Stability of central finite difference schemes for the Heston PDE

This paper deals with stability in the numerical solution of the prominent Heston partial differential equation from mathematical finance. We study the well-known central second-order finite difference discretization, which leads to large semi-discrete systems with non-normal matrices A. By employing the logarithmic spectral norm we prove practical, rigorous stability bounds. Our theoretical stability results are illustrated by ample numerical experiments

All pronouns are not acquired equally in Dutch: Elicitation of object and quantitative pronouns

This research reports the results of eliciting pronouns in two syntactic environments: Object pronouns and quantitative er (Q-er). Thus another type of language is added to the literature on subject and object clitic acquisition in the Romance languages (Jakubowicz et al., 1998; Hamann et al., 1996). Quantitative er is a unique pronoun in the Germanic languages; it has the same distribution as partitive clitics in Romance. Q-er is an N'-anaphor and occurs obligatorily with headless noun phrases with a numeral or weak quantifier. Q-er is licensed only when the context offers an antecedent; it binds an empty position in the NP. Data from typically-developing children aged 5;0-6;0 show that object and Q-er pronouns are not acquired equally; it is proposed that this is due to their different syntax. The use of Q-er involves more sophisticated syntactic knowledge: Q-er occurs at the left edge of the VP and binds an empty position in the NP, whereas object pronouns are simply stand-ins for full NPs and occur in the same position. These Dutch data reveal that pronouns are not used as exclusively as object clitics are in the Romance languages (Varlakosta, in prep.)

'Nee, ze heeft er twee': Acquisition of the Dutch quantitative 'er'

We present the first study on the acquisition of the Dutch quantitative pronoun er in sentences such as de vrouw draagt er drie ‘the woman is carrying three.’ There is a large literature on Dutch children’s interpretation of pronouns and a few recent production studies, all specifically looking at 3rd person singular pronouns and the so-called Delay of Principle B effect (Coopmans & Philip, 1996; Koster, 1993; Spenader, Smits and Hendriks, 2009). However, no one has studied children’s use of quantitative er. Dutch is the only Germanic language with such a pronoun

Patent Purchase as a Policy for Pharmaceuticals

We consider a proposal for pharmaceutical patenting policy: namely, for society to grant and purchase the patent of the first of a new class of drug, instead of purchasing the drug, and award no further patents to runner-up drugs, producing or licensing production with price set to maximise welfare subject to cover costs. It is often observed that when the first of a new class of drugs is patented, it does not necessarily halt the development of a second and a third drug of the same class. The result may be a number of rugs with similar efficacy at similar prices well above the production costs. Where this happens, society could substantially reduce the cost of duplicated R&D and the price of the drug by buying the first patent. This would benefit more patients and produce larger health gains. Under this policy social welfare is increased, the winner is fully compensated, while the runner-up firm incurs possible losses - but there are viable conditions under which firms would not lose on average. We take a drug life-cycle approach to the welfare gains of a patent purchase policy. The results are generated based upon a number of stylised facts regarding R&D in the pharmaceutical industry

Cross-linguistic constraints and lineage-specific developments in the semantics of cutting and breaking in Japonic and Germanic

Semantic variation in the cutting and breaking domain has been shown to be constrained across languages in a previous typological study, but it was unclear whether Japanese was an outlier in this domain. Here we revisit cutting and breaking in the Japonic language area by collecting new naming data for 40 videoclips depicting cutting and breaking events in Standard Japanese, the highly divergent Tohoku dialects, as well as four related Ryukyuan languages (Amami, Okinawa, Miyako and Yaeyama). We find that the Japonic languages recapitulate the same semantic dimensions attested in the previous typological study, confirming that semantic variation in the domain of cutting and breaking is indeed cross-linguistically constrained. We then compare our new Japonic data to previously collected Germanic data and find that, in general, related languages resemble each other more than unrelated languages, and that the Japonic languages resemble each other more than the Germanic languages do. Nevertheless, English resembles all of the Japonic languages more than it resembles Swedish. Together, these findings show that the rate and extent of semantic change can differ between language families, indicating the existence of lineage-specific developments on top of universal cross-linguistic constraints