Best constants in Chebyshev inequalities with various applications

In this article we describe some ways to significantly improve the Markov-Gauss-Camp-Meidell inequalities and provide specific applications. We also describe how the improved bounds are extendable to the multivariate case. Applications include explicit finite sample construction of confidence intervals for a population mean, upper bounds on a tail probability P(X>k) by using the density at k, approximation of P-values, simple bounds on the Riemann Zeta function, on the series , improvement of Minkowski moment inequalities, and construction of simple bounds on the tail probabilities of asymptotically Poisson random variables. We also describe how a game theoretic argument shows that our improved bounds always approximate tail probabilities to any specified degree of accuracy. Received: April 1999     

The investment decision of a Multinational Firm under uncertain quantity restrictions

In this paper we analyze the allocative investment decisions of a Multinational Firm (MNF) when it faces uncertain quantity restrictions such as a voluntary export restraint or a quota imposed by the host government. The model with uncertain quantity restrictions is analyzed further by introducing additional uncertainties such as a foreign tax rate, transfer prices, foreign exchange rates and foreign demand. The MNF invests more in the host country due to uncertain quantity restrictions. The risk averse MNF invests more in the host country despite its uncertain tax rate if the transfer price is less than the expected marginal revenue loss due to the uncertain quantity restriction. The uncertain transfer price leads the MNF to invest more in the foreign country if the tax rates are dissimilar between the two countries. Foreign demand uncertainty and foreign exchange rates uncertainty have the same effects on capital allocation between the host country and home country. In particular, we derive the condition under which the direction of investment is unambiguous.     

A local analysis of stability and regularity of stationary states in discrete symmetric optimal capital accumulation models

In discrete time optimal capital accumulation models, where the period utilities have a certain “symmetry” property, a complete characterization of local stability of stationary states is obtained in terms of the characteristic roots of the product of certain submatrices of the Hessian of the utility function. This is used to analyze the connection between stability and properties of the effects of parameter changes on the stationary state. Certain differences in the results in discrete and continuous models are noted. A special case where utilities are “separable” in initial stocks and net investment is also treated.