Notes on stochastic choice

A general formalism on stochastic choice is presented. Tje Rationalizability and Recoverability (Identification) problems are discussed. For the identification issue parametric examples are analyzed by means of techniques of mathematical tomography (Random transforms).

Linear stochastic differential algebraic equations with constant coefficients

We consider linear stochastic differential-algebraic equations with constant coefficients and additive white noise. Due to the nature of this class of equations, the solution must be defined as a generalised process (in the sense of Dawson and Fernique). We provide sufficient conditions for the law of the variables of the solution process to be absolutely continuous with respect to Lebesgue measure.

On the identification of monetary (and other) shocks

The purpose of this paper is twofold. First, we construct a DSGE model which spells out explicitly the instrumentation of monetary policy. The interest rate is determined every period depending on the supply and demand for reserves which in turn are affected by fundamental shocks: unforeseeable changes in cash withdrawal, autonomous factors, technology and government spending. Unexpected changes in the monetary conditions of the economy are interpreted as monetary shocks. We show that these monetary shocks have the usual effects on economic activity without the need of imposing additional frictions as limited participation in asset markets or sticky prices. Second, we show that this view of monetary policy may have important consequences for empirical research. In the model, the contemporaneous correlations between interest rates, prices and output are due to the simultaneous effect of all fundamental shocks. We provide an example where these contemporaneous correlations may be misinterpreted as a Taylor rule. In addition, we use the sign of the impact responses of all shocks on output, prices and interest rates derived from the model to identify the sources of shocks in the data.

The optimal behaviour of firms facing stochastic costs

This paper aims at assessing the optimal behavior of a firm facing stochastic costs of production. In an imperfectly competitive setting, we evaluate to what extent a firm may decide to locate part of its production in other markets different from which it is actually settled. This decision is taken in a stochastic environment. Portfolio theory is used to derive the optimal solution for the intertemporal profit maximization problem. In such a framework, splitting production between different locations may be optimal when a firm is able to charge different prices in the different local markets.

Stochastic dominance and absolute risk aversion

In this paper we propose the infimum of the Arrow-Pratt index of absolute risk aversion as a measure of global risk aversion of a utility function. We then show that, for any given arbitrary pair of distributions, there exists a threshold level of global risk aversion such that all increasing concave utility functions with at least as much global risk aversion would rank the two distributions in the same way. Furthermore, this threshold level is sharp in the sense that, for any lower level of global risk aversion, we can find two utility functions in this class yielding opposite preference relations for the two distributions.

Generalized backward doubly stochastic differential equations and SPDEs with nonlinear Neumann boundary conditions

In this paper, a new class of generalized backward doubly stochastic differential equations is investigated. This class involves an integral with respect to an adapted continuous increasing process. A probabilistic representation for viscosity solutions of semi-linear stochastic partial differential equations with a Neumann boundary condition is given.

Reflected Backward Stochastic Differential Equation with Jumps and RCLL Obstacle

In this paper we study one-dimensional reflected backward stochastic differential equation when the noise is driven by a Brownian motion and an independent Poisson point process when the solution is forced to stay above a right continuous left-hand limited obstacle. We prove existence and uniqueness of the solution by using a penalization method combined with a monotonic limit theorem.

Improving the risk concept: a revision of Arrow-Pratt theory in the context of controlled dynamic stochastic environments

In the literature on risk, one generally assume that uncertainty is uniformly distributed over the entire working horizon, when the absolute risk-aversion index is negative and constant. From this perspective, the risk is totally exogenous, and thus independent of endogenous risks. The classic procedure is "myopic" with regard to potential changes in the future behavior of the agent due to inherent random fluctuations of the system. The agent's attitude to risk is rigid. Although often criticized, the most widely used hypothesis for the analysis of economic behavior is risk-neutrality. This borderline case must be envisaged with prudence in a dynamic stochastic context. The traditional measures of risk-aversion are generally too weak for making comparisons between risky situations, given the dynamic �complexity of the environment. This can be highlighted in concrete problems in finance and insurance, context for which the Arrow-Pratt measures (in the small) give ambiguous.

Improving the effort concept: a revision of the traditional approach in the context of controlled Dynamic Stochastic Environments

The objective of this paper is to re-evaluate the attitude to effort of a risk-averse decision-maker in an evolving environment. In the classic analysis, the space of efforts is generally discretized. More realistic, this new approach emploies a continuum of effort levels. The presence of multiple possible efforts and performance levels provides a better basis for explaining real economic phenomena. The traditional approach (see, Laffont, J. J. & Tirole, J., 1993, Salanie, B., 1997, Laffont, J.J. and Martimort, D, 2002, among others) does not take into account the potential effect of the system dynamics on the agent's behavior to effort over time. In the context of a Principal-agent relationship, not only the incentives of the Principal can determine the private agent to allocate a good effort, but also the evolution of the dynamic system. The incentives can be ineffective when the environment does not incite the agent to invest a good effort. This explains why, some effici

