On the Lp-quantiles for the Student t distribution

L_p-quantiles represent an important class of generalised quantiles and are defined as the minimisers of an expected asymmetric power function, see Chen (1996). For p=1 and p=2 they correspond respectively to the quantiles and the expectiles. In his paper Koenker (1993) showed that the tau quantile and the tau expectile coincide for every tau in (0,1) for a class of rescaled Student t distributions with two degrees of freedom. Here, we extend this result proving that for the Student t distribution with p degrees of freedom, the tau quantile and the tau L_p-quantile coincide for every tau in (0,1) and the same holds for any affine transformation. Furthermore, we investigate the properties of L_p-quantiles and provide recursive equations for the truncated moments of the Student t distribution

Large deviations for risk measures in finite mixture models

Due to their heterogeneity, insurance risks can be properly described as a mixture of different fixed models, where the weights assigned to each model may be estimated empirically from a sample of available data. If a risk measure is evaluated on the estimated mixture instead of the (unknown) true one, then it is important to investigate the committed error. In this paper we study the asymptotic behaviour of estimated risk measures, as the data sample size tends to infinity, in the fashion of large deviations. We obtain large deviation results by applying the contraction principle, and the rate functions are given by a suitable variational formula; explicit expressions are available for mixtures of two models. Finally, our results are applied to the most common risk measures, namely the quantiles, the Expected Shortfall and the shortfall risk measures

Model uncertainty in risk capital measurement

The required solvency capital for a financial portfolio is typically given by a tail risk measure such as Value-at-Risk. Estimating the value of that risk measure from a limited, often small, sample of data gives rise to potential errors in the selection of the statistical model and the estimation of its parameters. We propose to quantify the effectiveness of a capital estimation procedure via the notions of residual estimation risk and estimated capital risk. It is shown that for capital estimation procedures that do not require the specification of a model (eg historical simulation) or for worst-case scenario procedures the impact of model uncertainty is substantial, while capital estimation procedures that allow for multiple candidate models using Bayesian methods, partially eliminate model error. In the same setting, we propose a way of quantifying model error that allows to disentangle the impact of model uncertainty from that of parameter uncertainty. We illustrate these ideas by simulation examples considering standard loss and return distributions used in banking and insuranc

Contributions to solvency risk measurement

The thesis focuses on risk measures used to calculate solvency capital requirements. It consists of three independent papers. The first paper (Chapter 2) investigates time-consistency, the relation that should hold across risk measurements of the same financial position at different time points. Sufficient conditions are provided for coherent risk measures, in order to satisfy the requirements of acceptance-, rejection- and sequential consistency. It is shown that risk measures used in practice usually do not satisfy these requirements. Hence a method is provided to systematically construct sequentially consistent risk measures. It is also emphasized that current approaches to dynamic risk measurement do not consider that risk measures at different time points have different arguments. Here we briefly discuss this new setting highlighting that the notions of time consistency presented in the literature need to be reinterpreted. The second and third papers (Chapters 3 and 4) consider respectively the risk arising from parameter and model mis-specification due to estimation from a limited amount of available data. This risk may have a substantial impact on risk measures used to quantify solvency capital requirements. We introduce a new method to quantify this impact measured as the additional capital needed to allow for randomness in the data sample used for the estimation procedure. This level of capital we call residual estimation risk. In the second paper, for parameter uncertainty we prove the effectiveness of three approaches for reducing residual estimation risk in the case of location-scale families. These are based on (a) raising the capital requirement by adjusting the risk measure, (b) Bayesian predictive distributions under probability-matching priors and (c) residual risk estimation via parametric bootstrap. Risk measures satisfying standard properties are used, for example the popular TVaR. For more general distributions only (a) and (b) are investigated and a truncated version of TVaR is used. Numerical results obtained via Monte-Carlo simulation demonstrate that the proposed methods perform well. In the third paper (Chapter 4), we compare the effectiveness of four different approaches to estimate capital requirements in the presence of model uncertainty. For a given set of candidate models the model posterior weights can be obtained via a Bayesian approach. Then we consider approaches based on: (a) worst case scenario, (b) highest model posterior, (c) averaging the capital under each model according to the model posterior weights and (d) determining the predictive distribution of the financial loss and using it to calculate the capital. It is shown that all these methods are very sensitive to the set of candidate models specified. If this has been carefully selected (for instance via expert judgement) the approach based on the highest posterior performs slightly better than the others. Alternatively, if there is poor prior information on the model set the effectiveness of all these approaches decreases substantially. In particular, the worst case approach has a very low performance. It also emerges that mis-specifiying the model by using distributions that are more heavy-tailed than the one generating the data, may reduce the capital and thus it is not a conservative approach

Sustainable Cements for Green Buildings Construction

The large amount of waste yearly disposed to landfill, the global impoverishing of natural resources and environment, the emergency of carbon dioxide emissions, are some of the motivations driving research institutes and industrial world to move towards sustainable solutions for civil engineering field. Accordingly, the use of sustainable materials for green buildings construction is an important goal that must be reached in short times. Sustainable cements can be designed by partially replacing clinker content with non hazardous waste. Indeed, recycling process can transform waste in secondary raw materials that work as new cement constituents usually leading to sustainable binders with peculiar environmental resistances. Details of cement manufacturing process and its effect on the environmental pollution as well as the route that can be carried out to tailor sustainable cements are reported and discussed

Parameter uncertainty and residual estimation risk

The notion of residual estimation risk is introduced to quantify the impact of parameter uncertainty on capital adequacy, for a given risk measure and capital estimation procedure. Residual risk equals the risk measure applied to the difference between a random loss and the corresponding capital estimator. Modified estimation procedures are proposed, based on parametric bootstrapping and predictive distributions, which compensate the impact of parameter uncertainty and lead to higher capital requirements. In the particular case of location-scale families, the analysis simplifies and a capital estimator can always be found that leads to a residual risk of exactly zer

How Superadditive Can a Risk Measure Be?

