Probabilistic Expectations Research Articles

Subjective expectations in the context of HIV/AIDS in Malawi.

In this paper we present a newly developed interactive elicitation methodology for collecting probabilistic expectations in a developing country context with low levels of literacy and numeracy, and we evaluate the feasibility and success of this method for a wide range of outcomes in rural Malawi. We find that respondents' answers about their subjective expectations take into account basic properties of probabilities, and vary meaningfully with observable characteristics and past experience. From a substantive point of view, the elicited expectations indicate that individuals are generally aware of differential risks. For example, individuals with lower incomes and less land rightly feel at greater risk of financial distress than people with higher socioeconomic status (SES), and people who are divorced or widowed rightly feel at greater risk of being infected with HIV than currently married individuals. Meanwhile many expectations-including the probability of being currently infected with HIV-are well-calibrated compared to actual probabilities, but mortality expectations are substantially overestimated compared to life table estimates. This overestimation may lead individuals to underestimate the benefits of adopting HIV risk-reduction strategies. The skewed distribution of expectations about condom use also suggests that a small group of innovators are the forerunners in the adoption of condoms within marriage for HIV prevention.

An estimation model of value-at-risk portfolio under uncertainty

A value-at-risk portfolio model under uncertainty is discussed. In the proposed model, randomness and fuzziness are evaluated, respectively, by the probabilistic expectation and the mean values with evaluation weights and λ -mean functions. The means, the variances and the measurements of imprecision for fuzzy numbers/fuzzy random variables are evaluated in the possibility case and the necessity case, and the rate of return in portfolio is estimated regarding the both random factors and imprecise factors. By analytical approach, we derive a solution of the value-at-risk portfolio problem. A numerical example is given to illustrate our idea.

PILL, PATCH, OR SHOT? SUBJECTIVE EXPECTATIONS AND BIRTH CONTROL CHOICE*

When choosing a contraception method, women base their decisions on their subjective expectations about the realizations of method‐related outcomes. Examples of outcomes include getting pregnant and contracting a sexually transmitted disease (STD). I combine innovative data on probabilistic expectations with observed contraceptive choices to estimate a random utility model of birth control choice. The availability of expectations data is essential to identify preferences from beliefs. Effectiveness, protection against STDs, and partner's disapproval are found to be the most important factors in the decision process. The elicited expectations and inferred preference parameters are used to simulate the impact of various policies.

Narrative Progression in the Short Story: First Steps in a Corpus Stylistic Approach

I am interested in the putative textual signalings of narrative progression, and thereafter the reader expectations that these foster; I am trying to identify such signalings (or narrative prospection, as it is also called) with new research methods, namely those of corpus linguistics. Research of this kind, blending a literary interest with use of corpus tools, is coming to be known as corpus stylistics (or more narrowly, corpus narratology). For readers of this journal I assume that neither explaining nor justifying an interest in narrative progression is necessary, so I will discuss this relatively briefly. I will spend a little more time outlining what corpus stylistics entails and what its limitations are; and then I will share some ways in which I have tried to make it useful in the pursuit of my research interest, the textualization of narrative prospection. Narrative prospection is itself only a stage in the experiential sequence of interest to me. I assume that the text's prospections cumulatively and serially guide the reader to expect the story currently being read to continue and terminate in one way rather than others (at the least, the prospections will foster probabilistic expectations). The ways in which the subsequent narrative text confirms or flouts

Subjective income and employment expectations and preferences for redistribution

Using probabilistic expectations data from the German Socio-Economic Panel, we establish a link between self-reported expectations of occupational mobility and preferences for redistribution. Our results provide new evidence on the validity of the “prospect of upward mobility” hypothesis.