A class of stochastic games with infinitely many interacting agents related to Glauber dynamics on random graphs

We introduce and study a class of infinite-horizon nonzero-sum non-cooperative stochastic games with infinitely many interacting agents using ideas of statistical mechanics. First we show, in the general case of asymmetric interactions, the existence of a strategy that allows any player to eliminate losses after a finite random time. In the special case of symmetric interactions, we also prove that, as time goes to infinity, the game converges to a Nash equilibrium. Moreover, assuming that all agents adopt the same strategy, using arguments related to those leading to perfect simulation algorithms, spatial mixing and ergodicity are proved. In turn, ergodicity allows us to prove “fixation”, i.e. that players will adopt a constant strategy after a finite time. The resulting dynamics is related to zerotemperature Glauber dynamics on random graphs of possibly infinite volume.

Strong solutions for stochastic porous media equations with jumps

We prove global well-posedness in the strong sense for stochastic generalized porous media equations driven by locally square integrable martingales with stationary independent increments.

From creative ideas to new emerging ventures: the process of identification and exploitation among finnish design entrepreneurs

This study focuses on identification and exploitation processes among Finnish design entrepreneurs (i.e. selfemployed industrial designers). More specifically, this study strives to find out what design entrepreneurs do when they create new ventures, how venture ideas are identified and how entrepreneurial processes are organized to identify and exploit such venture ideas in the given industrial context. Indeed, what does educated and creative individuals do when they decide to create new ventures, where do the venture ideas originally come from, and moreover, how are venture ideas identified and developed into viable business concepts that are introduced on the markets? From an academic perspective: there is a need to increase our understanding of the interaction between the identification and exploitation of emerging ventures, in this and other empirical contexts. Rather than assuming that venture ideas are constant in time, this study examines how emerging ideas are adjusted to enable exploitation in dynamic market settings. It builds on the insights from previous entrepreneurship process research. The interpretations from the theoretical discussion build on the assumption that the subprocesses of identification and exploitation interact, and moreover, they are closely entwined with each other (e.g. McKelvie & Wiklund, 2004, Davidsson, 2005). This explanation challenges the common assumption that entrepreneurs would first identify venture ideas and then exploit them (e.g. Shane, 2003). The assumption is that exploitation influences identification, just as identification influences exploitation. Based on interviews with design entrepreneurs and external actors (e.g. potential customers, suppliers and collaborators), it appears as identification and exploitation of venture ideas are carried out in close interaction between a number of actors, rather than alone by entrepreneurs. Due to their available resources, design entrepreneurs have a desire to focus on identification related activities and to find external actors that take care of exploitation related activities. The involvement of external actors may have a direct impact on decisionmaking and various activities along the processes of identification and exploitation, which is something that previous research does not particularly emphasize. For instance, Bhave (1994) suggests both operative and strategic feedback from the market, but does not explain how external parties are actually involved in the decisionmaking, and in carrying out various activities along the entrepreneurial process.

Development of specific ITS markers for plant DNA identification within herbivorous insects

DNA based techniques have proved to be very useful methods to study trophic relationships 17 between pests and their natural enemies. However, most predators are best defined as omnivores, 18 and the identification of plant-specific DNA should also allow the identification of the plant 19 species the predators have been feeding on. In this study, a PCR approach based on the 20 development of specific primers was developed as a self-marking technique to detect plant DNA 21 within the gut of one heteropteran omnivorous predator (Macrolophus pygmaeus) and two 22 lepidopteran pest species (Helicoverpa armigera and Tuta absoluta). Specific tomato primers 23 were designed from the ITS 1-2 region, which allowed the amplification of a tomato DNA 24 fragment of 332 bp within the three insect species tested in all cases (100% of detection at t = 0) 25 and did not detect DNA of other plants nor of the starved insects. Plant DNA half-lives at 25ºC 26 ranged from 5.8h, to 27.7h and 28.7h within M. pygmaeus, H. armigera and T. absoluta, 27 respectively. Tomato DNA detection within field collected M. pygmaeus suggests dietary mixing 28 in this omnivorous predator and showed a higher detection of tomato DNA in females and 29 nymphs than males. This study provides a useful tool to detect and to identify plant food sources 30 of arthropods and to evaluate crop colonization from surrounding vegetation in conservation 31 biological control programs.

Gaussian estimates for the density of the non-linear stochastic heat equation in any space dimension

In this paper, we establish lower and upper Gaussian bounds for the probability density of the mild solution to the stochastic heat equation with multiplicative noise and in any space dimension. The driving perturbation is a Gaussian noise which is white in time with some spatially homogeneous covariance. These estimates are obtained using tools of the Malliavin calculus. The most challenging part is the lower bound, which is obtained by adapting a general method developed by Kohatsu-Higa to the underlying spatially homogeneous Gaussian setting. Both lower and upper estimates have the same form: a Gaussian density with a variance which is equal to that of the mild solution of the corresponding linear equation with additive noise.