Optical properties of the charge-density-wave polychalcogenide compounds R2R_2Te5_5 (RR=Nd, Sm and Gd)

We investigate the rare-earth polychalcogenide $R_2$Te$_5$ ($R$=Nd, Sm and Gd) charge-density-wave (CDW) compounds by optical methods. From the absorption spectrum we extract the excitation energy of the CDW gap and estimate the fraction of the Fermi surface which is gapped by the formation of the CDW condensate. In analogy to previous findings on the related $R$Te$_n$ (n=2 and 3) families, we establish the progressive closing of the CDW gap and the moderate enhancement of the metallic component upon chemically compressing the lattice

A numerical investigation of the sea breeze and slope flows around Rome

A three-dimensional non-hydrostatic prognostic mesoscale model is used to simulate the circulation around Rome, Italy, on a cloudless summer day with weak synoptic winds, with the aim of characterising the local circulation on such days. The simulation shows that the sea breeze and slope flows play roles of comparable importance. At night the circulation is dominated by katabatic flow. During the late morning/early afternoon there is a sea breeze with a front curving pincer-like around Rome, and well-developed anabatic flows on all slopes. In the late afternoon, sea breeze and slope flows coalesce into a single circulation reaching hundreds of kilometers inland, with an offshore return flow aloft. Comparison with observations is favourable, particularly during the day

Cross-Currency Heath-Jarrow-Morton Framework in the Multiple-Curve Setting

We provide a general HJM framework for forward contracts written on abstract market indices with arbitrary fixing and payment adjustments. We allow for indices on any asset class, featuring collateralization in arbitrary currency denominations. The framework is pivotal for describing portfolios of interest rate products which are denominated in multiple currencies. The benchmark transition has created significant discrepancies among the market conventions of different currency areas: our framework simultaneously covers forward-looking risky IBOR rates, such as EURIBOR, and backward-looking rates based on overnight rates, such as SOFR. In view of this, we provide a thorough study of cross-currency markets in the presence of collateral, where the cash flows of the contract and the margin account can be denominated in arbitrary combinations of currencies. We finally consider cross-currency swap contracts as an example of a contract simultaneously depending on all the risk factors that we describe within our framework

Deep Quadratic Hedging

We present a novel computational approach for quadratic hedging in a high-dimensional incomplete market. This covers both mean-variance hedging and local risk minimization. In the first case, the solution is linked to a system of BSDEs, one of which being a backward stochastic Riccati equation (BSRE); in the second case, the solution is related to the Foellmer-Schweizer decomposition and is also linked to a BSDE. We apply (recursively) a deep neural network-based BSDE solver. Thanks to these approach, we solve high-dimensional quadratic hedging problems, providing the entire hedging strategies paths, which, in alternative, would require to solve high dimensional PDEs. We test our approach with a classical Heston model and with a multi-dimensional generalization of it. Due to the unboundedness of the variance process, existence and uniqueness results for the BSRE must be considered

Correlators of Polynomial Processes

In the setting of polynomial jump-diffusion dynamics, we provide a formula for computing correlators, namely, cross-moments of the process at different time points along its path. The formula involves only linear combinations of the exponential of the so-called generator matrix, extending the well-known moment formula for polynomial processes. The developed framework allows to replace costly simulations with more accurate estimates, and it may be used for increasing the accuracy in financial pricing, such as for path-dependent options or in a stochastic volatility models context.Comment: 48 page

Deep Quadratic Hedging

We present a novel computational approach for quadratic hedging in a high-dimensional incomplete market. This covers both mean-variance hedging and local risk minimization. In the first case, the solution is linked to a system of BSDEs, one of which being a backward stochastic Riccati equation (BSRE); in the second case, the solution is related to the F\"olmer-Schweizer decomposition and is also linked to a BSDE. We apply (recursively) a deep neural network-based BSDE solver. Thanks to this approach, we solve high-dimensional quadratic hedging problems, providing the entire hedging strategies paths, which, in alternative, would require to solve high dimensional PDEs. We test our approach with a classical Heston model and with a multi-dimensional generalization of it.Comment: 43 page

The upper-tropospheric forcing during the 10th-12th December 2003 storm over Calabria

In this study we revisit an intense and destructive storm that occurred over Calabria, southern Italy, on 10th-12th December 2003. This event was already analyzed by two of the authors at synoptic and planetary scales, however in this work we investigate the mesoscale of the storm by the RAMS (Regional Atmospheric Modeling System) model. Firstly it is shown that large-scale moisture source was mainly from the Mediterranean basin, then RAMS simulations are discussed to focus on the mesoscale of the storm. More precisely we evaluate the roles of Calabrian orography and the surface latent heat fluxes by the factor separation technique. Results show that the role of Calabrian orography, even if important, decreased during the event whilst the role of surface latent heat fluxes was less affected through the entire event. A prominent mid tropospheric trough or cut-off low can be identified through this event prior and during the period of heavy rain. The upper-tropospheric level disturbance, associated with high potential vorticity (PV) values, consequence of a deep tropospheric intrusion of stratospheric air masses, coupled with the surface cyclone and reinforced the whole meteorological system which resulted in the heavy impact rainstorm over Calabria, mainly during 11th and 12th December 2003