scholarly journals A Method to Pre-compile Numerical Integrals When Solving Stochastic Dynamic Problems

2021 ◽  
Author(s):  
Karolos Arapakis
Keyword(s):  
Numerical Integration ◽  
Sufficient Conditions ◽  
Partial Equilibrium ◽  
Stochastic Dynamic ◽  
Dynamic Problems ◽  
Labour Income

AbstractWe show how the interpolation step of numerical integration can be pre-compiled in partial equilibrium stochastic dynamic problems. We display the pre-compilation’s sufficient conditions and document its speed gains using a consumption-savings model with a discrete labour choice, wage uncertainty and stochastic non-labour income.

scholarly journals Approximate Controllability of Sobolev Type Nonlocal Fractional Stochastic Dynamic Systems in Hilbert Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Mourad Kerboua ◽  
Amar Debbouche ◽  
Dumitru Baleanu
Keyword(s):  
Control Systems ◽  
Hilbert Spaces ◽  
Dynamic Systems ◽  
Approximate Controllability ◽  
Dynamic Control ◽  
Sufficient Conditions ◽  
Sobolev Type ◽  
Stochastic Dynamic ◽  
Deterministic Control ◽  
Stochastic Dynamic Systems

We study a class of fractional stochastic dynamic control systems of Sobolev type in Hilbert spaces. We use fixed point technique, fractional calculus, stochastic analysis, and methods adopted directly from deterministic control problems for the main results. A new set of sufficient conditions for approximate controllability is formulated and proved. An example is also given to provide the obtained theory.

Optimal Dynamic Appointment Scheduling of Base and Surge Capacity

2021 ◽  
Author(s):  
Benjamin Grant ◽  
Itai Gurvich ◽  
R. Kannan Mutharasan ◽  
Jan A. Van Mieghem
Keyword(s):  
Waiting Times ◽  
Sufficient Conditions ◽  
Capacity Utilization ◽  
Healthcare Setting ◽  
Appointment Scheduling ◽  
Problem Definition ◽  
Stochastic Dynamic ◽  
Surge Capacity ◽  
Trade Off ◽  
Dynamic Stochastic

Problem definition: We study dynamic stochastic appointment scheduling when delaying appointments increases the risk of incurring costly failures, such as readmissions in healthcare or engine failures in preventative maintenance. When near-term base appointment capacity is full, the scheduler faces a trade-off between delaying an appointment at the risk of costly failures versus the additional cost of scheduling the appointment sooner using surge capacity. Academic/practical relevance: Most appointment-scheduling literature in operations focuses on the trade-off between waiting times and utilization. In contrast, we analyze preventative appointment scheduling and its impact on the broader service-supply network when the firm is responsible for service and failure costs. Methodology: We adopt a stochastic dynamic programming (DP) formulation to characterize the optimal scheduling policy and evaluate heuristics. Results: We present sufficient conditions for the optimality of simple policies. When analytical solutions are intractable, we solve the DP numerically and present optimality gaps for several practical policies in a healthcare setting. Managerial implications: Intuitive appointment policies used in practice are robust under moderate capacity utilization, but their optimality gap can quadruple under high load.

scholarly journals Investigation of error in evaluation of spectral statistical characteristics of numerical solution of stochastic dynamic system

2021 ◽  
pp. 60-65
Author(s):  
Yaroslav Beskrovnii ◽  
Oleksii Larin
Keyword(s):  
Confidence Interval ◽  
Dynamic System ◽  
Numerical Solution ◽  
Numerical Integration ◽  
Numerical Solutions ◽  
Stochastic Perturbation ◽  
Digital Processing ◽  
Statistical Characteristics ◽  
Stochastic Dynamic

In this paper, an algorithm for numerical simulations is developed for calculating a discrete dynamic system with a stochastic perturbation and an analysis of the quality of numerical solutions is carried out. For this, an algorithm for the numerical solution of a second-order differential equation with a stochastic right-hand side was developed and this algorithm was implemented as a program. The next step was to carry out a set of computational studies by varying the parameters of numerical integration with the subsequent assessment of their impact on the error and accuracy of simulations. To estimate the spectral density, the Welch periodogram method was used. To check the quality of simulations and assess the accuracy of solutions, it is proposed to compare the results of numerical integration and subsequent digital processing with analytical solutions that are known for the linear problem, given by the equation. As a result of the work, a comparative analysis of the dispersion of displacements relative to the lengths of signals from a different number of blocks was carried out, into which the signal is divided for the Welch method; the confidence interval of the error at different signal lengths and the confidence interval of the error with a different number of blocks at a certain signal length. Comparison of the variance with a different number of blocks showed that with a signal length of 30 s and from 90 s, there is a slight scatter of the variance values within an error of ± 5%.

scholarly journals Surplus Maximization and Optimality

2013 ◽  
Vol 103 (6) ◽  
pp. 2585-2611 ◽  
Author(s):  
Edward E Schlee
Keyword(s):  
Risk Aversion ◽  
Upper Bound ◽  
Sufficient Conditions ◽  
Partial Equilibrium ◽  
Pareto Optimal ◽  
Knife Edge ◽  
Indirect Utility ◽  
Equilibrium Conditions ◽  
Single Crossing ◽  
Quasilinear Utility

