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Context. Stellar activity consists of different phenomena, mainly spots and faculae, and it is one of the main sources of noise in exoplanetary observations because it affects both spectroscopic and photometric observations. If we want to study young active planetary systems we need to model the activity of the host stars in order to remove astrophysical noise from our observational data. Aims. We modelled the contribution of stellar spots in photometric observations. Through the use of multiband photometry, we aim to extract the geometric properties of the spots and constrain their temperature. Methods. We analyzed multiband photometric observations acquired with the 80 cm Marcon telescope of the Osservatorio Polifunzionale del Chianti of V1298 Tau, assuming that the photometric modulation observed in different bands should be due to cold spots. Results. We constrained the effective temperature of the active regions present on the surface of V1298 Tau, which is composed by the contemporary presence of spots and faculae. We tested our hypothesis on solar data, verifying that we measure the size of the dominant active region and its averaged effective temperature.

Randomised signature has been proposed as a flexible and easily implementable alternative to the well-established path signature. In this article, we employ randomised signature to introduce a generative model for financial time series data in the spirit of reservoir computing. Specifically, we propose a novel Wasserstein-type distance based on discrete-time randomised signatures. This metric on the space of probability measures captures the distance between (conditional) distributions. Its use is justified by our novel universal approximation results for randomised signatures on the space of continuous functions taking the underlying path as an input. We then use our metric as the loss function in a non-adversarial generator model for synthetic time series data based on a reservoir neural stochastic differential equation. We compare the results of our model to benchmarks from the existing literature., Comment: 33 pages

The super-Earth LHS 1140 b is an interesting target for atmospheric observations since it is close to the habitable zone of its star and falls in the gap of the radius distribution of small exoplanets, in the region thought to correspond to the transition between planets with and without atmospheres. Observations of the primary transit with WFC3 on board of the Hubble Space Telescope (HST) revealed a modulation in the planet transmission spectrum compatible with the presence of water; however this modulation may be also due to stellar activity-related phenomena. Here we present a detailed analysis of the WFC3/HST observations to probe the nature of this modulation and to understand if it can be attributable to the presence of unocculted spots on the stellar surface. Our analysis strongly suggests that LHS1140 is a rather quiet star with subsolar [Fe/H] and enriched in alpha elements. Therefore, we rule out the possibility that the planetary spectrum is affected by the presence of spots and faculae. This analysis shows the importance of a proper modelling of the stellar spectrum when analyzing transit observations. Finally, we modelled the planetary atmosphere of LHS1140 b to retrieve its atmospheric composition. However, the low resolution and the narrow spectral range of HST observations prevented us from definitively determining whether the spectral features are attributable to the presence of water or of other molecules in the planetary atmosphere., Comment: 12 pages, 10 figures

In this paper we introduce a definition of a multi-dimensional fractional Brownian motion of Hurst index $H \in (0, 1)$ under volatility uncertainty (in short G-fBm). We study the properties of such a process and provide first results about stochastic calculus with respect to a fractional G-Brownian motion for a Hurst index $H >\frac{1}{2}$ ., Comment: 33 pages

We derive quantitative error bounds for deep neural networks (DNNs) approximating option prices on a $d$-dimensional risky asset as functions of the underlying model parameters, payoff parameters and initial conditions. We cover a general class of stochastic volatility models of Markovian nature as well as the rough Bergomi model. In particular, under suitable assumptions we show that option prices can be learned by DNNs up to an arbitrary small error $\varepsilon \in (0,1/2)$ while the network size grows only sub-polynomially in the asset vector dimension $d$ and the reciprocal $\varepsilon^{-1}$ of the accuracy. Hence, the approximation does not suffer from the curse of dimensionality. As quantitative approximation results for DNNs applicable in our setting are formulated for functions on compact domains, we first consider the case of the asset price restricted to a compact set, then we extend these results to the general case by using convergence arguments for the option prices., Comment: 43 pages

