Related papers: Schr\"odinger's problem with constraints
We present several models to describe the stochastic evolution of stocks that show some strong resistance at some level and generalize to this situation the evolution based upon geometric Brownian motion. If volatility and drift are related…
Large-size populations consisting of a continuum of identical and non-cooperative agents with stochastic dynamics are useful in modeling various biological and engineered systems. This paper addresses the stochastic control problem of…
We introduce a simple model for addressing the controversy in the study of financial systems, sometimes taken as brownian-like processes and other as critical systems with fluctuations of arbitrary magnitude. The model considers a…
It is known that the Brownian bridge or L\'evy-Ciesielski construction of Brownian paths almost surely converges uniformly to the true Brownian path. In the present article the focus is on the uniform error. In particular, we show…
In this paper we consider non-intersecting Brownian bridges, under fairly general upper and lower boundaries, and starting and ending data. Under the assumption that these boundary data induce a smooth limit shape (without empty facets), we…
We consider an entropy-regularized version of optimal density control of deterministic discrete-time linear systems. Entropy regularization, or a maximum entropy (MaxEnt) method for optimal control has attracted much attention especially in…
We establish connections between optimal transport theory and the dynamic version of the Kyle model, including new characterizations of informed trading profits via conjugate duality and Monge-Kantorovich duality. We use these connections…
Accurate modeling of system dynamics holds intriguing potential in broad scientific fields including cytodynamics and fluid mechanics. This task often presents significant challenges when (i) observations are limited to cross-sectional…
This short paper announces the main results of \cite{SBB2026}, where the Schr\"odinger--Bass Bridge (SBB) problem is introduced and studied in full generality. Here we provide a direct PDE derivation of the SBB system in dimension one,…
As is known, an option price is a solution to a certain partial differential equation (PDE) with terminal conditions (payoff functions). There is a close association between the solution of PDE and the solution of a backward stochastic…
Recently there has been much progress in the development of stochastic models for state reduction in quantum mechanics. In such models, the collapse of the wave function is a physical process, governed by a nonlinear stochastic differential…
The Black-Litterman model is a framework for incorporating forward-looking expert views in a portfolio optimization problem. Existing work focuses almost exclusively on single-period problems with the forecast horizon matching that of the…
We study the Schr\"odinger-Bass problem, a one-parameter family of semimartingale optimal transport problems indexed by $\beta>0$, whose limiting regimes interpolate between the classical Schr\"odinger bridge, the Brenier-Strassen problem,…
An efficient conditioning technique, the so-called Brownian Bridge simulation, has previously been applied to eliminate pricing bias that arises in applications of the standard discrete-time Monte Carlo method to evaluate options written on…
We characterize the Schr\"odinger bridge problems by a family of Mckean-Vlasov stochastic control problems with no terminal time distribution constraint. In doing so, we use the theory of Hilbert space embeddings of probability measures and…
We consider a Schr\"odinger bridge problem where the Markov process is subject to parameter perturbations, forming an ensemble of systems. Our objective is to steer this ensemble from the initial distribution to the final distribution using…
We reconsider the multivariate Kyle model in a risk-neutral setting with a single, perfectly informed rational insider and a rational competitive market maker, setting the price of n correlated securities. We prove the unicity of a…
We consider asset price models whose dynamics are described by linear functions of the (time extended) signature of a primary underlying process, which can range from a (market-inferred) Brownian motion to a general multidimensional…
In this paper, we show a large deviation principle for certain sequences of static Schr\"{o}dinger bridges, typically motivated by a scale-parameter decreasing towards zero, extending existing large deviation results to cover a wider range…
This study rigorously investigates the Keynesian cross model of a national economy with a focus on the dynamic relationship between government spending and economic equilibrium. The model consists of two ordinary differential equations…