Related papers: On Equilibrium Prices in Continuous Time
The chaotic hypothesis is proposed as a basis for a general theory of nonequilibrium stationary states. Version 2: new comments added after presenting this talk at the Meeting mentioned in the Acknowledgement. One typo corrected.
We generalize the thermodynamic uncertainty relation, providing an entropic upper bound for average fluxes in time-continuous steady-state systems (Gingrich et al., Phys. Rev. Lett. 116, 120601 (2016)), to time-discrete Markov chains and to…
The fluctuations in nonequilibrium systems are under intense theoretical and experimental investigation. Topical ``fluctuation relations'' describe symmetries of the statistical properties of certain observables, in a variety of models and…
We combine the two classical topological concepts, time-preserving topological factors and synchronizing time-changes of a continuous flow, and explore some of their thermodynamic consequences. Particular focus is put on equilibrium states…
We introduce and study a non-equilibrium continuous-time dynamical model of the price of a single asset traded by a population of heterogeneous interacting agents in the presence of uncertainty and regulatory constraints. The model takes…
Concerning Numerical Stochastic Perturbation Theory, we discuss the convergence of the stochastic process (idea of the proof, features of the limit distribution, rate of convergence to equilibrium). Then we also discuss the expected…
In this paper, a mathematically rigorous solution overturns existing wisdom regarding New Keynesian Dynamic Stochastic General Equilibrium. I develop a formal concept of stochastic equilibrium. I prove uniqueness and necessity, when agents…
The price-bubble and crash process formation is theoretically investigated in a two-asset equilibrium model. Sufficient and necessary conditions are derived for the existence of average equilibrium price dynamics of different agent-based…
In this paper we provide a comprehensive analysis of a structural model for the dynamics of prices of assets traded in a market originally proposed in [1]. The model takes the form of an interacting generalization of the geometric Brownian…
In this paper, we develop new optional stopping theorems for scenarios where the stopping rules are defined by bounded continuity regions. Moreover, we establish a wide variety of inequalities on the supremums and infimums of functions of…
We introduce a stochastic price model where, together with a random component, a moving average of logarithmic prices contributes to the price formation. Our model is tested against financial datasets, showing an extremely good agreement…
A new definition of events of game-theoretic probability zero in continuous time is proposed and used to prove results suggesting that trading in financial markets results in the emergence of properties usually associated with randomness.…
This paper investigates a time-inconsistent portfolio selection problem in the incomplete mar ket model, integrating expected utility maximization with risk control. The objective functional balances the expected utility and variance on log…
A new definition of continuous-time equilibrium controls is introduced. As opposed to the standard definition, which involves a derivative-type operation, the new definition parallels how a discrete-time equilibrium is defined, and allows…
We provide an overview of theories of continuous time computation. These theories allow us to understand both the hardness of questions related to continuous time dynamical systems and the computational power of continuous time analog…
Mathematical methods of population genetics and framework of exchangeability provide a Markov chain model for analysis and interpretation of stochastic behaviour of equity markets, explaining, in particular, market shape formation,…
This paper integrates two strands of the literature on stability of general state Markov chains: conventional, total variation based results and more recent order-theoretic results. First we introduce a complete metric over Borel…
We connect the rare fluctuations of an Equilibrium (EQ) process and the typical fluctuations of a nonequilibrium (NE) stationary process. In the framework of large deviation theory, this observation allows us to introduce NE thermodynamic…
We present a construction of non-equilibrium steady states in one-dimensional quantum critical systems carrying energy and charge fluxes. This construction is based on a scattering approach within a real-time hamiltonian reservoir…
We consider a stochastic model described by two stochastic differential equations of motion; one is for the stochastic evolution forward in time and the other for backward in time. We further introduce averaged quantities for the two…