Clark-Ocone type formula for non-semimartingales with finite quadratic variation

We provide a suitable framework for the concept of finite quadratic variation for processes with values in a separable Banach space $B$ using the language of stochastic calculus via regularizations, introduced in the case $B= \R$ by the second author and P. Vallois. To a real continuous process $X$ we associate the Banach valued process $X(\cdot)$, called {\it window} process, which describes the evolution of $X$ taking into account a memory $\tau>0$. The natural state space for $X(\cdot)$ is the Banach space of continuous functions on $[-\tau,0]$. If $X$ is a real finite quadratic variation process, an appropriated It\^o formula is presented, from which we derive a generalized Clark-Ocone formula for non-semimartingales having the same quadratic variation as Brownian motion. The representation is based on solutions of an infinite dimensional PDE

From Query to Usable Code: An Analysis of Stack Overflow Code Snippets

Enriched by natural language texts, Stack Overflow code snippets are an invaluable code-centric knowledge base of small units of source code. Besides being useful for software developers, these annotated snippets can potentially serve as the basis for automated tools that provide working code solutions to specific natural language queries. With the goal of developing automated tools with the Stack Overflow snippets and surrounding text, this paper investigates the following questions: (1) How usable are the Stack Overflow code snippets? and (2) When using text search engines for matching on the natural language questions and answers around the snippets, what percentage of the top results contain usable code snippets? A total of 3M code snippets are analyzed across four languages: C\#, Java, JavaScript, and Python. Python and JavaScript proved to be the languages for which the most code snippets are usable. Conversely, Java and C\# proved to be the languages with the lowest usability rate. Further qualitative analysis on usable Python snippets shows the characteristics of the answers that solve the original question. Finally, we use Google search to investigate the alignment of usability and the natural language annotations around code snippets, and explore how to make snippets in Stack Overflow an adequate base for future automatic program generation.Comment: 13th IEEE/ACM International Conference on Mining Software Repositories, 11 page

Calculus via regularizations in Banach spaces and Kolmogorov-type path-dependent equations

The paper reminds the basic ideas of stochastic calculus via regularizations in Banach spaces and its applications to the study of strict solutions of Kolmogorov path dependent equations associated with "windows" of diffusion processes. One makes the link between the Banach space approach and the so called functional stochastic calculus. When no strict solutions are available one describes the notion of strong-viscosity solution which alternative (in infinite dimension) to the classical notion of viscosity solution.Comment: arXiv admin note: text overlap with arXiv:1401.503

The Emersion Effect: an analysis on labor tax evasion in Italy

We analyze how different policy interventions may incentive emersion from unde-clared work. We use Italian data over the period 1998-2003 to investigate whether the 2003 Italian labor market reform was able to reach the objective to reduce the share of shadow economy. We develop a search and matching model, á la Mortensen, on the basis of our empirical investigation to determine the right mix of policy interventions which maybe effective in generating an emersion effect. Our preliminary findings show that differentiated forms of taxations and enforcement might create a good combination of incentives to achieve a significant reduction in undeclared work

On stochastic calculus related to financial assets without semimartingales

This paper does not suppose a priori that the evolution of the price of a financial asset is a semimartingale. Since possible strategies of investors are self-financing, previous prices are forced to be finite quadratic variation processes. The non-arbitrage property is not excluded if the class $\mathcal{A}$ of admissible strategies is restricted. The classical notion of martingale is replaced with the notion of $\mathcal{A}$-martingale. A calculus related to $\mathcal{A}$-martingales with some examples is developed. Some applications to no-arbitrage, viability, hedging and the maximization of the utility of an insider are expanded. We finally revisit some no arbitrage conditions of Bender-Sottinen-Valkeila type

The “emersion” effect: an ex post and ex ante social program evaluation on labor tax evasion in Italy

We analyze how different policy interventions may incentive the transition of workers from the informal to the formal sector. We use Italian data over the period 1998-2008 to evaluate ex post whether the 2003 Italian labor market reform was able to reach the objective to reduce the share of shadow employment. Based on our empirical results, we develop an ex ante evaluation based on a search and matching model, á la Mortensen and Pissarides to determine the right combination of policy interventions which may be effective in generating a significant reduction in undeclared work together with an expansion of the formal sector. We find that in an economy where permanent and temporary contracts coexist, the combination of lower payroll taxes for permanent jobs and higher probability of being audited generates a compression of the informal sector, leaving unemployment unchanged. A similar result can be obtained through a reduction of the firing cost associated with permanent jobs, even though this causes temporary contracts to increase relatively more than permanent contracts

Dolphin Morbillivirus Associated with a Mass Stranding of Sperm Whales, Italy

In September 2014, 7 sperm whales stranded along the Adriatic Italian coastlines. Postmortem investigations on 3 dead females dead and in 1 fetus harbored by the largest one revealed molecular and immunoistochemical evidences of dolphin morbillivirus infection. A possible role of the virus in the stranding event was considered

Stack Overflow in Github: Any Snippets There?

When programmers look for how to achieve certain programming tasks, Stack Overflow is a popular destination in search engine results. Over the years, Stack Overflow has accumulated an impressive knowledge base of snippets of code that are amply documented. We are interested in studying how programmers use these snippets of code in their projects. Can we find Stack Overflow snippets in real projects? When snippets are used, is this copy literal or does it suffer adaptations? And are these adaptations specializations required by the idiosyncrasies of the target artifact, or are they motivated by specific requirements of the programmer? The large-scale study presented on this paper analyzes 909k non-fork Python projects hosted on Github, which contain 290M function definitions, and 1.9M Python snippets captured in Stack Overflow. Results are presented as quantitative analysis of block-level code cloning intra and inter Stack Overflow and GitHub, and as an analysis of programming behaviors through the qualitative analysis of our findings.Comment: 14th International Conference on Mining Software Repositories, 11 page