Orthogonal gamma-based expansions for volatility option prices under jump-diffusion dynamics

In my work I derive closed-form pricing formulas for volatility based options by suitably approximating the volatility process risk-neutral density function. I exploit and adapt the idea, which stands behind popular techniques already employed in the context of equity options such as Edgeworth and Gram-Charlier expansions, of approximating the underlying process as a sum of some particular polynomials weighted by a kernel, which is typically a Gaussian distribution. I propose instead a Gamma kernel to adapt the methodology to the context of volatility options. VIX vanilla options closed-form pricing formulas are derived and their accuracy is tested for the Heston model (1993) as well as for the jump-diffusion SVJJ model proposed by Duffie et al. (2000).

Anisotropic seismic tomography with the reversible jump Markov chain Monte Carlo

The established isotropic tomographic models show the features of subduction zones in terms of seismic velocity anomalies, but they are generally subjected to the generation of artifacts due to the lack of anisotropy in forward modelling. There is evidence for the significant influence of seismic anisotropy in the mid-upper mantle, especially for boundary layers like subducting slabs. As consequence, in isotropic models artifacts may be misinterpreted as compositional or thermal heterogeneities. In this thesis project the application of a trans-dimensional Metropolis-Hastings method is investigated in the context of anisotropic seismic tomography. This choice arises as a response to the important limitations introduced by traditional inversion methods which use iterative procedures of optimization of a function object of the inversion. On the basis of a first implementation of the Bayesian sampling algorithm, the code is tested with some cartesian two-dimensional models, and then extended to polar coordinates and dimensions typical of subduction zones, the main focus proposed for this method. Synthetic experiments with increasing complexity are realized to test the performance of the method and the precautions for multiple contexts, taking into account also the possibility to apply seismic ray-tracing iteratively. The code developed is tested mainly for 2D inversions, future extensions will allow the anisotropic inversion of seismological data to provide more realistic imaging of real subduction zones, less subjected to generation of artifacts.

A comprehensive study on robotic manipulation of deformable linear objects

There are many deformable objects such as papers, clothes, ropes in a person’s living space. To have a robot working in automating the daily tasks it is important that the robot works with these deformable objects. Manipulation of deformable objects is a challenging task for robots because these objects have an infinite-dimensional configuration space and are expensive to model, making real-time monitoring, planning and control difficult. It forms a particularly important field of robotics with relevant applications in different sectors such as medicine, food handling, manufacturing, and household chores. In this report, there is a clear review of the approaches used and are currently in use along with future developments to achieve this task. My research is more focused on the last 10 years, where I have systematically reviewed many articles to have a clear understanding of developments in this field. The main contribution is to show the whole landscape of this concept and provide a broad view of how it has evolved. I also explained my research methodology by following my analysis from the past to the present along with my thoughts for the future.

Monitoring of macro- and microlitter in the Venice lagoon and coastal area

Marine litter and plastics are a significant and growing marine contaminant that has become a global problem. Macrolitter is subject to fragmentation and degradation due to physical, chemical and biological processes, leading to the formation of micro-litter, the so-called microplastics. The purpose of this research is to assess marine litter pollution by using remote sensing tools to identify areas of macrolitter accumulation and to evaluate the concentrations of microplastics in different environmental matrices: water, sediment and biota (i.e. mussels and fish) and to contribute to the European project MAELSTROM (Smart technology for MArinE Litter SusTainable RemOval and Management). The aim is to monitor the presence of macro- and microlitter at two sites of the Venice coastal area: an abandoned mussel farm at sea and a lagoon site near the artificial Island of Sacca Fisola; The results showed that both study areas are characterised by high amounts of marine litter, but the type of observed litter is different. In fact, in the mussel farm area, most of the litter is linked to aquaculture activities (ropes, nets, mooring blocks and floating buoys). In the Venice lagoon site, the litter comes more from urban activities and from the city of Venice (car tyres, crates, wrecks, etc.). Microplastics is present in both sites and in all the analysed matrices. Generally, higher microplastics concentrations were found at Sacca Fisola (i.e., in surface waters, mussels and fish). Moreover, some differences were also observed in shapes and colours comparing the two sites. At Sacca Fisola, white irregular fragments predominate in water samples, blue filaments in sediment and mussels, and transparent irregular fragments in fish. At the Mussel Farm, blue filaments predominate in water, sediment and mussels, while flat black fragments predominate in fish. These differences are related to the different types of macrolitter that characterised the two areas.