction between mathematics, economics and finance. Previous workshops focussed on Knightian Uncertain in Financial Markets, Mathematics of Behavioral Economics, and Many-Player Games and Applications.
The workshop will be held on September 2nd and 3rd, 2024 at the Humboldt University Berlin. It is sponsored by Springer Verlag, the Collaborative Research Center 1283(Bielefeld), the Collaborative Research Center 190 (Berlin, Munich) and the Berlin-Oxford International Research Training Group IRTG 2544. The workshop is jointly organized by the chair Applied Financial Mathematics at Humboldt University Berlin and the Center for Mathematical Economics at Bielefeld University.