Expected consumer's surplus rarely represents preferences over price lotteries. Still, I give sufficient conditions for policies which maximize aggregate expected surplus to be interim Pareto Optimal. Besides two standard partial equilibrium conditions, I assume that feasible prices satisfy a single-crossing property; and each consumer's indirect utility satisfies increasing differences in the price and income. I use the result to extend well-known welfare conclusions beyond the knife-edge quasilinear utility case. Since increasing differences puts no upper bound on risk aversion, the result is useful for applications in which risk aversion is important. (JEL D11, D24, D42, D81, D83, L42)

scholarly journals The effect of numerical integration in mixed finite element approximation in the simulation of miscible displacement

2017 ◽  
Vol 6 (2) ◽  
pp. 44
Author(s):  
Pongui ngoma Diogene Vianney ◽  
Nguimbi Germain ◽  
Likibi Pellat Rhoss Beaunheur
Keyword(s):  
Finite Element ◽  
Numerical Integration ◽  
Mixed Finite Element ◽  
Sufficient Conditions ◽  
Finite Element Approximation ◽  
Miscible Displacement ◽  
Optimal Order ◽  
Element Approximation ◽  
Quadrature Scheme ◽  
Effect Of Numerical Integration

We consider the effect of numerical integration in finite element  procedures applied to a nonlinear system of two coupled partial differential equations describing the miscible displacement of one incompressible fluid by another in a porous meduim. We consider the use of the numerical quadrature scheme for approximating the pressure and velocity by a mixed method using Raviart - Thomas space of index  and the concentration by a standard Galerkin method. We also give some sufficient conditions on the quadrature scheme to ensure that the order of convergence is unaltered in the presence of numerical integration. Optimal order estimates are derived when the imposed external flows are smoothly distributed.

scholarly journals Stochastic Controllability of Systems with Multiple Delays in Control

2009 ◽  
Vol 19 (1) ◽  
pp. 39-48 ◽  
Author(s):  
Jerzy Klamka
Keyword(s):  
Dynamic System ◽  
Dynamic Systems ◽  
Sufficient Conditions ◽  
Time Interval ◽  
Multiple Delays ◽  
Stochastic Dynamic ◽  
Relative Controllability ◽  
Linear Dynamic Systems ◽  
Linear Dynamic ◽  
Controllability Of Systems

Stochastic Controllability of Systems with Multiple Delays in ControlFinite-dimensional stationary dynamic control systems described by linear stochastic ordinary differential state equations with multiple point delays in control are considered. Using the notation, theorems and methods used for deterministic controllability problems for linear dynamic systems with delays in control as well as necessary and sufficient conditions for various kinds of stochastic relative controllability in a given time interval are formulated and proved. It will be proved that, under suitable assumptions, relative controllability of an associated deterministic linear dynamic system is equivalent to stochastic relative exact controllability and stochastic relative approximate controllability of the original linear stochastic dynamic system. As a special case, relative stochastic controllability of dynamic systems with a single point delay is also considered. Some remarks and comments on the existing results for stochastic controllability of linear dynamic systems are also presented.

scholarly journals Sharp multidimensional numerical integration for strongly convex functions on convex polytopes

Filomat ◽  
2020 ◽  
Vol 34 (2) ◽  
pp. 601-607
Author(s):  
Osama Alabdali ◽  
Allal Guessab
Keyword(s):  
Numerical Integration ◽  
Convex Polytopes ◽  
Sufficient Conditions ◽  
Approximation Error ◽  
Quadratic Function ◽  
Characterization Theorem ◽  
Strongly Convex ◽  
Cubature Formulas ◽  
Voronoi Tesselations ◽  
Necessary And Sufficient

This paper introduces and studies a new class of multidimensional numerical integration, which we call ?strongly positive definite cubature formulas?. We establish, among others, a characterization theorem providing necessary and sufficient conditions for the approximation error (based on such cubature formulas) to be bounded by the approximation error of the quadratic function. This result is derived as a consequence of two characterization results, which are of independent interest, for linear functionals obtained in a more general seeting. Thus, this paper extends some result previously reported in [2, 3] when convexity in the classical sense is only assumed. We also show that the centroidal Voronoi Tesselations provide an efficient way for constructing a class of optimal of cubature formulas. Numerical results for the two-dimensional test functions are given to illustrate the efficiency of our resulting cubature formulas.

scholarly journals Stochastic Controllability of Linear Systems With State Delays

2007 ◽  
Vol 17 (1) ◽  
pp. 5-13 ◽  
Author(s):  
Jerzy Klamka
Keyword(s):  
Dynamic System ◽  
Linear Systems ◽  
Single Point ◽  
Minimum Energy ◽  
Sufficient Conditions ◽  
Stochastic Dynamic ◽  
Relative Controllability ◽  
Stochastic Dynamic System ◽  
Linear Dynamic ◽  
State Delays

Stochastic Controllability of Linear Systems With State DelaysA class of finite-dimensional stationary dynamic control systems described by linear stochastic ordinary differential state equations with a single point delay in the state variables is considered. Using a theorem and methods adopted directly from deterministic controllability problems, necessary and sufficient conditions for various kinds of stochastic relative controllability are formulated and proved. It will be demonstrated that under suitable assumptions the relative controllability of an associated deterministic linear dynamic system is equivalent to the stochastic relative exact controllability and the stochastic relative approximate controllability of the original linear stochastic dynamic system. Some remarks and comments on the existing results for the controllability of linear dynamic systems with delays are also presented. Finally, a minimum energy control problem for a stochastic dynamic system is formulated and solved.

Sign in / Sign up

Export Citation Format

Share Document