simulated moments estimation of markov models of asset prices this paper provides a simulated moments estimator sme of the parameters of dynamic models in which the state vector follows a time homogeneous markov process conditions are provided for both weak and strong consistency as well as asymptotic normality various tradeoffs among the regularity conditions underlying the large sample properties of the sme are discussed in the context of an asset pricing model this paper provides conditions for the consistency and asymptotic normality of a simulated moments estimator sme of the parameters of asset pricing models with time homogeneous markov representations of the stochastic forc ing process sme s for economic models have been proposed by mcfadden 1989 and pakes and pollard 1989 for i i d environments and by lee and ingram 1991 for a time series environment the sme for time series models examined in this paper is as follows the state vector yt that determines asset prices is assumed to follow a time homogeneous markov process whose transi tion function depends on an unknown parameter vector 3 0 asset prices and possibly other relevant data are observed as f yt 0 for some given function f of the underlying state and parameter vector in parallel a simulated state process y is generated analytically or numerically from the economic model and corresponding simulated observations f yj3 13 are taken for a given parameter choice f3 the parameter is chosen so as to match moments that is to minimize the distance between sample moments of the data f y 8030 and those of the simulated series f yt f3 in a sense to be made precise the proposed sme extends the generalized method of moments gmm estimator hansen 1982 to a large class of asset pricing models for which the moment restrictions of interest do not have analytic representations in terms of observable variables and the unknown parameter vector we provide conditions on the transition function of yt and the observation function f under which the sme of 030 is consistent and characterize the normalized asymptotic distribu tion of the estimator for two reasons neither the regularity conditions underly ing hansen s 1982 analysis of gmm estimators for time series models without

jump control of probability densities with applications to autonomous vehicle motion we investigate the problem of controlling the probability density of the state of a process that is observed by the controller via a fixed but unknown scalar non negative function of the state the goal is to control the process so that its probability density at a point in the state space becomes proportional to the value of the function observed at that point our solution inspired by bacterial chemotaxis involves a randomized controller that switches among different deterministic modes we show that under appropriate existence conditions this controller guarantees convergence of the probability density to the desired function the results can be applied to the problem of in loco optimization of a measurable signal using a team of autonomous vehicles that measure the signal but do not have access to position measurements alternative applications in the area of mobile robotics include deployment and environmental monitoring

stability analysis for stochastic hybrid systems this survey addresses stability analysis for stochastic hybrid systems shs which are dynamical systems that combine continuous change and instantaneous change and that also include random effects we re emphasize the common features found in most of the models that have appeared in the literature which include stochastic switched systems markov jump systems impulsive stochastic systems switching diffusions stochastic impulsive systems driven by renewal processes diffusions driven by levy processes piecewise deterministic markov processes general stochastic hybrid systems and stochastic hybrid inclusions then we review many of the stability concepts that have been studied including lyapunov stability lagrange stability asymptotic stability and recurrence next we detail lyapunov based sufficient conditions for these properties and additional relaxations of lyapunov conditions many other aspects of stability theory for shs like converse lyapunov theorems and robustness theory are not fully developed hence we also formulate some open problems to serve as a partial roadmap for the development of the underdeveloped pieces

an application of stochastic control theory to financial economics we consider a portfolio optimization problem which is formulated as a stochastic control problem risky asset prices obey a logarithmic brownian motion and interest rates vary according to an ergodic markov diffusion process the goal is to choose optimal investment and consumption policies to maximize the infinite horizon expected discounted hyperbolic absolute risk aversion hara utility of consumption a dynamic programming principle is used to derive the dynamic programming equation dpe the subsolution supersolution method is used to obtain existence of solutions of the dpe the solutions are then used to derive the optimal investment and consumption policies

on controlability of linear systems with stochastic jump parameters this note studies the notion of stochastic e controllability in probability for linear systems subject to sudden jumps in parameter values by using a lyapunov like approach sufficient conditions are obtained in terms of a set of coupled bernoulli equations the potential use of the results is illustrated by an example

