Chebyshev polynomial approximation to approximate partial differential equations

This paper suggests a simple method based on Chebyshev approximation at Chebyshev nodes to approximate partial differential equations. The methodology simply consists in determining the value function by using a set of nodes and basis functions. We provide two examples. Pricing an European option and determining the best policy for chatting down a machinery. The suggested method is flexible, easy to program and efficient. It is also applicable in other fields, providing efficient solutions to complex systems of partial differential equations.

A Soft Edge Target Zone Model: Theory And Application To Hong Kong

Hong Kong’s currency is pegged to the US dollar in a currency board arrangement. In autumn 2003, the Hong Kong dollar appreciated from close to 7.80 per US dollar to 7.70, as investors feared that the currency board would be abandoned. In the wake of this appreciation, the monetary authorities revamped the one-sided currency board mechanism into a symmetric two-sided system with a narrow exchange rate band. This paper reviews the characteristics of the new currency board arrangement and embeds a theoretical soft edge target zone model typifying many intermediate regimes, to explain the notable achievement of speculative peace and credibility since May 2005.

Efficient Nash Equilibrium under Adverse Selection

This paper revisits the problem of adverse selection in the insurance market of Rothschild and Stiglitz [28]. We propose a simple extension of the game-theoretic structure in Hellwig [14] under which Nash-type strategic interaction between the informed customers and the uninformed firms results always in a particular separating equilibrium. The equilibrium allocation is unique and Pareto-efficient in the interim sense subject to incentive-compatibility and individual rationality. In fact, it is the unique neutral optimum in the sense of Myerson [22].

Efficient Competition through Cheap Talk: Competing Auctions and Competitive Search without Ex Ante Price

We consider a frictional two-sided matching market in which one side uses public cheap talk announcements so as to attract the other side. We show that if the first-price auction is adopted as the trading protocol, then cheap talk can be perfectly informative, and the resulting market outcome is efficient, constrained only by search frictions. We also show that the performance of an alternative trading protocol in the cheap-talk environment depends on the level of price dispersion generated by the protocol: If a trading protocol compresses (spreads) the distribution of prices relative to the first-price auction, then an efficient fully revealing equilibrium always (never) exists. Our results identify the settings in which cheap talk can serve as an efficient competitive instrument, in the sense that the central insights from the literature on competing auctions and competitive search continue to hold unaltered even without ex ante price commitment.

An Empirical Examination of the R&D Boundaries of the Firm - A Problem-Solving Perspective

We consider, both theoretically and empirically, how different organization modes are aligned to govern the efficient solving of technological problems. The data set is a sample from the Chinese consumer electronics industry. Following mainly the problem solving perspective (PSP) within the knowledge based view (KBV), we develop and test several PSP and KBV hypotheses, in conjunction with competing transaction cost economics (TCE) alternatives, in an examination of the determinants of the R&D organization mode. The results show that a firm’s existing knowledge base is the single most important explanatory variable. Problem complexity and decomposability are also found to be important, consistent with the theoretical predictions of the PSP, but it is suggested that these two dimensions need to be treated as separate variables. TCE hypotheses also receive some support, but the estimation results seem more supportive of the PSP and the KBV than the TCE.