An analysis of the effect of noise in a heterogeneous agent financial market model

Heterogeneous agent models (HAMs) in finance and economics are often characterised by high dimensional nonlinear stochastic differential or difference systems. Because of the complexity of the interaction between the nonlinearities and noise, a commonly used, often called indirect, approach to the study of HAMs combines theoretical analysis of the underlying deterministic skeleton with numerical analysis of the stochastic model. However, it is well known that this indirect approach may not properly characterise the nature of the stochastic model. This paper aims to tackle this issue by developing a direct and analytical approach to the analysis of a stochastic model of speculative price dynamics involving two types of agents, fundamentalists and chartists, and the market price equilibria of which can be characterised by the stationary measures of a stochastic dynamical system. Using the stochastic method of averaging and stochastic bifurcation theory, we show that the stochastic model displays behaviour consistent with that of the underlying deterministic model when the time lag in the formation of price trends used by the chartists is far away from zero. However, when this lag approaches zero, such consistency breaks down.     

Two-stage stochastic integer programming: a survey

Stochastic integer programming is more complicated than stochastic linear programming, as will be explained for the case of the two-stage stochastic programming model. A survey of the results accomplished in this recent field of research is given.     

Exchange rate bifurcation in a stochastic evolutionary finance model

This paper analyzes the stability and fluctuations of the exchange rate with a speculative bubble using the methods of evolutionary finance and stochastic differential equations. It constructs a hybrid stochastic system for the financial market involving a discrete time process and a continuous time process. The discrete process models the bubble and is meant to capture the behavior of less sophisticated investors who trade infrequently. The continuous time process is a stochastic differential equation for monetary policy together with a backward stochastic equation for the exchange rate. Monetary policy is affected by the bubble and in turn affects the exchange rate as well as speculation. The bubble and exchange rate exhibit a form of bifurcation. This means the bubble and exchange rate experience fluctuations as the propensity to chase trends or switch predictors changes.     

Stochastic growth with social-status concern: The existence of a unique stable distribution

This paper extends Kurz’s (1968) growth model to a stochastic growth framework with social-status concern and unbounded production shocks. Using the stochastic monotonicity of a stochastic dynamic system and the methods adopted in Zhang (2007), the existence, uniqueness, and stability of invariant distribution are investigated. Different from the existence of multiple steady states under certainty, it is shown here that there exists a unique stable invariant distribution under uncertainty.     

Asymmetric outcome in a symmetric dynamic duopoly

In a dynamic duopoly, will an initial asymmetry between firms increase or decrease over time? We examine this issue within a stochastic dynamic alternate-move duopoly model that explicitly accounts for action and reaction between firms. We consider two firms that are symmetric with regard to all primitives such as demand, cost and production functions, and which are subject to the same stochastic environment. The only asymmetry is with regard to their initial capital stocks which in turn asymmetrically influences their current and future profit and investment possibilities. We offer a characterization of the stochastic steady state and its supporting ergodic set for each firm. We are then able to identify the precise restrictions on the initial conditions under which the two firms either converge or diverge in the long run.     

Stochastic programming in production planning: a case with none-simple recourse

Abstract  In modeling real world planning problems as optimization programs the assumption that all parameters are known with certainty is often more seriously violated than the assumption that the objective function and the constraints can be approximated sufficiently accurate by lineair functions. In this paper we discuss the concrete application of stochastic programming to a multiperiod production planning problem in which the demand for the products during the various periods is assumed stochastic with known probability distribution. Since the resulting stochastic program does not possess the property of "simple" recourse no direct use can be made of existing methods that have been proposed in literature for solving problems of this type.     

Nowcasting GDP with a pool of factor models and a fast estimation algorithm

We propose a novel mixed-frequency dynamic factor model with time-varying parameters and stochastic volatility for macroeconomic nowcasting and develop a fast estimation algorithm. This enables us to generate forecast densities based on a large space of factor models. We apply our framework to nowcast US GDP growth in real time. Our results reveal that stochastic volatility seems to improve the accuracy of point forecasts the most, compared to the constant-parameter factor model. These gains are most prominent during unstable periods such as the Covid-19 pandemic. Finally, we highlight indicators driving the US GDP growth forecasts and associated downside risks in real time.     

