TRYING TO FIT AN OVAL SHAPED ISLAND INTO A SQUARE CONSTITUTION: ARGUMENTS FOR PUERTO RICAN STATEHOOD

This Comment focuses on the limits placed on Puerto Rico under the United States Constitution and concludes that Puerto Rico must become the 51st state to improve its status under the Constitution. It explores Puerto Rico\u27s relationship with the United States and its unusual position under the Constitution. This Comment then examines the voting rights issues facing Puerto Ricans, including a First Circuit case which denied Puerto Ricans the right to vote in presidential elections. The Comment concludes that this case was correctly decided and the Supreme Court, in other decisions, has only recognized a limited right to vote under the Equal Protection Clause. Based on this case law, the Comment argues that Puerto Rico must become the 51st state to alleviate these voting rights issues

Subconvex bounds on GL(3) via degeneration to frequency zero

For a fixed cusp form $\pi$ on $\operatorname{GL}_3(\mathbb{Z})$ and a varying Dirichlet character $\chi$ of prime conductor $q$, we prove that the subconvex bound $$L(\pi \otimes \chi, \tfrac{1}{2}) \ll q^{3/4 - \delta}$$ holds for any $\delta < 1/36$. This improves upon the earlier bounds $\delta < 1/1612$ and $\delta < 1/308$ obtained by Munshi using his $\operatorname{GL}_2$ variant of the $\delta$-method. The method developed here is more direct. We first express $\chi$ as the degenerate zero-frequency contribution of a carefully chosen summation formula \`a la Poisson. After an elementary "amplification" step exploiting the multiplicativity of $\chi$, we then apply a sequence of standard manipulations (reciprocity, Voronoi, Cauchy--Schwarz and the Weil bound) to bound the contributions of the nonzero frequencies and of the dual side of that formula.Comment: 17 pages; to appear in Math. Annalen; minor correction

An algorithm for moment-matching scenario generation with application to financial portfolio optimization

We present an algorithm for moment-matching scenario generation. This method produces scenarios and corresponding probability weights that match exactly the given mean, the covariance matrix, the average of the marginal skewness and the average of the marginal kurtosis of each individual component of a random vector. Optimisation is not employed in the scenario generation process and thus the method is computationally more advantageous than previous approaches. The algorithm is used for generating scenarios in a mean-CVaR portfolio optimisation model. For the chosen optimisation example, it is shown that desirable properties for a scenario generator are satisfied, including in-sample and out-of-sample stability. It is also shown that optimal solutions vary only marginally with increasing number of scenarios in this example; thus, good solutions can apparently be obtained with a relatively small number of scenarios. The proposed method can be used either on its own as a computationally inexpensive scenario generator or as a starting point for non-convex optimisation based scenario generators which aim to match all the third and the fourth order marginal moments (rather than average marginal moments)

An asset and liability management (ALM) model using integrated chance constraints

This paper discusses and develops a Two Stage Integrated Chance Constraints Programming for the Employees Provident Fund Malaysia. The main aim is to manage, that is, balance assets and liabilities. Integrated Chance Constraints not only limit the event of underfunding but also the amount of underfunding. This paper includes the numerical illustration

Imperfect Knowledge and Asset Price Dynamics: Modeling the Forecasting of Rational Agents, Dynamic Prospect Theory and Uncertainty Premia on Foreign Exchange.

Models using the Rational Expectations Hypothesis (REH) are widely recognized to be inconsistent with the observed behavior of premia in financial markets, as well as other features of asset price dynamics. Moreover, many reasons have been advanced as to why the REH cannot generally represent, even approximately, the expectations behavior of individually rational agents. In this paper, we develop a new model of the equilibrium premium in the foreign exchange market that replaces the REH with the Imperfect Knowledge Forecasting (IKF) framework. Because we maintain that agents must cope with imperfect knowledge and that they are not grossly irrational, our IKF approach imposes only qualitative conditions on the formation of individual forecasting models and their updating. We also develop a dynamic extension of the original formulation of Kahneman and Tversky’s prospect theory. We find that under IKF and dynamic prospect theory, the equilibrium premium on foreign exchange is positively related to the gap between the aggregate forecast of the exchange rate and its historical benchmark level. We test this implication, using survey data on the German mark-U.S. dollar exchange rate, and find that the behavior of the ex ante premium on foreign exchange is consistent with our model of the premium.exchange rates; risk premium; imperfect knowledge; individual rationality; expectations; prospect theory