Can patent duration hinder medical innovation.

We argue that, in the pharmaceutical industry, excessive patent duration can deter investments in innovative treatments in favor of me-too drugs. The point is that too-long durations foster incentives to collude to delay investments in R&D for innovative treatments. We give a set of sufficient conditions for which collusion is a subgame-perfect equilibrium; that is, the threat of punishing any deviator is credible. We then show that reducing current duration always breaks down market discipline, and so does an increase in duration for innovative treatments. Optimal patent duration must then be a trade-off between breaking down market discipline and rewarding innovation.

The antagonism of push and pull strategies, and the current funding campaigns to fight orphan diseases.

We argue that an increase in investments in R&D for innovative treatments to eradicate neglected diseases in developing countries leads to a rational decrease in investments in available treatment technologies. In a formal model where the government of a developing country seeks to optimally allocate public resources, we show that the higher the odds of appearance of an innovative treatment, as occurring when investments in R&D increase, the lower the optimal provision of current treatments and other health expenditures. We also show that this phenomenon is aggravated when the opportunity cost of investments in current treatments increases. This implies that welfare in developing countries deteriorates as innovative treatments are more likely to become available. We also describe an insurance scheme that remedies these issues, and that leads to Pareto-optimal allocations regardless of the investment level in R&D for innovative treatments.

Designing the financial tools to promote universal access to AIDS care.

We argue that reluctance to invest in drug treatments to fight the AIDS epidemics in developing countries is largely motivated by severe losses occurring from the future albeit uncertain appearance of a curative vaccine. We design a set of securities generating full insurance coverage against such losses, while achieving full risk-sharing with vaccine development agencies. In a General Equilibrium framework, we show that those securities are demanded to improve social welfare in developing countries, to increase current investment in treatments and the provision of public goods. Even though designed for AIDS, those securities can also be applied to other epidemics such as malaria and tuberculosis, as well as any innovative treatment to fight orphan diseases.

Long-range out-of-sample properties of autoregressive neural networks.

We consider already-trained discrete autoregressive neural networks in their most general representations, with the exclusion of time-varying input though, and we provide tight sufficient conditions and elementary proofs for the existence of an attractor, uniqueness, and global convergence. Those conditions can be used as easy-to-check criteria when convergence (or not) of long-range predictions is desirable.