V1298 Tau hosts at least four planets. Since its discovery, this system has been a target of intensive photometric and spectroscopic monitoring. The characterisation of its architecture and planets' fundamental properties turned out to be very challenging so far. The determination of the orbital ephemeris of the outermost planet V1298 Tau $e$ remains an open question. Only two transits have been detected so far by $Kepler/K2$ and TESS, allowing for a grid of reference periods to be tested with new observations, without excluding the possibility of transit timing variations. Observing a third transit would allow to better constrain the orbital period, and would also help determining an accurate radius of V1298 Tau $e$ because the former transits showed different depths. We observed V1298 Tau with the CHEOPS space telescope to search for a third transit of planet $e$ within observing windows that have been selected in order to test three of the shortest predicted orbital periods. We also collected ground-based observations to verify the result found with CHEOPS. We reanalysed $Kepler/K2$ and TESS light curves to test how the results derived from these data are affected by alternative photometric extraction and detrending methods. We report the detection with CHEOPS of a transit that could be attributed to V1298 Tau $e$. If so, that result implies that the orbital period calculated from fitting a linear ephemeris to the three available transits is close to $\sim45$ days. Results from the ground-based follow-up marginally support this possibility. We found that $\textit{i}$) the transit observed by CHEOPS has a longer duration compared to that of the transits observed by $Kepler/K2$ and TESS; $\textit{ii}$) the transit observed by TESS is $>30\%$ deeper than that of $Kepler/K2$ and CHEOPS, and deeper than the measurement previously reported in the literature, according to our reanalysis., Comment: Accepted for publication on A&A. The abstract has been edited to fulfill the arXiv requirements

We introduce the notions of Collective Arbitrage and of Collective Super-replication in a discrete-time setting where agents are investing in their markets and are allowed to cooperate through exchanges. We accordingly establish versions of the fundamental theorem of asset pricing and of the pricing-hedging duality. A reduction of the price interval of the contingent claims can be obtained by applying the collective super-replication price.

The chromatic contamination that arises from photospheric heterogeneities e.g. spots and faculae on the host star presents a significant noise source for exoplanet transmission spectra. If this contamination is not corrected for, it can introduce substantial bias in our analysis of the planetary atmosphere. We utilise two stellar models of differing complexity, StARPA and ASteRA, to explore the biases introduced by stellar contamination in retrieval under differing degrees of stellar activity. We use the retrieval framework TauREx3 and a grid of 27 synthetic, spot-contaminated transmission spectra to investigate potential biases and to determine how complex our stellar models must be in order to accurately extract the planetary parameters from transmission spectra. The input observation is generated using the more complex model (StARPA), in which the spot latitude is an additional, fixable parameter. This observation is then fed into a combined stellar-planetary retrieval which contains a simplified stellar model (ASteRA). Our results confirm that the inclusion of stellar activity parameters in retrieval minimises bias under all activity regimes considered. ASteRA performs very well under low to moderate activity conditions, retrieving the planetary parameters with a high degree of accuracy. For the most active cases, characterised by larger, higher temperature contrast spots, some minor residual bias remains due to ASteRA neglecting the interplay between the spot and the limb darkening effect. As a result of this, we find larger errors in retrieved planetary parameters for central spots (0 degrees) and those found close to the limb (60 degrees) than those at intermediate latitudes (30 degrees)., Comment: 34 pages, 20 figures, accepted for publication in ApJ

Total factor productivity (TFP) is a key determinant of farm development, a sector that receives substantial public support. The issue has taken on great importance today, where the conflict in Ukraine has led to repercussions on the cereal markets. This paper investigates the effects of different subsidies on the productivity of cereal farms, accounting that farms differ according to the level of TFP. We relied on a three-step estimation strategy: i) estimation of production functions, ii) evaluation of TFP, and iii) assessment of the relationship between CAP subsidies and TFP. To overcome multiple endogeneity problems, the System-GMM estimator is adopted. The investigation embraces farms in France, Germany, Italy, Poland, Spain and the United Kingdom using the FADN samples from 2008 to 2018. Adding to previous analyses, we compare results from different countries and investigate three subsets of farms with varying levels of TFP. The outcomes confirm how CAP negatively impacts farm TFP, but the extent differs according to the type of subsidies, the six countries and, within these, among farms with different productivity groups. Therefore there is room for policy improvements in order to foster the productivity of cereal farms., Comment: Working Paper May 2022

