Related papers: Schr\"odinger's problem with constraints
We prove empirical central limit theorems for the distribution of levels of various random fields defined on high-dimensional discrete structures as the dimension of the structure goes to $\infty$. The random fields considered include costs…
We consider a generic market model with a single stock and with random volatility. We assume that there is a number of tradable options for that stock with different strike prices. The paper states the problem of finding a pricing rule that…
Depending on the persistence of the underlying Markov chain shock, the standard New Keynesian model predicts starkly different conclusions at the Effective Lower Bound. We clear up this morass by using a truncated Markov chain. We prove…
We consider optimal stopping problems for a Brownian motion and a geometric Brownian motion with a "disorder", assuming that the moment of a disorder is uniformly distributed on a finite interval. Optimal stopping rules are found as the…
The thermodynamic uncertainty relation expresses a seemingly universal trade-off between the cost for driving an autonomous system and precision in any output observable. It has so far been proven for discrete systems and for overdamped…
In a recent paper [1304.6846], Racorean introduced a formal similarity of the Black-Sholes stock pricing model with a Schr\"odinger equation. We use a previously introduced method of a resonant transmission line for arbitrary 2nd order…
The problem of stopping a Brownian bridge with an unknown pinning point to maximise the expected value at the stopping time is studied. A few general properties, such as continuity and various bounds of the value function, are established.…
We introduce a rational inattention model which produces a unique, interior, weighted multinomial logit conditional choice probability for an agent who acquires costly information about the hedonic characteristics (e.g. whether an insurance…
We consider the bail-out optimal dividend problem under fixed transaction costs for a L\'evy risk model. Furthermore, we consider the version with a constraint expected net present value of injected capital. To characterize the solution to…
We propose a new approach to utilities that is consistent with state-dependent utilities. In our model utilities reflect the level of consumption satisfaction of flows of cash in future times as they are valued when the economic agents are…
In this paper, the Kyle model of insider trading is extended by characterizing the trading volume with long memory and allowing the noise trading volatility to follow a general stochastic process. Under this newly revised model, the…
This work considers a stochastic model in which the uncertainty is driven by a multidimensional Brownian motion. The market price of risk process makes the transition between real world probability measure and risk neutral probability…
Let $(B(t))_{t\in [0,1]}$ be the linear Brownian motion and $(X_n(t))_{t\in [0,1]}$ be the $(n-1)$-fold integral of Brownian motion, $n$ being a positive integer: $$ X_n(t)=\int_0^t \frac{(t-s)^{n-1}}{(n-1)!} \,\dd B(s) for any $t\in[0,1]$.…
This paper investigates the equilibrium interactions between trading targets and private information in a multi-period Kyle (1985) market. There are two investors who each follow dynamic trading strategies: A strategic portfolio rebalancer…
We study the line ensembles of non-crossing Brownian bridges above a hard wall, each tilted by the area of the region below it with geometrically growing pre-factors. This model, which mimics the level lines of the $(2+1)$D SOS model above…
An initial-boundary value problem for the $n$-dimensional ($n\geq 2$) time-dependent Schr\"odinger equation in a semi-infinite (or infinite) parallelepiped is considered. Starting from the Numerov-Crank-Nicolson finite-difference scheme, we…
We study the problem of identifying an optimal coupling between input-output distributional data generated by a causal dynamical system. The coupling is required to satisfy prescribed marginal distributions and a causality constraint…
We study the least-energy way to reshape a probability distribution when motion is constrained to a horizontal bundle, that is, optimal transport and distribution steering in sub-Riemannian geometry, motivated by density control over…
Inspired by the Melan equation we propose a model for suspension bridges with two cables linked to a deck, through inextensible hangers. We write the energy of the system and we derive from variational principles two nonlinear and nonlocal…
We study optimal liquidation in the presence of linear temporary and transient price impact along with taking into account a general price predicting finite-variation signal. We formulate this problem as minimization of a cost-risk…