Optimal budgetary and monetary policies under uncertainty: A stochastic control approach

In this paper, we determine optimal budgetary and monetary policies for Austria using a small macroeconometric model. We use a Keynesian model of the Austrian economy, called FINPOL1, estimated by ordinary least squares, which relates the main objective variables of Austrian economic policies, such as the growth rate of real gross domestic product, the rate of unemployment, the rate of inflation, the balance of payments, and the ratio of the federal budget deficit to GDP, to fiscal and monetary policy instruments, namely expenditures and revenues of the federal budget and money supply. Optimal fiscal and monetary policies are calculated for the model under a quadratic objective function using the algorithm OPTCON for the optimum control of nonlinear stochastic dynamic systems. Several control experiments are performed in order to assess the influence of different kinds of uncertainty on optimal budgetary and monetary policies. Apart from deterministic optimization runs, different assumptions about parameter uncertainties are introduced; the results of these different stochastic optimum control experiments are compared and interpreted.     

Transversality condition for infinite-horizon problems

We present necessary conditions of optimality for an infinitehorizon optimal control problem. The transversality condition is derived with the help of stability theory and is formulated in terms of the Lyapunov exponents of solutions to the adjoint equation. A problem without an exponential factor in the integral functional is considered. Necessary and sufficient conditions of optimality are proved for linear quadratic problems with conelike control constraints.     

Another Jacobi sufficiency criterion for optimal control with smooth constraints

In order to tighten the gap between necessary and sufficient conditions, new second-order sufficient conditions are developed for optimal control problems, where the control set is given by smooth functions. When the control set is polyhedral, our criterion generalizes prior results of the same kind, namely, the Jacobi criterion in Hamiltonian form and that in Lagrangian form (Refs. 1–3).The research of V. Zeidan was supported by NSERC Grant A-8570, which is gratefully acknowledged.     

Testing the Gumbel Hypothesis Via the Pot-Method

We consider an i.i.d. sample, generated by some distribution function, which belongs to the domain of attraction of an extreme value distribution with unknown shape and scale parameters. We treat the scale parameter as a nuisance parameter and establish for the hypothesis of Gumbel domain of attraction an asymptotically optimal test based on those observations among the sample, which exceed a given threshold sequence. Asymptotic optimality is achieved along certain contiguous extreme value alternatives within the concept of local asymptotic normality (LAN). Adaptive test procedures exist under restrictive assumptions. The finite sample size behavior of the proposed test is studied by simulations and it is compared to that of a test based on the sample coefficient of variation.     

线性脉冲控制系统的能控性与最优控制

首先讨论了一类线性随机脉冲控制系统的精确能控性质,给出了该类控制系统的脉冲精确能控的等价的代数判据.然后提出了一个确定性的二维线性脉冲控制系统的时间-脉冲强度最优控制问题;利用动态规划原理,给出了脉冲最优控制的反馈形式和值函数的显式表达式;说明了值函数在整个平面上是连续的,在左右两个半平面的内部还是连续可微的.     

Admissible investment strategies in continuous trading

We consider a situation where relative prices of assets may change continuously and also have discrete jumps at random time points. The problem is the one of portfolio optimization. If the utility function used is the logarithm, we first argue that an optimal investment plan exists. Secondly, we show that any such plan has a certain optimality property known to hold also in discrete time models. Moreover, we show that this optimality criterion can be simplified significantly. In particular we show how admissibility can be related directly to observable characteristics of the investment strategy.     

A non-linear congestion network model for planning internal movement in the Hajj

A non-linear congestion network model is developed for the Hajj case. The Hajj is one of the World's largest mass movements, according to religious rituals. Every year about two and a half million people gather to perform religious rituals. The objective of the model is to minimize traffic congestion and overcrowding of holy sites. The constraints of the model are religious, spatial and time constraints. The model developed and applied for this case assisted in easing overcrowding and planning for expansions in routes and holy sites. The model is effective in providing quantitative background for general policy decision on the Hajj transportation.     

Heterogeneous time preferences and the distribution of wealth

This paper shows that when households are heterogeneous with respect to time preference, the capital market functions as a powerful mechanism generating and maintaining a highly skewed distribution of wealth. A simple model of household savings is embedded into (1) a consumption loans economy and (2) a productive capital economy. The robustness of the conclusions is tested by relaxing some of the simplifying assumptions. Various counteracting instruments of social policy are discussed.     

Investigation of polynomial algorithms for solving the three-index planar assignment problem

Under certain additional conditions imposed on the coefficients of the objective function in the three-index planar assignment problem, a large series of computational experiments aimed at the investigation of four polynomial algorithms for finding an asymptotically optimal solution of this problem is conducted.     

Approximate Gradient Projection Method with Runge-Kutta Schemes for Optimal Control Problems

We consider an optimal control problem for systems governed by ordinary differential equations with control constraints. The state equation is discretized by the explicit fourth order Runge-Kutta scheme and the controls are approximated by discontinuous piecewise affine ones. We then propose an approximate gradient projection method that generates sequences of discrete controls and progressively refines the discretization during the iterations. Instead of using the exact discrete directional derivative, which is difficult to calculate, we use an approximate derivative of the cost functional defined by discretizing the continuous adjoint equation by the same Runge-Kutta scheme and the integral involved by Simpson's integration rule, both involving intermediate approximations. The main result is that accumulation points, if they exist, of sequences constructed by this method satisfy the weak necessary conditions for optimality for the continuous problem. Finally, numerical examples are given.