This paper evaluates Machine Learning (ML) in establishing ratemaking for new insurance schemes. To make the evaluation feasible, we established expected indemnities as premiums. Then, we use ML to forecast indemnities using a minimum set of variables. The analysis simulates the introduction of an income insurance scheme, the so-called Income Stabilization Tool (IST), in Italy as a case study using farm-level data from the FADN from 2008-2018. We predicted the expected IST indemnities using three ML tools, LASSO, Elastic Net, and Boosting, that perform variable selection, comparing with the Generalized Linear Model (baseline) usually adopted in insurance investigations. Furthermore, Tweedie distribution is implemented to consider the peculiarity shape of the indemnities function, characterized by zero-inflated, no-negative value, and asymmetric fat-tail. The robustness of the results was evaluated by comparing the econometric and economic performance of the models. Specifically, ML has obtained the best goodness-of-fit than baseline, using a small and stable selection of regressors and significantly reducing the gathering cost of information. However, Boosting enabled it to obtain the best economic performance, balancing the most and most minor risky subjects optimally and achieving good economic sustainability. These findings suggest how machine learning can be successfully applied in agricultural insurance.This study represents one of the first to use ML and Tweedie distribution in agricultural insurance, demonstrating its potential to overcome multiple issues.

Identifying factors that affect participation is key to a successful insurance scheme. This study's challenges involve using many factors that could affect insurance participation to make a better forecast.Huge numbers of factors affect participation, making evaluation difficult. These interrelated factors can mask the influence on adhesion predictions, making them misleading.This study evaluated how 66 common characteristics affect insurance participation choices. We relied on individual farm data from FADN from 2016 to 2019 with type 1 (Fieldcrops) farming with 10,926 observations.We use three Machine Learning (ML) approaches (LASSO, Boosting, Random Forest) compare them to the GLM model used in insurance modelling. ML methodologies can use a large set of information efficiently by performing the variable selection. A highly accurate parsimonious model helps us understand the factors affecting insurance participation and design better products.ML predicts fairly well despite the complexity of insurance participation problem. Our results suggest Boosting performs better than the other two ML tools using a smaller set of regressors. The proposed ML tools identify which variables explain participation choice. This information includes the number of cases in which single variables are selected and their relative importance in affecting participation.Focusing on the subset of information that best explains insurance participation could reduce the cost of designing insurance schemes.

In this paper we study the evolution of asset price bubbles driven by contagion effects spreading among investors via a random matching mechanism in a discrete-time version of the liquidity based model of [25]. To this scope, we extend the Markov conditionally independent dynamic directed random matching of [13] to a stochastic setting to include stochastic exogenous factors in the model. We derive conditions guaranteeing that the financial market model is arbitrage-free and present some numerical simulation illustrating our approach., Comment: 37 pages, 3 figures

In this paper we employ deep learning techniques to detect financial asset bubbles by using observed call option prices. The proposed algorithm is widely applicable and model-independent. We test the accuracy of our methodology in numerical experiments within a wide range of models and apply it to market data of tech stocks in order to assess if asset price bubbles are present. Under a given condition on the pricing of call options under asset price bubbles, we are able to provide a theoretical foundation of our approach for positive and continuous stochastic asset price processes. When such a condition is not satisfied, we focus on local volatility models. To this purpose, we give a new necessary and sufficient condition for a process with time-dependent local volatility function to be a strict local martingale., Comment: 31 pages, 3 figures

The ExoClock project has been created with the aim of increasing the efficiency of the Ariel mission. It will achieve this by continuously monitoring and updating the ephemerides of Ariel candidates over an extended period, in order to produce a consistent catalogue of reliable and precise ephemerides. This work presents a homogenous catalogue of updated ephemerides for 450 planets, generated by the integration of $\sim$18000 data points from multiple sources. These sources include observations from ground-based telescopes (ExoClock network and ETD), mid-time values from the literature and light-curves from space telescopes (Kepler/K2 and TESS). With all the above, we manage to collect observations for half of the post-discovery years (median), with data that have a median uncertainty less than one minute. In comparison with literature, the ephemerides generated by the project are more precise and less biased. More than 40\% of the initial literature ephemerides had to be updated to reach the goals of the project, as they were either of low precision or drifting. Moreover, the integrated approach of the project enables both the monitoring of the majority of the Ariel candidates (95\%), and also the identification of missing data. The dedicated ExoClock network effectively supports this task by contributing additional observations when a gap in the data is identified. These results highlight the need for continuous monitoring to increase the observing coverage of the candidate planets. Finally, the extended observing coverage of planets allows us to detect trends (TTVs - Transit Timing Variations) for a sample of 19 planets. All products, data, and codes used in this work are open and accessible to the wider scientific community., Comment: Recommended for publication to ApJS (reviewer's comments implemented). Main body: 13 pages, total: 77 pages, 7 figures, 7 tables. Data available at http://doi.org/10.17605/OSF.IO/P298N

