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. 

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.

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.

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)

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.