Stochastic optimal growth with a non-compact state space

This paper studies the stability of a stochastic optimal growth economy introduced by Brock and Mirman [Brock, W.A., Mirman, L., 1972. Optimal economic growth and uncertainty: the discounted case. Journal of Economic Theory 4, 479–513] by utilizing stochastic monotonicity in a dynamic system. The construction of two boundary distributions leads to a new method of studying systems with non-compact state space. The paper shows the existence of a unique invariant distribution. It also shows the equivalence between the stability and the uniqueness of the invariant distribution in this dynamic system.     

The mean-variance investment problem in a constrained financial market

This paper extends the mean-variance analysis and the two-fund separation theorem to a market with some constraints, such as, the incompleteness, prohibition of short-selling, and partial information, with stochastic interest rate, and with stochastic volatility for risky assets. By maximizing a quadratic utility of terminal wealth, we show that the efficient frontier for the problem is a straight line in the mean-standard-deviation diagram. The quadratic utility function exhibits mean-variance efficiency. Our results apply to portfolios of claims in a single period, multiperiod, and continuous time.     

Roots and effects of financial misperception in a stochastic dominance framework

This work deals with the issue of investors’ irrational behavior and financial products’ misperception. The theoretical analysis of the mechanisms driving erroneous assessment of investment performances is explored. The study is supported by the application of Monte Carlo simulations to the remarkable case of structured financial products. Some motivations explaining the popularity of these complex financial instruments among retail investors are also provided. In particular, investors are assumed to compare the performances of different projects through stochastic dominance rules. Unreasonably and in contrast with results obtained by the application of the selected criteria, investors prefer complex securities to standard ones. In this paper, introducing a new definition for stochastic dominance which presents asymmetric property, we provide theoretical and numerical results showing how investors distort stochastic returns and make questionable investment choices. Results are explained in terms of framing and representative effects, which are behavioral finance type arguments showing how decisions may depend on the way the available alternatives are presented to investors.     

Estimating heterogeneous capacity and capacity utilization in a multi-species fishery

We use a stochastic production frontier model to investigate the presence of heterogeneous production and its impact on fleet capacity and capacity utilization in a multi-species fishery. We propose a new fleet capacity estimate that incorporates complete information on the stochastic differences between vessel-specific technical efficiency distributions. Results indicate that ignoring heterogeneity in production technologies within a multi-species fishery as well as the complete distribution of a vessel’s technical efficiency score, may lead to erroneous fleet-wide production profiles and estimates of capacity. Our new estimate of capacity enables out-of-sample production predictions which may be useful to policy makers.     

Cointegration in a macroeconomic system

This paper investigates the long-run relationships within a set of six quarterly time-series on the Austrian economy by means of cointegration. After analysing the univariate properties, especially with respect to the appropriate seasonal filter, the maximum-likelihood method proposed by Johansen (1988) is applied to estimate and test the cointegrating relationships. We found three such relations, implying that the system is driven by three independent stochastic time trends. In a next stage we investigate whether the empirically determined cointegrating relationships are compatible with implications derived from the neoclassical growth model with exogenous stochastic technical progress. It is found that the Austrian data strongly reject the propositions that the real interest rate and the log ratios of consumption to output, investment to output, and the real gross wage sum to output are stationary.     

Estimating Technological Change Using a Stochastic Frontier Production Function Framework: Evidence from U.S. Firm-Level Data

This paper presents a methodology for estimating an index of technological change using firm-level data in a stochastic frontier production function model that takes into account time-varying technical inefficiency. In contrast to the Solow divisia index approach, econometric estimation of the index with panel data allows the researcher to separate technical progress from the stochastic measurement error. Applying the econometric methodology to a panel of 908 publicly-traded U.S. firms from the COMPUSTAT database, we find evidence of a significant downturn in general technological change for the period, 1970– 1989, whereas the divisia index methodology applied to the same data shows stagnation. When the sample is divided into Manufacturing, Services, and Miscellaneous categories we find that estimates of technological change for the three groups display markedly different stochastic behavior and that the Services group is the source of the downturn.     