on an infinite dimensional perturbed riccati differential equation arising in stochastic control existence and uniqueness of solutions for a class of infinite dimensional perturbed riccati differential equations in a certain banach space is our main concern in this paper besides the interest in its own right this class arises in control problems involving linear systems with countably infinite markov jump parameters

nonparametric identification and semiparametric estimation of classical measurement error models without side information virtually all methods aimed at correcting for covariate measurement error in regressions rely on some form of additional information e g validation data known error distributions repeated measurements or instruments in contrast we establish that the fully nonparametric classical errors in variables model is identifiable from data on the regressor and the dependent variable alone unless the model takes a very specific parametric form this parametric family includes but is not limited to the linear specification with normally distributed variables as a well known special case this result relies on standard primitive regularity conditions taking the form of smoothness constraints and nonvanishing characteristic functions assumptions our approach can handle both monotone and nonmonotone specifications provided the latter oscillate a finite number of times given that the very specific unidentified parametric functional form is arguably the exception rather than the rule this identification r

simulated minimum distance estimation of dynamic models with errors in variables abstract empirical analysis often involves using inexact measures of the predictors suggested by economic theory the bias created by the correlation between the mismeasured regressors and the error term motivates the need for instrumental variable estimation this paper considers a class of estimators that can be used in dynamic models with measurement errors when external instruments may not be available or are weak the idea is to exploit the relation between the parameters of the model and the least squares biases in cases when the latter are not analytically tractable a special algorithm is designed to simulate the model without completely specifying the processes that generate the latent predictors the proposed estimators perform well in simulations of the autoregressive distributed lag model the methodology is used to estimate the long run risks model

electric load model synthesis by diffusion approximation of a high order hybrid state stochastic system a statistical approach is used to model the dynamics of the electric demand of large aggregates of electric space heaters or air conditioners the importance of such loads is twofold first they account for a significant portion of power system dynamics following a power outage second because they are associated with energy storage they are often selected for load shedding within a load management program the derivation of the aggregate electrical dynamics is considered first for a homogeneous group of devices subsequently a perturbation analysis yields the dynamics for a nonhomogeneous group the homogeneons group aggregrate load model is a system of coupled ordinary and partial differential equations fokker planck equations it is obtained by writing evolution equations for the probability density of a hybrid state markov system used to model the switching dynamics of individual devices this result is new and could give a clue to the analysis of a broad class of hybrid state stochastic systems in turn this could provide a new impetus not only in the area of electric load modeling but other areas such as power system reliability and the design of relay control systems where stochastic hybrid state models occur frequently simulation results which illustrate the dynamical properties of the model are presented

higher moment estimators for linear regression models with errors in the variables abstract this paper proposes consistent instrumental variable estimators for linear regression models with errors in the variables that require no extraneous information these estimators are based on sample moments of order higher than two while similar estimators proposed previously in the literature seem to be quite erratic our experimental f findings suggest that our estimators perform better than ordinary least squares estimators in terms of root mean squared errors and also in terms of size of type i errors of standard tests in many typical situations of economic analyses tests for the presence of errors in the variables are also described

on the influence of noise on jump linear systems jump linear systems are considered in a random environment where they are subject to additive and multiplicative noises stochastic notions of stabilizability and detectability are introduced to characterize the asymptotic behavior of the optimal jump linear quadratic gaussian regulator and a dual kalman filter

jump linear quadratic control with random state discontinuities abstract in a random environment jump linear quadratic control problems are studied random state discontinuities are included in the analysis and the corresponding optimal regulator is obtained the introduction of stochastic notions of stabilizability and detectability gives a direct characterization of the asymptotic behaviour of the optimal system

