Search Results (5)

This paper is devoted to the study of stochastic optimal control of averaged stochastic differential delay equations (SDDEs) with semi-Markov switchings and their applications in economics. By using the Dynkin formula and solution of the Dirichlet–Poisson problem, the Hamilton–Jacobi–Bellman (HJB) equation and the inverse HJB equation are derived. Applications are given to a new Ramsey stochastic models in economics, namely the averaged Ramsey diffusion model with semi-Markov switchings. A numerical example is presented as well. Full article

Energy policy investments are usually evaluated using a cost-benefit analysis (CBA), which requires an estimation of the social discount rate (SDR). The choice of SDR can be crucial for the outcome of the appraisal, as energy-related investments generate long-term impacts affecting climate change. Once discounted, these impacts are highly sensitive to slight changes in the value of the SDR. Some countries (the UK and France) switched from a constant SDR to the declining rate scheme—a solution that limits the impact sensitivity. To our knowledge, none of the CEE countries apply DDR in CBA. While a constant SDR is a relatively well-established approach, declining SDRs are estimated to be used much less frequently, particularly for CEE EU member countries and energy policies. The rationale for the decline can rest on uncertainty over future discount rates, as shown by the approach developed by Weitzman and Gollier, which extends the classical Ramsey model. We applied this approach in our paper, as the Ramsey formula is the prevailing formula for EU countries’ SDR estimates. We estimated a flat SDR via the Ramsey formula with Gollier’s “precautionary term”, and next, we calculated Weitzman’s certainty equivalent rates for the 500-year horizon. Ramsey’s SDRs, obtained using consumption growth rates dating back to 1996, varied between 6.77% for Lithuania and 2.95% for Czechia and declined by 0.15% on average (Gollier’s term). Declining SDRs for the longest horizon dropped to approx. 0.5% (from 0.35% for Bulgaria to 0.67% for Poland), and the descent is deeper and faster when forward SDRs (following the UK Green Book approach) were considered (0.01% to 0.04%). The results are important for long-term policies regarding energy and climate change in CEE EU member countries, but they are still dependent on fossil fuels and experience an investment gap to fulfil EU climate goals. Full article

A model of production funds acquisition, which includes two differential links of the zero order and two series-connected inertial links, is considered in a one-sector economy. Zero-order differential links correspond to the equations of the Ramsey model. These equations contain scalar bounded control, which determines the distribution of the available funds into two parts: investment and consumption. Two series-connected inertial links describe the dynamics of the changes in the volume of the actual production at the current production capacity. For the considered control system, the problem is posed to maximize the average consumption value over a given time interval. The properties of optimal control are analytically established using the Pontryagin maximum principle. The cases are highlighted when such control is a bang-bang, as well as the cases when, along with bang-bang (non-singular) portions, control can contain a singular arc. At the same time, concatenation of singular and non-singular portions is carried out using chattering. A bang-bang suboptimal control is presented, which is close to the optimal one according to the given quality criterion. A positional terminal control is proposed for the first approximation when a suboptimal control with a given deviation of the objective function from the optimal value is numerically found. The obtained results are confirmed by the corresponding numerical calculations. Full article

Metabolic flux analysis (MFA) is an indispensable tool in metabolic engineering. The simplest variant of MFA relies on an overdetermined stoichiometric model of the cell’s metabolism under the pseudo-steady state assumption to evaluate the intracellular flux distribution. Despite its long history, the issue of model error in overdetermined MFA, particularly misspecifications of the stoichiometric matrix, has not received much attention. We evaluated the performance of statistical tests from linear least square regressions, namely Ramsey’s Regression Equation Specification Error Test (RESET), the F-test, and the Lagrange multiplier test, in detecting model misspecifications in the overdetermined MFA, particularly missing reactions. We further proposed an iterative procedure using the F-test to correct such an issue. Using Chinese hamster ovary and random metabolic networks, we demonstrated that: (1) a statistically significant regression does not guarantee high accuracy of the flux estimates; (2) the removal of a reaction with a low flux magnitude can cause disproportionately large biases in the flux estimates; (3) the F-test could efficiently detect missing reactions; and (4) the proposed iterative procedure could robustly resolve the omission of reactions. Our work demonstrated that statistical analysis and tests could be used to systematically assess, detect, and resolve model misspecifications in the overdetermined MFA. Full article

The Ramsey regression equation specification error test (RESET) furnishes a diagnostic for omitted variables in a linear regression model specification (i.e., the null hypothesis is no omitted variables). Integer powers of fitted values from a regression analysis are introduced as additional covariates in a second regression analysis. The former regression model can be considered restricted, whereas the latter model can be considered unrestricted; this first model is nested within this second model. A RESET significance test is conducted with an F-test using the error sums of squares and the degrees of freedom for the two models. For georeferenced data, eigenvectors can be extracted from a modified spatial weights matrix, and included in a linear regression model specification to account for the presence of nonzero spatial autocorrelation. The intuition underlying this methodology is that these synthetic variates function as surrogates for omitted variables. Accordingly, a restricted regression model without eigenvectors should indicate an omitted variables problem, whereas an unrestricted regression model with eigenvectors should result in a failure to reject the RESET null hypothesis. This paper furnishes eleven empirical examples, covering a wide range of spatial attribute data types, that illustrate the effectiveness of eigenvector spatial filtering in addressing the omitted variables problem for georeferenced data as measured by the RESET. Full article