Coherence and Coreference Revisited

For more than three decades, research into the psycholinguistics of pronoun interpretation has argued that hearers use various interpretation 'preferences' or 'strategies' that are associated with specific linguistic properties of antecedent expressions. This focus is a departure from the type of approach outlined in Hobbs (1979), who argues that the mechanisms supporting pronoun interpretation are driven predominantly by semantics, world knowledge and inference, with particular attention to how these are used to establish the coherence of a discourse. On the basis of three new experimental studies, we evaluate a coherence-driven analysis with respect to four previously proposed interpretation biases-based on grammatical role parallelism, thematic roles, implicit causality, and subjecthood-and argue that the coherence-driven analysis can explain the underlying source of the biases and predict in what contexts evidence for each will surface. The results further suggest that pronoun interpretation is incrementally influenced by probabilistic expectations that hearers have regarding what coherence relations are likely to ensue, together with their expectations about what entities will be mentioned next, which, crucially, are conditioned on those coherence relations.

Characterizing and reasoning about probabilistic and non-probabilistic expectation

Expectation is a central notion in probability theory. The notion of expectation also makes sense for other notions of uncertainty. We introduce a propositional logic for reasoning about expectation, where the semantics depends on the underlying representation of uncertainty. We give sound and complete axiomatizations for the logic in the case that the underlying representation is (a) probability, (b) sets of probability measures, (c) belief functions, and (d) possibility measures. We show that this logic is more expressive than the corresponding logic for reasoning about likelihood in the case of sets of probability measures, but equi-expressive in the case of probability, belief, and possibility. Finally, we show that satisfiability for these logics is NP-complete, no harder than satisfiability for propositional logic.

Biogeography of European land mammals shows environmentally distinct and spatially coherent clusters

AbstractAim To produce a spatial clustering of Europe on the basis of species occurrence data for the land mammal fauna.Location Europe defined by the following boundaries: 11°W, 32°E, 71°N, 35°N.Methods Presence/absence records of mammal species collected by the Societas Europaea Mammalogica with a resolution of 50 × 50 km were used in the analysis. After pre‐processing, the data provide information on 124 species in 2183 grid cells. The data were clustered using thek‐means and probabilistic expectation maximization (EM) clustering algorithms. The resulting geographical pattern of clusters was compared against climate variables and against an environmental stratification of Europe based on climate, geomorphology and soil characteristics (EnS).Results The mammalian presence/absence data divide naturally into clusters, which are highly connected spatially and most strongly determined by the small mammals with the highest grid cell incidence. The clusters reflect major physiographic and environmental features and differ significantly in the values of basic climate variables. The geographical pattern is a fair match for the EnS stratification and is robust between non‐overlapping subsets of the data, such as trophic groups.Main conclusions The pattern of clusters is regarded as reflecting the spatial expression of biologically distinct, metacommunity‐like entities influenced by deterministic forces ultimately related to the physical environment. Small mammals give the most spatially coherent clusters of any subgroup, while large mammals show stronger relationships to climate variables. The spatial pattern is mainly due to small mammals with high grid cell incidence and is robust to noise from other subsets. The results support the use of spatially resolved environmental reconstructions based on fossil mammal data, especially when based on species with the highest incidence.

A new evaluation of mean value for fuzzy numbers and its application to American put option under uncertainty

This paper discusses two topics on fuzzy random variables in decision making. One is a new evaluation method of fuzzy random variables, and the other is to present a mathematical model in financial engineering by fuzzy random variables. The evaluation method is introduced as mean values defined by fuzzy measures, and it is also applicable to fuzzy numbers and fuzzy stochastic process defined by fuzzy random variables. The other is to apply the method to an American put option with uncertainty formulated as an optimal stopping problem for fuzzy random variables, and the randomness and fuzziness are estimated by the probabilistic expectation and the mean values. The optimal expected price of the American put option is given by the mean values with decision maker's subjective parameters. Numerical examples are given to illustrate our idea.

Measuring Pension-benefit Expectations Probabilistically

. Research aiming to understand the impact of public and private pension plans on individual decision making has been hampered by a dearth of empirical evidence on benefit expectations. We review the occasional national surveys that have sought to measure pension-benefit expectations and describe our recent efforts to improve the measurement of US Social Security benefit expectations by elicitation of probabilistic expectations about well-defined outcomes. We document striking uncertainty and heterogeneity of beliefs about the long-term existence of the Social Security system and about the level of benefits should the system survive. In so doing, we highlight the additional information that is extracted using our probabilistic elicitation method as opposed to more traditional methods that only seek point forecasts.