We study representations of a random variable $\xi$ as an integral of an adapted process with respect to the Lebesgue measure. The existence of such representations in two different regularity classes is characterized in terms of the quadratic variation of (local) martingales closed by $\xi$.

We discuss the goals, the designs, the state of technical readiness, and the critical R&D needs of the accelerators that are currently under discussion as Higgs and electroweak factories. We also address the respective staging options enabling future energy-frontier colliders. The accelerators covered are based on many different techniques and approaches. They include several circular colliders, various linear colliders, colliders based on energy recovery linacs (ERLs), ERL-ring combinations, as well as gamma-gamma colliders. The linear colliders proposed consist of options for the International Linear Collider (ILC), for the Compact Linear Collider (CLIC), for the Cold Copper Collider (C^3), and for the more recent Higgs-Energy Lepton Collider (HELEN). ERLs are key components of the Recycling Linear e+e- Collider (ReLiC), of the Energy Recovery Linear Collider (ERLC), and of the Circular Energy Recovery Collider (CERC). Among the more conventional ring colliders, the following proposals are featured: the Future Circular Collider (FCC-ee), the Circular Electron Positron Collider (CEPC), the Electron Positron Circular Collider at Fermilab (EPCCF), and the Large Electron Positron collider $\#$3 (LEP-3). In addition, we consider the X-ray FEL based gamma-gamma Collider Higgs Factory (XCC) and the High-Energy High-Luminosity gamma-gamma collider (HE&HL gamma-gamma). Finally, a Higgs factory based on a circular muon collider is mentioned for completeness., Comment: Submitted to Snowmass 2021

A multi-TeV muon collider offers a spectacular opportunity in the direct exploration of the energy frontier. Offering a combination of unprecedented energy collisions in a comparatively clean leptonic environment, a high energy muon collider has the unique potential to provide both precision measurements and the highest energy reach in one machine that cannot be paralleled by any currently available technology. The topic generated a lot of excitement in Snowmass meetings and continues to attract a large number of supporters, including many from the early career community. In light of this very strong interest within the US particle physics community, Snowmass Energy, Theory and Accelerator Frontiers created a cross-frontier Muon Collider Forum in November of 2020. The Forum has been meeting on a monthly basis and organized several topical workshops dedicated to physics, accelerator technology, and detector R&D. Findings of the Forum are summarized in this report.

We present a probabilistic construction of $\mathbb{R}^d$-valued non-linear affine processes with jumps. Given a set $\Theta$ of affine parameters, we define a family of sublinear expectations on the Skorokhod space under which the canonical process $X$ is a (sublinear) Markov process with a non-linear generator. This yields a tractable model for Knightian uncertainty for which the sublinear expectation of a Markovian functional can be calculated via a partial integro-differential equation., Comment: 31 pages

The ExoClock project is an inclusive, integrated, and interactive platform that was developed to monitor the ephemerides of the Ariel targets to increase the mission efficiency. The project makes the best use of all available resources, i.e., observations from ground telescopes, mid-time values from the literature and finally, observations from space instruments. Currently, the ExoClock network includes 280 participants with telescopes capable of observing 85\% of the currently known Ariel candidate targets. This work includes the results of $\sim$1600 observations obtained up to the 31st of December 2020 from the ExoClock network. These data in combination with $\sim$2350 mid-time values collected from the literature are used to update the ephemerides of 180 planets. The analysis shows that 40\% of the updated ephemerides will have an impact on future scheduling as either they have a significantly improved precision, or they have revealed biases in the old ephemerides. With the new observations, the observing coverage and rate for half of the planets in the sample has been doubled or more. Finally, from a population perspective, we identify that the differences in the 2028 predictions between the old and the new ephemerides have an STD that is double what is expected from gaussian uncertainties. These findings have implications for planning future observations, where we will need to account for drifts potentially greater than the prediction uncertainties. The updated ephemerides are open and accessible to the wider exoplanet community both from our Open Science Framework (OSF) repository and our website., Comment: 9 pages (47 with appendices and references), 8 figures, 2 tables. Submitted to ApJS. Revised based on the reviewer's comments

