Route Planning: B

There is a class of control problems that admit a particularly elegant solution: the linear quadratic Gaussian (LQG) problems. In these problems, the state dynamics and observations are linear, the cost is quadratic, and the noise is Gaussian. Section 14.1 explains the theory of LQG problems when one observes the state. Section 14.2 discusses the situation when the observations are noisy and shows the remarkable certainty equivalence property of the solution. Section 14.3 explains how noisy observations affect Markov decision problems.

LOSS AVERSION IS CONSISTENT WITH STOCK MARKET BEHAVIOR

The purpose of this paper is to verify that discrete statistical distributions of the US stock market are consistent with loss aversion. Loss aversion has the following tenets: an S-shaped valuation function, characterized by diminishing sensitivity, a loss aversion coefficient higher than +1, probability weighting, and reference-dependence. Diminishing sensitivity implies that the exponent of the valuation function is between 0 and +1. It is expected that this exponent be higher for losses. Probability weighting replaces objective with subjective probabilities. Loss aversion is indicated by a coefficient higher than +1 for the valuation of losses. There are three parameters: the two exponents of the valuation function, and the loss aversion coefficient. There is one non-linear equation: the certainty equivalence relation. The procedure is to fix two parameters and find the third parameter by solving the non-linear certainty equivalence equation, using the EXCEL spreadsheet. The program is repeated for more than one case about the fixed parameters, and by enriching the analysis with probability weighting. The calibrations executed point strongly to the conclusion that loss aversion is consistent with six discrete distributions of the first two moments of returns of the US stock markets. The calibration process provides for reasonable estimates of the key parameters of loss aversion. These estimates suggest a more pronounced diminishing sensitivity, and a higher than expected coefficient of loss aversion, especially when probability weighting is imposed.

Creating Multilingual Legal Texts

This chapter assesses the challenges in producing multilingual legal texts, especially where these texts are supposed to be equally authentic. The first of these challenges is translation. The risk is that a failure to achieve translation equivalence compromises legal certainty. Equivalence aside, there are also deeper political tensions in the process of legal translation: power struggles among speakers of the source and target language may be reflected in translation strategies adopted. Apart from translating the law, the legislature also needs to revise drafting procedures to ensure that different language versions of the law are consistent with one another, and that they respect linguistic equality where it is emphasized by the law. Where the new official language has not developed a legal vocabulary and a formal register, further linguistic engineering may be necessary. Sometimes ideological engineering is also called for.