Patent Valuation under Spatial Point Processes with Delayed and Decreasing Jump Intensity

This article is set within the real options approach applied to patent valuation. Such evaluation is based on the knowledge of the impact of some events on the underlying state, which is modeled in discrete time as a spatial point process, i.e. both size and time of the jumps can be treated as random variables. This assumption allows us to improve upon the current theory of patent valuation in some respects. In particular, the propagation of the jumps from the economic environment to the patent value is not restricted to be immediate, but can occur with a random delay and with varying intensity, depending on the time to maturity. These actual features lead to a more general formula for patent value that may give rise to a non-trivial difference not accounted for in the existing literature

Innovation, imitation and policy inaction

The paper deals with the controversial issue of intellectual property rights. We deal with an optimization problem to model the optimal government's behavior in presence of dynamic uncertainty and intervention costs. More specifically, we search for the optimal strategies to be implemented by a policy maker to optimally balance the number of innovators and imitators. The problem is first tackled from a purely theoretical perspective and then by implementing extensive numerical simulations on the basis of empirical data. By the theoretical perspective, we obtain a rigorous proof that optimal strategies depend on the initial value of the number of imitators and not on the initial ratio between innovators and imitators, whereas the simulations provide us with intuitive insights from an economic point of view, along with a validation of the theoretical results. The results support the evidence that governments choose the possible widest bandwidth and minimize the size of interventions so as to curb intervention costs

Optimal Investment in Research and Development Under Uncertainty

This paper explores the optimal expenditure rate that a firm should employ to develop a new technology and pursue the registration of the related patent. Our model takes into account an economic environment with indus-trial competition among firms operating in the same sector and in presence of uncertainty in knowledge accumulation. We develop a stochastic optimal control problem with random horizon, and solve it theoretically by adopting a dynamic programming approach. An extensive numerical analysis suggests that the optimal expenditure rate is a decreasing function in time and its sen-sitivity to uncertainty depends on the stage of the race. The odds for the firm to preempt the rivals non-linearly depend on the degree of competition in the market

Exploring Financial Microblogs: Analysis of Users' Trading Profiles with Multivariate Statistical Methods

StockTwits is a Social Media focused on finance that is receiving increasing attention from finance experts and enthusiasts. In this work, StockTwits’ users are studied considering some of their self-declared characteristics, such as trading experience, holding period of the stocks, and trading approach. A Correspondence Analysis is carried out to investigate the relationships among these characteristics, the Simple Correspondence Analysis is applied to study the relationships between the approach and the holding period. The association between these variables and the experience is studied with the Multiple Correspondence Analysis. In the end, a cluster analysis carried out with hierarchical clustering is used to study the structure of the StockTwits community on the basis of the same characteristics. The analyses highlighted that the way users label their own approach and primary holding period reflect the objective relation linking technical strategy with short-term investments and fundamental approach with long-term ones. Moreover, it showed a weak relation of the experience in trading with the other features, configuring self-reported experience as a more cross-sectional characteristic

Dust formation around AGB and SAGB stars: a trend with metallicity?

We calculate the dust formed around AGB and SAGB stars of metallicity Z=0.008 by following the evolution of models with masses in the range 1M<M<8M throughthe thermal pulses phase, and assuming that dust forms via condensation of molecules within a wind expanding isotropically from the stellar surface. We find that, because of the strong Hot Bottom Burning (HBB) experienced, high mass models produce silicates, whereas lower mass objects are predicted to be surrounded by carbonaceous grains; the transition between the two regimes occurs at a threshold mass of 3.5M. These fndings are consistent with the results presented in a previous investigation, for Z=0.001. However, in the present higher metallicity case, the production of silicates in the more massive stars continues for the whole AGB phase, because the HBB experienced is softer at Z=0.008 than at Z=0.001, thus the oxygen in the envelope, essential for the formation of water molecules, is never consumed completely. The total amount of dust formed for a given mass experiencing HBB increases with metallicity, because of the higher abundance of silicon, and the softer HBB, both factors favouring a higher rate of silicates production. This behaviour is not found in low mass stars,because the carbon enrichment of the stellar surface layers, due to repeated Third Drege Up episodes, is almost independent of the metallicity. Regarding cosmic dust enrichment by intermediate mass stars, we find that the cosmic yield at Z=0.008 is a factor 5 larger than at Z=0.001. In the lower metallicity case carbon dust dominates after about 300 Myr, but at Z=0.008 the dust mass is dominated by silicates at all times,with a prompt enrichment occurring after about 40 Myr, associated with the evolution of stars with masses M =7.5 -8M.Comment: 14 pages, 10 figures, 2 Tables, accepted for publication in MNRA

The rotational shear layer inside the early red-giant star KIC 4448777

We present the asteroseismic study of the early red-giant star KIC 4448777, complementing and integrating a previous work (Di Mauro et al. 2016), aimed at characterizing the dynamics of its interior by analyzing the overall set of data collected by the {\it Kepler} satellite during the four years of its first nominal mission. We adopted the Bayesian inference code DIAMOND (Corsaro \& De Ridder 2014) for the peak bagging analysis and asteroseismic splitting inversion methods to derive the internal rotational profile of the star. The detection of new splittings of mixed modes, more concentrated in the very inner part of the helium core, allowed us to reconstruct the angular velocity profile deeper into the interior of the star and to disentangle the details better than in Paper I: the helium core rotates almost rigidly about 6 times faster than the convective envelope, while part of the hydrogen shell seems to rotate at a constant velocity about 1.15 times lower than the He core. In particular, we studied the internal shear layer between the fast-rotating radiative interior and the slow convective zone and we found that it lies partially inside the hydrogen shell above $r \simeq 0.05R$ and extends across the core-envelope boundary. Finally, we theoretically explored the possibility for the future to sound the convective envelope in the red-giant stars and we concluded that the inversion of a set of splittings with only low-harmonic degree $l\leq 3$, even supposing a very large number of modes, will not allow to resolve the rotational profile of this region in detail.Comment: accepted for publication on Ap

The sooner the better: lives saved by the lockdown during the COVID-19 outbreak. The case of Italy

Summary This paper estimates the effects of non-pharmaceutical interventions – mainly, the lockdown – on the COVID-19 mortality rate for the case of Italy, the first Western country to impose a national shelter-in-place order. We use a new estimator, the augmented synthetic control method (ASCM), that overcomes some limits of the standard synthetic control method (SCM). The results are twofold. From a methodological point of view, the ASCM outperforms the SCM in that the latter cannot select a valid donor set, assigning all the weights to only one country (Spain) while placing zero weights to all the remaining. From an empirical point of view, we find strong evidence of the effectiveness of non-pharmaceutical interventions in avoiding losses of human lives in Italy: conservative estimates indicate that the policy saved in total more than 21,000 human lives