Seat share distribution of parties: Models and empirical patterns

We find that strategic sequencing and other factors sort parties roughly into two groups. Low-ranking parties lose part of their inherent support, compared to probabilistic expectations, while high-ranking parties profit from the shift. Our method is to graph the worldwide mean seat shares of parties at various ranks by size against the largest party share (Nagayama triangle format). The resulting empirical pattern looks complex, yet when we adjust a probabilistic model to account for strategic and other factors that may hurt the smaller parties, the fit becomes close. The number of parties that profit from transfers is close to the inverse of the fractional share of the largest party. The model fits best when the transfer is assumed to involve about one-half of inherent minor party support. This is a novel way to estimate the universal average strength of strategic and other factors that work against the smaller parties. The empirical worldwide mean pattern offers us a norm against which seat share distributions in individual countries or single elections can be compared.

A Conditional Valuation Approach for Path-Dependent Instruments

Credit exposure is the amount a bank can potentially lose in the event that one of its counterparties default. The measurement of exposure on derivative contracts is very important because it is used not only to set up the trading limits but also as an essential input to the bank's economic and regulatory capital calculation. The new Basel guideline has recommanded for a more forward-looking approach (in contrast to the tradtional loan-based method) to the treatment of counterparty exposure to the bank's trading book. We present a value-at-future methodology for calculating the exposures of derivative instruments across the future times. The standard valuation models used to price the instruments for mark-to-market are not applicable for calculating exposure on path-dependent instruments whose value at the future time may depend on either some event at an ealier time or in some cases on the entire path leading to the future date. For such path-dependent instruments, we propose in this paper the notion of conditional valuation, which is based on probabilistic conditional expectation techniques. Using the properties of the Brownian bridges, we show that analytic solutions are readily availabe for the exposure or value-at-future on a number of path-dependent instruments such as barrier options, average options, variance swaps and swap-settled swaptions.

Expectation-oriented modeling

This work introduces expectation-oriented modeling (EOM) as a conceptual and formal framework for the modeling and influencing of black- or gray-box agents and agent interaction from the viewpoint of modelers like artificial agents and application designers. EOM is unique in that autonomous agent behavior is not restricted in advance, but only if it turns out to be necessary at runtime, and does so exploiting a seamless combination of evolving probabilistic and normative behavioral expectations as the key modeling abstraction and as the primary level of analysis and influence. Expectations are attitudes which allow for the relation of observed actions and other events to the modelers intentions and beliefs in an integrated, adaptive manner. In this regard, this work introduces a formal framework for the representation and the semantics of expectations embedded in social contexts. We see the applicability of EOM especially in open domains with a priori unknown and possibly unreliable and insincere actors, where the modeler cannot rely on cooperation or pursue her goals through the exertion of strictly normative power, e.g. the development and assertion of flexible interaction policies for trading platforms in the Internet, as illustrated in a case study. To our knowledge, EOM is the first approach to the modeling, cognitive analysis and influencing of social interaction that aims at tackling the level of expectations explicitly and systematically.

Extreme points of Banach lattices related to conditional expectations

Let ( X , F , μ ) be a complete probability space, B a sub- σ-algebra, and Φ the probabilistic conditional expectation operator determined by B . Let K be the Banach lattice { f ∈ L 1 ( X , F , μ ) : ‖ Φ ( | f | ) ‖ ∞ < ∞ } with the norm ‖ f ‖ = ‖ Φ ( | f | ) ‖ ∞ . We prove the following theorems: (1) The closed unit ball of K contains an extreme point if and only if there is a localizing set E for B such that supp ( Φ ( χ E ) ) = X . (2) Suppose that there is n ∈ N such that f ⩽ n Φ ( f ) for all positive f in L ∞ ( X , F , μ ) . Then K has the uniformly λ-property and every element f in the complex K with ‖ f ‖ ⩽ 1 n is a convex combination of at most 2 n extreme points in the closed unit ball of K .

