The fundamental theorem of asset pricing, the hedging problem and maximal claims in financial markets with short sales prohibitions

This paper consists of two parts. In the first part we prove the fundamental theorem of asset pricing under short sales prohibitions in continuous-time financial models where asset prices are driven by nonnegative, locally bounded semimartingales. A key step in this proof is an extension of a well-known result of Ansel and Stricker. In the second part we study the hedging problem in these models and connect it to a properly defined property of "maximality" of contingent claims.Comment: Published in at http://dx.doi.org/10.1214/12-AAP914 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

[Review of] E. Ellis Cashmore. ed. Dictionary of Race and Ethnic Relations. 2nd ed.

A recurrent theme in the sociological study of racial and ethnic relations is the discipline\u27s inability to provide a clear and focused research agenda. Scholars in the field are troubled by their inability to agree as to the nature and scope of the discipline, and hence, the lack of an all-encompassing definition for the study of racial and ethnic relations. For example, a continual semantic debate exists over the appropriate usage and application of such concepts as race versus racial in sociological discourse. The Dictionary of Race and Ethnic Relations has been developed with this concern in mind

[Review of] Benjamin B. Ringer and Elinor R. Lawless. Race-Ethnicity and Society

The heritage of European colonization in the New World left a legacy of dualism for the contemporary nation-states of South, Central, and North America, according to Ringer and Lawless. As a major focus of their work, their duality thesis contends that European colonists constructed a society modeled in their racial, religious, and national image, resulting in the formation of a lasting colonial plural structure with a permanently established elite. Racial and ethnic groups emerged first as sojourner colonizers and then formalized their relationship with the establishment of colonies and the creation of racially segmented and subjugated societies. Dominant ethnic/racial groups promulgated policies and enacted legal-normative codes and controls that vitally affected the life chances and circumstance of the various ethnic and racial groups already within the territorial boundaries of the society or newly entering groups

Are You An Emissary of Jesus Christ?: Justice, The Catholic Church and the Chicano Movement

In 1969, Católicos Por La Raza (CPLR) emerged as an ethnic protest group against the injustices of the American Catholic Church in San Diego and Los Angeles, California. CPLR was critical of the Catholic hierarchy\u27s inconsistencies in relation to the Chicano community. As one of the wealthiest institutions, the Catholic Church was doing very little for a community that made up the largest part of the Church\u27s membership. For CPLR, the Christian message of justice was not practiced by the leaders of the Church. In Los Angeles, Chicanos were asking why the Archdiocese chose to close a high school in the barrio, due to lack of funds, but could still afford to build a three million dollar cathedral in downtown Los Angeles. In San Diego, Chicanos were asking the Catholic Church to become intimately involved in the everyday struggles of the Chicano community. Within this dialogue emerged a clear concept of justice and its meaning for CPLR members in relationship to the hierarchy of the American Catholic Church

Acts or events? A perspective from the marketing mix

La literatura existente en torno a las relaciones píublicas, el ceremonial y el protocolo alterna como sinónimos los términos actos y eventos. A través de una revisión teóricoconceptual, el principal objetivo de este trabajo es demostrar que ambos términos obedecen a realidades diferentes. Los resultados demuestran que, mientras que la organización de actos responde, desde la perspectiva de las relaciones públicas, a las necesidades comunicativas de las organizaciones; los eventos son herramientas que, desde la perspectiva del Mix de Marketing, permiten satisfacer las necesidades económicas, fundamentalmente, de las empresas.The existing public relations, ceremonial and protocol literature alternates the terms acts and events as synonyms. Through a theoretical-conceptual revision, the main objective of this work is to demonstrate that both terms obey different realities. The results show that, while the organization of acts responds, from the perspective of public relations, to the communicative needs of the organizations; Events are tools that, from the perspective of the Marketing Mix, allow meeting, mainly, the economic needs of companies

Density of the set of probability measures with the martingale representation property

Let $\psi$ be a multi-dimensional random variable. We show that the set of probability measures $\mathbb{Q}$ such that the $\mathbb{Q}$-martingale $S^{\mathbb{Q}}_t=\mathbb{E}^{\mathbb{Q}}\left[\psi\lvert\mathcal{F}_{t}\right]$ has the Martingale Representation Property (MRP) is either empty or dense in $\mathcal{L}_\infty$-norm. The proof is based on a related result involving analytic fields of terminal conditions $(\psi(x))_{x\in U}$ and probability measures $(\mathbb{Q}(x))_{x\in U}$ over an open set $U$. Namely, we show that the set of points $x\in U$ such that $S_t(x) = \mathbb{E}^{\mathbb{Q}(x)}\left[\psi(x)\lvert\mathcal{F}_{t}\right]$ does not have the MRP, either coincides with $U$ or has Lebesgue measure zero. Our study is motivated by the problem of endogenous completeness in financial economics.Comment: 24 pages, forthcoming in Annals of Probabilit

Polynomial diffusions on compact quadric sets

Polynomial processes are defined by the property that conditional expectations of polynomial functions of the process are again polynomials of the same or lower degree. Many fundamental stochastic processes, including affine processes, are polynomial, and their tractable structure makes them important in applications. In this paper we study polynomial diffusions whose state space is a compact quadric set. Necessary and sufficient conditions for existence, uniqueness, and boundary attainment are given. The existence of a convenient parameterization of the generator is shown to be closely related to the classical problem of expressing nonnegative polynomials---specifically, biquadratic forms vanishing on the diagonal---as a sum of squares. We prove that in dimension $d\le 4$ every such biquadratic form is a sum of squares, while for $d\ge6$ there are counterexamples. The case $d=5$ remains open. An equivalent probabilistic description of the sum of squares property is provided, and we show how it can be used to obtain results on pathwise uniqueness and existence of smooth densities.Comment: Forthcoming in Stochastic Processes and their Application