In this paper, we study the extent to which any risk measure can lead to superadditive risk assessments, implying the potential for penalizing portfolio diversification. For this purpose we introduce the notion of extreme-aggregation risk measures. The extreme-aggregation measure characterizes the most superadditive behavior of a risk measure, by yielding the worst-possible diversification ratio across dependence structures. One of the main contributions is demonstrating that, for a wide range of risk measures, the extreme-aggregation measure corresponds to the smallest dominating coherent risk measure. In our main result, it is shown that the extremeaggregation measure induced by a distortion risk measure is a coherent distortion risk measure. In the case of convex risk measures, a general robust representation of coherent extreme-aggregation measures is provided. In particular, the extreme-aggregation measure induced by a convex shortfall risk measure is a coherent expectile. These results show that, in the presence of dependence uncertainty, quantification of a coherent risk measure is often necessary, an observation that lends further support to the use of coherent risk measures in portfolio risk management

Novel fiber-reinforced composite materials based on sustainable geopolymer matrix

Geopolymers are representing the most promising green and eco-friendly alternative to ordinary Portland cement and cementitious materials, thanks to their proven durability, mechanical and thermal properties. However, despite these features, the poor tensile and bending strengths usually exhibited by geopolymers due to their brittle and ceramic-like nature, can easily lead to catastrophic failure and represent the main drawback limiting the use of those materials in several applications. Fiber reinforced geopolymer composites may be considered a solution to improve flexural strength and fracture toughness. Different types of dispersed short fibers are here investigated as a reinforcing fraction for a geopolymer matrix based on an alkali-activated ladle-slag. It has been demonstrated that both organic and inorganic fibers can lead to a significant flexural strength enhancement. Moreover, the investigated geopolymers exhibit an increase in toughness, thus determining a switch from a brittle failure mode to a more ductile one

Durability of lightweight geopolymers for passive fire protection: steel corrosion behavior in chloride-rich environment

Different technologies are currently developed as promising passive fire protective coatings, due to the fact that fire protection of steel structures is an important requirement for structural components for several civil and industrial applications. Among the others, geopolymers have attracted lot of attention as promising materials suitable for high temperature applications. An optimized mix-design makes their amorphous structure more stable, when exposed to direct fire or heating from high temperatures, compared to ordinary Portland cement-based materials (OPC). However, the durability of a fire protective coating strongly depends on its adhesion on steel and its ability to prevent and/or mitigate steel corrosion phenomena. For these reasons, the understanding of the corrosion behavior of steel coated with geopolymer-based fireproofing coatings is necessary for ensuring the service life of the structure. This study aims at characterizing the corrosion behavior of carbon steel coated by different geopolymeric mortars applied as passive fire protection systems. In particular, fly ash-based geopolymeric mortars were applied as coatings on carbon steel plates. They were lightened by the combination of lightweight aggregates, e.g. expanded perlite, and chemical foaming agents, such as hydrogen peroxide (H2O2), in order to ensure good properties at high temperatures. In addition, geopolymeric paste and mortar containing quartz aggregate were also prepared as reference samples. The corrosion process was evaluated using an electrochemical approach. The samples have been tested by accelerated ageing methods, such as exposure to salt spray chamber to simulate a chloride-rich environment, such as marine aerosol. The monitoring process has been done applying non-destructive techniques and it is still ongoing. In particular, open circuit potential (OCP) and linear polarization resistance (LPR) have been recorded during the exposure. In parallel, polarization curves have also been carried out at different stages of the ageing exposure to better characterize the corrosion condition of the steel substrates. In addition, adhesion between the different geopolymeric coatings and the carbon steel plates has been evaluated before and after the artificial ageing in the salt spray chamber. Finally, density and porosity measurements were also carried out to better characterize the physical properties of the geopolymers. In this contribute, preliminary results are reported about short-term exposure. They show that in absence of any aggressive species, fly ash-based geopolymeric mortars provide a highly alkaline environment in the early curing time, enabling the passivation of carbon steel. Finally, steel corrosion behavior has been analyzed as a function of the pore structure of the geopolymeric matrix

Fly ash-based one-part alkali activated mortars cured at room temperature: Effect of precursor pre-treatments

One-part or “just add water” alkali activated materials (AAMs) have attracted a lot of attention thanks to the use of solid alkaline activators that makes these materials more suitable to commercialization compared to conventional AAMs (two-part). This is mainly because large quantities of caustic solutions should be handled for producing conventional AAMs. So, one-part AAMs have a great potential for in-situ applications. However, heat curing (<100 ◦C) has been demonstrated to be the best condition to obtain optimized performances of one-part AAMs. This study investigates how to obtain high strength one-part alkali mortars cured at room temperature, considering a newly developed mix design, precursor pre-treatments and curing time. The mechanical performances (i.e., elasticity modulus, compressive and flexural strength) of the developed materials were reported, as well as physical properties, in terms of water absorption, open porosity and pore size distribution and microstructure (by means of FEG-SEM observations coupled with elemental analysis by EDS and FT-IR measurements). Class F fly ash have been activated by potassium hydroxide (KOH) and anhydrous sodium metasilicate. It was found that high strength one-part AAMs can be achieved by activating coal fly ash with a mix of KOH and anhydrous sodium metasilicate at room temperature. In particular, room temperature-cured one-part mortars obtained by pre-treated fly ash exhibited mechanical performance similar to those obtained by heat-cured mortars (at 70 ◦C, tested after 7 days), reaching a compressive strength (Rc) greater than 60 MPa at 28 days of curing when mechanochemical activation of fly ash was applied