EXTREME POINTS OF CERTAIN BANACH SPACES RELATED TO CONDITIONAL EXPECTATIONS

Let $(X,\mathcal{F},\mu)$ be a complete probability space and let $\mathcal{B}$ be a sub- $\sigma$ -algebra of $\mathcal{F}$ . We consider the extreme points of the closed unit ball $\mathbb{B}(\mathcal{A})$ of the normed space $\mathcal{A}$ whose points are the elements of $L^\infty(X,\mathcal{F},\mu)$ with the norm $\Vert\, f \Vert = \Vert\Phi(\vert\, f \vert)\Vert_\infty$ , where $\Phi$ is the probabilistic conditional expectation operator determined by $\mathcal{B}$ . No $\mathcal{B}$ - measurable function is an extreme point of the closed unit ball of $\mathcal{A}$ , and in certain cases there are no extreme points of $\mathbb{B}(\mathcal{A})$ . For an interesting family of examples, depending on a parameter $n$ , we characterize the extreme points of the unit ball and show that every element of the open unit ball is a convex combination of extreme points. Although in these examples every element of the open ball of radius $\frac{1}{n}$ can be shown to be a convex combination of at most $2n$ extreme points by elementary arguments, our proof for the open unit ball requires use of the $\lambda$ -function of Aron and Lohman. In the case of the open unit ball, we only obtain estimates for the number of extreme points required in very special cases, e.g. the $\mathcal{B}$ -measurable functions, where $2n$ extreme points suffice.

A discrete-time model of American put option in an uncertain environment

A discrete-time mathematical model for American put option with uncertainty is presented, and the randomness and fuzziness are evaluated by both probabilistic expectation and fuzzy expectation defined by a possibility measure from the viewpoint of fuzzy expectation, taking account of decision-maker’s subjective judgment. An optimality equation for the optimal stopping problem in a fuzzy stochastic process is derived and an optimal exercise time is given for the American put option. It is shown that the optimal fuzzy price is a solution of the optimality equation under a reasonable assumption. The permissible range of the writer’s (seller’s) optimal expected price in the American put option is presented, and the meaning and properties of the optimal expected prices are discussed in numerical examples. In a numerical example, the discrete-time approximation model is discussed for the continuous-time model.

A multiobjective fuzzy stopping in a stochastic and fuzzy environment

In a stochastic and fuzzy environment, a multiobjective fuzzy stopping problem is discussed. The randomness and fuzziness are evaluated by probabilistic expectations and linear ranking functions, respectively. Pareto optimal fuzzy stopping times are given under the assumption of regularity for stopping rules, by using γ-optimal stopping times.

The valuation of European options in uncertain environment

A new model on European options with uncertainty of both randomness and fuzziness in output is presented, by introducing fuzzy logic to the stochastic financial model. The randomness and fuzziness in the systems are evaluated by both probabilistic expectation and fuzzy expectation, taking account of seller’s/buyer’s subjective judgment. Prices of European call/put options with uncertainty are given and their valuation and properties are discussed under a reasonable assumption. This paper demonstrates Black–Scholes formula to give rational expected price of the European options and buyer’s/writer’s (seller’s) permissible range of expected prices. The meaning and properties of rational expected prices are discussed in a numerical example. The hedging strategies are also considered for marketability of the European options for portfolio selection.

Venetian Sea Levels, British Bread Prices, and the Principle of the Common Cause

When two causally independent processes each have a quantity that increases monotonically (either deterministically or in probabilistic expectation), the two quantities will be correlated, thus providing a counterexample to Reichenbach's principle of the common cause. Several philosophers have denied this, but I argue that their efforts to save the principle are unsuccessful. Still, one salvage attempt does suggest a weaker principle that avoids the initial counterexample. However, even this weakened principle is mistaken, as can be seen by exploring the concepts of homology and homoplasy used in evolutionary biology. I argue that the kernel of truth in the principle of the common cause is to be found by separating metaphysical and epistemological issues; as far as the epistemology is concerned, the Likelihood Principle is central.

The 26 dimensions of heterotic strings as a probabilistic standard deviation and expectation value of an infinite dimensional space

We give a short derivation showing that the 26 dimensions as indeed the 10 dimensions of heterotic string theory may be derived using classical probability theory as higher-order expectation and standard deviation of combined spaces within an infinite dimensional transfinite manifold.