Certainty equivalence principle in stochastic differential games: An inverse problem approach

Producción CientíficaThis paper aims to characterize a class of stochastic differential games, which satisfy the certainty equivalence principle beyond the cases with quadratic, linear, or logarithmic value functions. We focus on scalar games with linear dynamics in the players' strategies and with separable payoff functionals. Our results are based on the resolution of an inverse problem that determines strictly concave utility functions of the players so that the game satisfies the certainty equivalence principle. Besides establishing necessary and sufficient conditions, the results obtained in this paper are also a tool for discovering new closed-form solutions, as we show in two specific applications: in a generalization of a dynamic advertising model and in a game of noncooperative exploitation of a productive asset.Este trabajo se ha hecho con ayuda de los proyectos del Ministerio de Economía, Industria y Competitividad, Grant/Award Number: ECO2017-86261-P, ECO2014-56384-P, y MDM 2014-0431, de la Consejería de Educación, Juventud y Deporte de la Comunidad de Madrid, Grant/Award Number: MadEco-CM S2015/HUM-3444, y de la Consejería de Educación de la Junta de Castilla y León VA148G18

Markov Perfect Nash Equilibrium in stochastic differential games as solution of a generalized Euler Equations System

This paper gives a new method to characterize Markov Perfect Nash Equilibrium in stochastic differential games by means of a set of Generalized Euler Equations. Necessary and sufficient conditions are given

Quantum Gravity as a Dissipative Deterministic System

It is argued that the so-called holographic principle will obstruct attempts to produce physically realistic models for the unification of general relativity with quantum mechanics, unless determinism in the latter is restored. The notion of time in GR is so different from the usual one in elementary particle physics that we believe that certain versions of hidden variable theories can -- and must -- be revived. A completely natural procedure is proposed, in which the dissipation of information plays an essential role. Unlike earlier attempts, it allows us to use strictly continuous and differentiable classical field theories as a starting point (although discrete variables, leading to fermionic degrees of freedom, are also welcome), and we show how an effective Hilbert space of quantum states naturally emerges when one attempts to describe the solutions statistically. Our theory removes some of the mysteries of the holographic principle; apparently non-local features are to be expected when the quantum degrees of freedom of the world are projected onto a lower-dimensional black hole horizon. Various examples and models illustrate the points we wish to make, notably a model showing that massless, non interacting neutrinos are deterministic.Comment: 20 pages plain TeX, 2 figures PostScript. Added some further explanations, and the definitions of `beable' and `changeable'. A minor error correcte

Optimal investment with intermediate consumption under no unbounded profit with bounded risk

We consider the problem of optimal investment with intermediate consumption in a general semimartingale model of an incomplete market, with preferences being represented by a utility stochastic field. We show that the key conclusions of the utility maximization theory hold under the assumptions of no unbounded profit with bounded risk (NUPBR) and of the finiteness of both primal and dual value functions.Comment: 10 pages, revised version, to appear in the Applied Probability Journal

Controllability Metrics on Networks with Linear Decision Process-type Interactions and Multiplicative Noise

This paper aims at the study of controllability properties and induced controllability metrics on complex networks governed by a class of (discrete time) linear decision processes with mul-tiplicative noise. The dynamics are given by a couple consisting of a Markov trend and a linear decision process for which both the "deterministic" and the noise components rely on trend-dependent matrices. We discuss approximate, approximate null and exact null-controllability. Several examples are given to illustrate the links between these concepts and to compare our results with their continuous-time counterpart (given in [16]). We introduce a class of backward stochastic Riccati difference schemes (BSRDS) and study their solvability for particular frameworks. These BSRDS allow one to introduce Gramian-like controllability metrics. As application of these metrics, we propose a minimal intervention-targeted reduction in the study of gene networks