Production under uncertainty: a simulation study

In this paper we model production technology in a state-contingent framework. Our model analyzes production under uncertainty without being explicit about the nature of producer risk preferences. In our model producers’ risk preferences are captured by the risk-neutral probabilities they assign to the different states of nature. Using a state-general state-contingent specification of technology we show that rational producers who encounter the same stochastic technology can make significantly different production choices. Further, we develop an econometric methodology to estimate the risk-neutral probabilities and the parameters of stochastic technology when there are two states of nature and only one of which is observed. Finally, we simulate data based on our state-general state-contingent specification of technology. Biased estimates of the technology parameters are obtained when we apply conventional ordinary least squares estimator on the simulated data.     

Estimation of inefficiency in stochastic frontier models: a Bayesian kernel approach

We propose a kernel-based Bayesian framework for the analysis of stochastic frontiers and efficiency measurement. The primary feature of this framework is that the unknown distribution of inefficiency is approximated by a transformed Rosenblatt-Parzen kernel density estimator. To justify the kernel-based model, we conduct a Monte Carlo study and also apply the model to a panel of U.S. large banks. Simulation results show that the kernel-based model is capable of providing more precise estimation and prediction results than the commonly-used exponential stochastic frontier model. The Bayes factor also favors the kernel-based model over the exponential model in the empirical application.

     

Regression Analysis with a Stochastic Design Variable

In regression models, the design variable has primarily been treated as a nonstochastic variable. In numerous situations, however, the design variable is stochastic. The estimation and hypothesis testing problems in such situations are considered. Real life examples are given.     

Consumption optimization for recursive utility in a jump-diffusion model

In this paper, we consider a market model with prices and consumption following a jump-diffusion dynamics. In this setting, we first characterize the optimal consumption plan for an investor with recursive stochastic differential utility on the basis of his/her own beliefs, then we solve the inverse problem to find what beliefs make a given consumption plan optimal. The problem is viewed in general for a class of homogeneous recursive utility, and later we choose a logarithmic model for the utility aggregator as an explicitly computable example. When beliefs, represented via Girsanov’s theorem, get incorporated into the model, the change of measure gives rise, up to a transformation, to a backward stochastic differential equation whose generator exhibits a quadratic behavior in the Brownian component and a locally Lipschitz one in the jump component, which is solvable on the basis of some recent results.     

Stationary Markov equilibria on a non-compact self-justified set

The existence of stationary processes of temporary equilibria is examined in an OLG model, where there are finitely many commodities and consumers in each period, and endowments profiles and expectations profiles are subject to stochastic shocks. A state space is taken as the set of all payoff-relevant variables, and dynamics of the economy is captured as a stochastic process in the state space. In our model, however, the state space does not necessarily admit a compact-truncation consistent with the intertemporal restrictions because distributions over expectations profiles may have non-compact supports. As shown in Duffie et al. [Duffie, D., Geanakoplos, J., Mas-Colell, A., McLennan, A., 1994. Stationary Markov equilibria. Econometrica 62, 745–781), such a compact-truncation, called a self-justified set, is essential for the existence of stationary Markov equilibria. We extend their existence theorem so as to be applicable to our model.     

Extracting a common stochastic trend: Theory with some applications

This paper investigates the statistical properties of estimators of the parameters and unobserved series for state space models with integrated time series. In particular, we derive the full asymptotic results for maximum likelihood estimation using the Kalman filter for a prototypical class of such models—those with a single latent common stochastic trend. Indeed, we establish the consistency and asymptotic mixed normality of the maximum likelihood estimator and show that the conventional method of inference is valid for this class of models. The models we explicitly consider comprise a special–yet useful–class of models that may be employed to extract the common stochastic trend from multiple integrated time series. Such models can be very useful to obtain indices that represent fluctuations of various markets or common latent factors that affect a set of economic and financial variables simultaneously. Moreover, our derivation of the asymptotics of this class makes it clear that the asymptotic Gaussianity and the validity of the conventional inference for the maximum likelihood procedure extends to a larger class of more general state space models involving integrated time series. Finally, we demonstrate the utility of this class of models extracting a common stochastic trend from three sets of time series involving short- and long-term interest rates, stock return volatility and trading volume, and Dow Jones stock prices.     

Estimating efficiency effects in a panel data stochastic frontier model

Journal of Productivity Analysis - This paper proposes a panel data based stochastic frontier model which accommodates time-invariant unobserved heterogeneity along with efficiency effects. The...