In this paper we introduce a sublinear conditional operator with respect to a family of possibly nondominated probability measures in presence of multiple ordered default times. In this way we generalize the results of [5], where a reduced-form framework under model uncertainty for a single default time is developed. Moreover, we use this operator for the valuation of credit portfolio derivatives under model uncertainty., Comment: 36 pages

This article examines neural network-based approximations for the superhedging price process of a contingent claim in a discrete time market model. First we prove that the $\alpha$-quantile hedging price converges to the superhedging price at time $0$ for $\alpha$ tending to $1$, and show that the $\alpha$-quantile hedging price can be approximated by a neural network-based price. This provides a neural network-based approximation for the superhedging price at time $0$ and also the superhedging strategy up to maturity. To obtain the superhedging price process for $t>0$, by using the Doob decomposition it is sufficient to determine the process of consumption. We show that it can be approximated by the essential supremum over a set of neural networks. Finally, we present numerical results.

We extend the super-replication theorems of [27] in a dynamic setting, both in the num\'eraire-based as well as in the num\'eraire-free setting. For this purpose, we generalize the notion of admissible strategies. In particular, we obtain a well-defined super-replication price process, which is right-continuous under some regularity assumptions.

Since its inception, the E.U.'s Common Agricultural Policy (CAP) aimed at ensuring an adequate and stable farm income. While recognizing that the CAP pursues a larger set of objectives, this thesis focuses on the impact of the CAP on the level and the stability of farm income in Italian farms. It uses microdata from a high standardized dataset, the Farm Accountancy Data Network (FADN), that is available in all E.U. countries. This allows if perceived as useful, to replicate the analyses to other countries. The thesis first assesses the Income Transfer Efficiency (i.e., how much of the support translate to farm income) of several CAP measures. Secondly, it analyses the role of a specific and relatively new CAP measure (i.e., the Income Stabilisation Tool - IST) that is specifically aimed at stabilising farm income. The assessment of the potential use of Machine Learning procedures to develop an adequate ratemaking in IST. These are used to predict indemnity levels because this is an essential point for a similar insurance scheme. The assessment of ratemaking is challenging: indemnity distribution is zero-inflated, not-continuous, right-skewed, and several factors can potentially explain it. We address these problems by using Tweedie distributions and three Machine Learning procedures. The objective is to assess whether this improves the ratemaking by using the prospective application of the Income Stabilization Tool in Italy as a case study. We look at the econometric performance of the models and the impact of using their predictions in practice. Some of these procedures efficiently predict indemnities, using a limited number of regressors, and ensuring the scheme's financial stability., Comment: 127 page

We present a robust version of the life-cycle optimal portfolio choice problem in the presence of labor income, as introduced in Biffis, Gozzi and Prosdocimi ("Optimal portfolio choice with path dependent labor income: the infinite horizon case", SIAM Journal on Control and Optimization, 58(4), 1906-1938.) and Dybvig and Liu ("Lifetime consumption and investment: retirement and constrained borrowing", Journal of Economic Theory, 145, pp. 885-907). In particular, in Biffis, Gozzi and Prosdocimi the influence of past wages on the future ones is modelled linearly in the evolution equation of labor income, through a given weight function. The optimisation relies on the resolution of an infinite dimensional HJB equation. We improve the state of art in three ways. First, we allow the weight to be a Radon measure. This accommodates for more realistic weighting of the sticky wages, like, e.g., on a discrete temporal grid according to some periodic income. Second, there is a general correlation structure between labor income and stocks market. This naturally affects the optimal hedging demand, which may increase or decrease according to the correlation sign. Third, we allow the weight to change with time, possibly lacking perfect identification. The uncertainty is specified by a given set of Radon measures $K$, in which the weight process takes values. This renders the inevitable uncertainty on how the past affects the future, and includes the standard case of error bounds on a specific estimate for the weight. Under uncertainty averse preferences, the decision maker takes a maxmin approach to the problem. Our analysis confirms the intuition: in the infinite dimensional setting, the optimal policy remains the best investment strategy under the worst case weight.

