Dynamic bid–ask pricing under Dempster-Shafer uncertainty

We deal with the problem of pricing in a multi-period binomial market model, allowing for frictions in the form of bid–ask spreads. We introduce and characterize time-homogeneous Markov multiplicative binomial processes under Dempster-Shafer uncertainty together with the induced conditional Choquet expectation operator. Given a market formed by a frictionless risk-free bond and a non-dividend paying stock with frictions, we prove the existence of an equivalent one-step Choquet martingale belief function. We then propose a dynamic Choquet pricing rule with bid–ask spreads showing that the discounted lower price process of a European derivative contract on the stock is a Choquet super-martingale. We finally provide a normative justification in terms of a dynamic generalized no-arbitrage condition relying on the notion of partially resolving uncertainty due to Jaffray

A Dutch book coherence condition for conditional completely alternating Choquet expectations

Stemming from de Finetti’s coherence for finitely additive (conditional) probabilities, the paradigm of coherence has been extended to other uncertainty calculi. We study the notion of coherence for conditional completely alternating Choquet expectations, providing an avoiding Dutch book like condition

The IAS-MEEG Package: A Flexible Inverse Source Reconstruction Platform for Reconstruction and Visualization of Brain Activity from M/EEG Data

We present a standalone Matlab software platform complete with visualization for the reconstruction of the neural activity in the brain from MEG or EEG data. The underlying inversion combines hierarchical Bayesian models and Krylov subspace iterative least squares solvers. The Bayesian framework of the underlying inversion algorithm allows to account for anatomical information and possible a priori belief about the focality of the reconstruction. The computational efficiency makes the software suitable for the reconstruction of lengthy time series on standard computing equipment. The algorithm requires minimal user provided input parameters, although the user can express the desired focality and accuracy of the solution. The code has been designed so as to favor the parallelization performed automatically by Matlab, according to the resources of the host computer. We demonstrate the flexibility of the platform by reconstructing activity patterns with supports of different sizes from MEG and EEG data. Moreover, we show that the software reconstructs well activity patches located either in the subcortical brain structures or on the cortex. The inverse solver and visualization modules can be used either individually or in combination. We also provide a version of the inverse solver that can be used within Brainstorm toolbox. All the software is available online by Github, including the Brainstorm plugin, with accompanying documentation and test data

BIAS IN THE ITEMS OF THE CALIFORNIA ACHIEVEMENT TESTS FOR CHILDREN FROM THREE SOCIO-CULTURAL GROUPS.

This study investigated bias at the item level in six subtests of the California Achievement Tests (CAT). Variability of performance across all individual items of the CAT for fourth graders from three ethnic groups was examined. A two-factor (item scores and ethnicity) ANOVA procedure was used to examine the interaction between Anglo and Hispanic children and between Anglo and black subjects on individual test items of the subtests. Significant F-ratios for the Items x Groups interaction were further examined by using Bonerroni's post-hoc test for the purpose of identifying specific items reflecting cultural bias. A total of twenty-one items was identified as culturally biased. Of these items, sixteen were biased against Hispanics, three items were found to contain bias against blacks, and two items reflected bias against both Hispanic and black children. Of these twenty-one items identified as biased, eighteen belonged to four verbal subtests and three items are part of the two mathematics subtests. In addition to these items identified as being statistically biased, this study suggests that ethnocultural differences exist on overall performance levels between groups. For example, on the verbal subtests, there was a total of only three items on which Hispanic children scored higher than Anglo subjects, and only one item which reflected a better performance by black children than Anglo students. Higher performance levels by Anglo subjects were also noted on mathematic subtests, wherein Hispanic children scored higher on six items than their Anglo counterparts, and black subjects outperformed Anglo children on only one item. These data reflected a tendency of higher performance by Anglo students across all subtests when by an examination of the number of items passed or failed by members of each ethnic group was made. The examination of the verbal subtests additionally showed that Anglos passed sixty-five items, Hispanic children passed twenty-four items and thirty-two items were passed by black subjects. This trend continued on the mathematics subtests, where thirty-one items were passed by Anglo students and seventeen and fifteen items were passed by Hispanic and black children respectively. The findings of this study led to the conclusion that the majority of items on the CAT does not reflect evidence of cultural bias. There were, however, a limited number of items on which either Hispanic or black children out-performed their Anglo counterparts. Implications of these findings were discussed and recommendations were made for future studies to examine bias at the item level

Conditional independence in a finite coherent setting

A definition of stochastic independence which avoids the inconsistencies (related to events of probability 0 or 1) of the classic one has been proposed by Coletti and Scozzafava for two events. We extend it to conditional independence among finite sets of events. In particular, the case of (finite) discrete random variables is studied. We check which of the relevant properties connected with graphical structures hold. Hence, an axiomatic characterization of these independence models is given and it is compared to the classic ones

Graphical Representation of Asymmetric Graphoid Structures

Independence models induced by some uncertainty measures (e.g. conditional probability, possibility) do not obey the usual graphoid properties, since they do not satisfy the symmetry property. They are efficiently representable through directed acyclic l-graphs by using L-separation criterion

Possibility theory: conditional independence

The subtle notion of conditioning is controversial in several contexts, for example in possibility theory where, in fact, different definitions have been introduced. We refer to a general axiomatic definition of conditional possibility and then we deal with “partial assessments” on (not necessarily structured) domains containing only elements of interest. We study a notion of coherence, which assures the extendability of an assessment as a conditional possibility and we introduce a procedure for checking coherence. Moreover, we propose a definition of independence for conditional possibility, which avoids some counterintuitive situations, and we study its main properties in order to compare it with other definitions introduced in literature. Then, we check which properties among the graphoid ones are satisfied: this allows to compare our definition with other independence notions given in the context of other uncertainty formalisms. This analysis is relevant for graphical models in order to single out and visualize dependence relations among random variables

Modeling agent's conditional preferences under objective ambiguity in Dempster-Shafer theory

We manage decisions under “objective” ambiguity by considering generalized Anscombe-Aumann acts, mapping states of the world to generalized lotteries on a set of consequences. A generalized lottery is modeled through a belief function on consequences, interpreted as a partially specified randomizing device. Preference relations on these acts are given by a decision maker focusing on different scenarios (conditioning events). We provide a system of axioms which are necessary and sufficient for the representability of these “conditional preferences” through a conditional functional parametrized by a unique full conditional probability P on the algebra of events and a cardinal utility function u on consequences. The model is able to manage also “unexpected” (i.e., “null”) conditioning events and distinguishes between a systematically pessimistic or optimistic behavior, either referring to “objective” belief functions or their dual plausibility functions. Finally, an elicitation procedure is provided, reducing to a Quadratically Constrained Linear Program (QCLP)