optimal control for continuous time linear quadratic problems with infinite markov jump parameters the subject matter of this paper is the optimal control problem for continuous time linear systems subject to markovian jumps in the parameters and the usual infinite time horizon quadratic cost what essentially distinguishes our problem from previous ones inter alia is that the markov chain takes values on a countably infinite set to tackle our problem we make use of powerful tools from semigroup theory in banach space and a decomplexification technique the solution for the problem relies in part on the study of a countably infinite set of coupled algebraic riccati equations icare conditions for existence and uniqueness of a positive semidefinite solution of the icare are obtained via the extended concepts of stochastic stabilizability ss and stochastic detectability sd these concepts are couched into the theory of operators in banach space and parallel to the classical linear quadratic lq case bound up with the spectrum of a certain infinite dimensional linear operator

stochastic portfolio optimization with default risk abstract a stochastic portfolio optimization problem with default risk on an infinite time horizon is investigated the default risk premium and the default intensity corresponding to the defaultable bond are assumed to rely on a stochastic factor formulated by a diffusion process we study the optimal allocation and consumption policies to maximize the infinite horizon expected discounted non log hara utility of the consumption and we use the dynamic programming principle to derive the hamilton jacobi bellman hjb equation then we explore the hjb equation by employing a so called sub super solution approach the optimal allocation and consumption policies are finally presented in a verification theorem and also a numerical simulation is given at the end of the paper

a renewal theoretic analysis of a class of manufacturing systems the authors present the partial differential equations pdes describing the transients of the probability density functions pdfs characterizing the statistical evolution of a manufacturing system producing a single product under hedging point control policies the authors demonstrate the markov renewal nature of the dynamics of the controlled process and use the system of pdes to compute the transition kernel of that renewal process this markov renewal viewpoint is particularly useful in discussing ergodicity in view of the abundant literature on the asymptotic behavior of markov renewal processes moreover besides allowing direct determination of system steady state when it exists it permits the computation of various statistics as well as in some cases the derivation of bounds on the speed of convergence to steady state

probabilistic reachability and safety for controlled discrete time stochastic hybrid systems in this work probabilistic reachability over a finite horizon is investigated for a class of discrete time stochastic hybrid systems with control inputs a suitable embedding of the reachability problem in a stochastic control framework reveals that it is amenable to two complementary interpretations leading to dual algorithms for reachability computations in particular the set of initial conditions providing a certain probabilistic guarantee that the system will keep evolving within a desired safe region of the state space is characterized in terms of a value function and maximally safe markov policies are determined via dynamic programming these results are of interest not only for safety analysis and design but also for solving those regulation and stabilization problems that can be reinterpreted as safety problems the temperature regulation problem presented in the paper as a case study is one such case

constructing instruments for regressions with measurement error when no additional data are available with an application to patents and r d constructing instruments for regressions with measurement error when no additional data are available with an application to patents and r d

an optimal portfolio model with stochastic volatility and stochastic interest rate we consider a portfolio optimization problem under stochastic volatility as well as stochastic interest rate on an infinite time horizon it is assumed that risky asset prices follow geometric brownian motion and both volatility and interest rate vary according to ergodic markov diffusion processes and are correlated with risky asset price we use an asymptotic method to obtain an optimal consumption and investment policy and find some characteristics of the policy depending upon the correlation between the underlying risky asset price and the stochastic interest rate

minimum distance estimation of the errors in variables model using linear cumulant equations abstract we consider a multiple mismeasured regressor errors in variables model we develop closed form minimum distance estimators from any number of estimating equations which are linear in the third and higher cumulants of the observable variables using the cumulant estimators alters qualitative inference relative to ordinary least squares in two applications related to investment and leverage regressions the estimators perform well in monte carlos calibrated to resemble the data from our applications although the cumulant estimators are asymptotically equivalent to the moment estimators from erickson and whited 2002 the finite sample performance of the cumulant estimators exceeds that of the moment estimators

large population cost coupled lqg problems with nonuniform agents individual mass behavior and decentralized varepsilon nash equilibria we consider linear quadratic gaussian lqg games in large population systems where the agents evolve according to nonuniform dynamics and are coupled via their individual costs a state aggregation technique is developed to obtain a set of decentralized control laws for the individuals which possesses an epsiv nash equilibrium property a stability property of the mass behavior is established and the effect of inaccurate population statistics on an isolated agent is also analyzed by variational techniques