We consider the problem of reducing the carbon emissions of a set of firms over a finite horizon. A regulator dynamically allocates emission allowances to each firm. Firms face idiosyncratic as well as common economic shocks on emissions, and have linear quadratic abatement costs. Firms can trade allowances so to minimise total expected costs, from abatement and trading plus a quadratic terminal penalty. Using variational methods, we exhibit in closed-form the market equilibrium in function of regulator's dynamic allocation. We then solve the Stackelberg game between the regulator and the firms. Again, we obtain a closed-form expression of the dynamic allocation policies that allow a desired expected emission reduction. Optimal policies are not unique but share common properties. Surprisingly, all optimal policies induce a constant abatement effort and a constant price of allowances. Dynamic allocations outperform static ones because of adjustment costs and uncertainty, in particular given the presence of common shocks. Our results are robust to some extensions, like risk aversion of firms or different penalty functions.

We study an agent's lifecycle portfolio choice problem with stochastic labor income, borrowing constraints and a finite retirement date. Similarly to arXiv:2002.00201, wages evolve in a path-dependent way, but the presence of a finite retirement time leads to a novel, two-stage infinite dimensional stochastic optimal control problem with explicit optimal controls in feedback form. This is possible as we find an explicit solution to the associated Hamilton-Jacobi-Bellman (HJB) equation, which is an infinite dimensional PDE of parabolic type. The identification of the optimal feedbacks is delicate due to the presence of time-dependent state constraints, which appear to be new in the infinite dimensional stochastic control literature. The explicit solution allows us to study the properties of optimal strategies and discuss their implications for portfolio choice. As opposed to models with Markovian dynamics, path dependency can now modulate the hedging demand arising from the implicit holding of risky assets in human capital, leading to richer asset allocation predictions consistent with wage rigidity and the agents learning about their earning potential.

In this paper we provide a generalization of a Feynmac-Kac formula under volatility uncertainty in presence of a linear term in the PDE due to discounting. We state our result under different hypothesis with respect to the derivation given by Hu, Ji, Peng and Song (Comparison theorem, Feynman-Kac formula and Girsanov transformation for BSDEs driven by G-Brownian motion, Stochastic Processes and their Application, 124 (2)), where the Lipschitz continuity of some functionals is assumed which is not necessarily satisfied in our setting. In particular, we show that the $G$-conditional expectation of a discounted payoff is a viscosity solution of a nonlinear PDE. In applications, this permits to calculate such a sublinear expectation in a computationally efficient way., Comment: 35 pages, 3 figures

We assess the correlation between CAP support provided to farmers and their income and use of capital and labour in the first year of the new CAP regime. This is done applying three regression models on the Italian FADN farms controlling for other farm characteristics. CAP annual payments are positively correlated with farm income and capital but are negatively correlated with labour use. Farm investment support provided by RDP measures is positively correlated to the amount of capital. Results suggest that CAP is positively affecting farm income directly but also indirectly by supporting the substitution of labour with capital, Comment: New paper available

In this paper we extend the reduced-form setting under model uncertainty introduced in [5] to include intensities following an affine process under parameter uncertainty, as defined in [15]. This framework allows to introduce a longevity bond under model uncertainty in a consistent way with the classical case under one prior, and to compute its valuation numerically. Moreover, we are able to price a contingent claim with the sublinear conditional operator such that the extended market is still arbitrage-free in the sense of "No Arbitrage of the first kind" as in [6]., Comment: 27 pages

Motivation for this paper is to understand the impact of information on asset price bubbles and perceived arbitrage opportunities. This boils down to study optional projections of $\mathbb{G}$-adapted strict local martingales into a smaller filtration $\mathbb{F}$ under equivalent martingale measures. We give some general results as well as analyze in details two specific examples given by the inverse three dimensional Bessel process and a class of stochastic volatility models., Comment: 30 pages, no figures, no tables