Related papers: Kyle-Back Models with risk aversion and non-Gaussi…

Linear-quadratic optimal control problem for systems governed by forward-backward stochastic differential equations has been extensively studied over the past three decades. Recent research has revealed that for forward-backward control…

In an arbitrage-free simple market, we demonstrate that for a class of state-dependent exponential utilities, there exists a unique prediction of the random risk aversion that ensures the consistency of optimal strategies across any time…

We study time-inconsistent recursive stochastic control problems, i.e., for which the Bellman principle of optimality does not hold. For this class of problems classical optimal controls may fail to exist, or to be relevant in practice, and…

We propose a stochastic game modelling the strategic interaction between market makers and traders of optimal execution type. For traders, the permanent price impact commonly attributed to them is replaced by quoting strategies implemented…

This paper proposes a theory of stock market predictability patterns based on a model of heterogeneous beliefs. In a discrete finite time framework, some agents receive news about an asset's fundamental value through a noisy signal. The…

We consider the problem of estimating the possibly non-convex cost of an agent by observing its interactions with a nonlinear, non-stationary and stochastic environment. For this inverse problem, we give a result that allows to estimate the…

A recently proposed stochastic hidden variable model for quantum mechanics has been claimed to involve "retrocausality" due to the appearance of equations of motion with future-time boundary conditions. We formulate an equivalent system of…

This paper builds a model of high-frequency equity returns by separately modeling the dynamics of trade-time returns and trade arrivals. Our main contributions are threefold. First, we characterize the distributional behavior of…

In this paper we discuss backward stochastic differential equations with Markov chain noise, having continuous drivers. We obtain the existence of a solution which is possibly not unique. Moreover, we show there is a minimal solution for…

We study a continuous time economy where throughout time, insiders receive private signals regarding the risky assets' terminal payoff. We prove existence of a partial communication equilibrium where, at each private signal time, the public…

We establish existence, uniqueness and regularity of solution results for a class of backward stochastic partial differential equations with singular terminal condition. The equation describes the value function of non-Markovian stochastic…

We prove existence and uniqueness of stochastic equilibria in a class of incomplete continuous-time financial environments where the market participants are exponential utility maximizers with heterogeneous risk-aversion coefficients and…

This work is devoted to the analysis of the quantum drift-diffusion model derived by Degond et al. The model is obtained as the diffusive limit of the quantum Liouville-BGK equation, where the collision term is defined after a local quantum…

This paper presents an empirical investigation of the intraday Brazilian stock market price fluctuations, considering q-Gaussian distributions that emerge from a non-extensive statistical mechanics. Our results show that, when returns are…

We derive a backward and forward nonlinear PDEs that govern the implied volatility of a contingent claim whenever the latter is well-defined. This would include at least any contingent claim written on a positive stock price whose payoff at…

Discrete-time stochastic optimal control remains a challenging problem for general, nonlinear systems under significant uncertainty, with practical solvers typically relying on the certainty equivalence assumption, replanning and/or…

The paper is devoted to the optimal control of a system with two time-scales, in a regime when the limit equation is not of averaging type but, in the spirit of Wong-Zakai principle, it is a stochastic differential equation for the slow…

We establish a variant of Monge--Kantorovich duality for a constrained optimal transport problem with a continuum of agents, a finite set of alternatives, and general linear constraints. As an application, we revisit the large-market model…

This paper presents an axiomatic scheme for interest rate models in discrete time. We take a pricing kernel approach, which builds in the arbitrage-free property and provides a link to equilibrium economics. We require that the pricing…

We study risk-sharing economies where heterogenous agents trade subject to quadratic transaction costs. The corresponding equilibrium asset prices and trading strategies are characterised by a system of nonlinear, fully-coupled…