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

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

Chemistry and light - part 2: light and energy

The conversion of solar energy into more useful forms of energy, such as chemical fuels or electricity, is one of the central problems facing modern science. Progress in photochemistry and chemical synthesis has led to a point where light energy conversion by means of artificial molecular devices can be rationally attempted. In this article, a general approach towards this challenging goal is presented

Robust and Pareto optimality of insurance contracts

The optimal insurance problem represents a fast growing topic that explains the most efficient contract that an insurance player may get. The classical problem investigates the ideal contract under the assumption that the underlying risk distribution is known, i.e. by ignoring the parameter and model risks. Taking these sources of risk into account, the decision-maker aims to identify a robust optimal contract that is not sensitive to the chosen risk distribution. We focus on Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR)-based decisions, but further extensions for other risk measures are easily possible. The Worst-case scenario and Worst-case regret robust models are discussed in this paper, which have been already used in robust optimisation literature related to the investment portfolio problem. Closed-form solutions are obtained for the VaR Worst-case scenario case, while Linear Programming (LP) formulations are provided for all other cases. A caveat of robust optimisation is that the optimal solution may not be unique, and therefore, it may not be economically acceptable, i.e. Pareto optimal. This issue is numerically addressed and simple numerical methods are found for constructing insurance contracts that are Pareto and robust optimal. Our numerical illustrations show weak evidence in favour of our robust solutions for VaR-decisions, while our robust methods are clearly preferred for CVaR-based decisions

Characterization and Construction of Sequentially Consistent Risk Measures

In dynamic risk measurement the problem emerges of assessing the risk of a financial position at different times. Sufficient conditions are provided for conditional coherent risk measures, in order that the requirements of acceptance, rejection and sequential consistency are satisfied. It is shown that these conditions are often violated for standard methods of updating. A method is consequently proposed for constructing a sequentially consistent risk measure, which entails the modification of the set of probability measures used to obtain the risk assessment at an initial time. This is demonstrated for the coherent entropic risk measure and for the class of Choquet risk measures, which generalizes the well-known TVaR. Finally we consider the situation where the term of risk exposures is longer than the time horizon used in solvency assessment. Then, regulation such as Solvency II requires replacing the financial position itself with its fair value at the time horizon. We show that in this setting acceptance consistency can be preserved, though the same is not true about rejection consistency

Efficient Anodically Grown WO3 for Photoelectrochemical Water Splitting

Abstract The potentiostatic anodization of metallic tungsten has been investigated in different solvent/electrolyte compositions with the aim of improving the photoelectrochemical performances of the tungsten oxide layer. Among the explored electrolytes, the anodization in the NMF/H2O/NH4F solvent mixture was found to produce the most efficient WO3 photoanodes, which, combining spectral sensitivity, high electrochemically active surface and improved charge transfer kinetics, outperform, under simulated solar illumination, most of the reported nanocrystalline substrates produced by anodization in aqueous electrolytes and by sol gel methods. While the preparation of the photoelectrodes is a slow process at room temperature (20 °C), it could be greatly accelerated (x 10) by carrying out the anodization at 40-50 °C, thus proving to be a fast and convenient approach to the production of high performing WO3 photoactive substrates directly connected to a metal electron collector

Conditional expectiles, time consistency and mixture convexity properties

We study conditional expectiles, defined as a natural generalisation of conditional expectations by means of the minimisation of an asymmetric quadratic loss function. We show that conditional expectiles can be equivalently characterised by a conditional first order condition and we derive their main properties. For possible applications as dynamic risk measures, we discuss their time consistency properties

Insurance valuation: A two-step generalised regression approach

Current approaches to fair valuation in insurance often follow a two-step approach, combining quadratic hedging with application of a risk measure on the residual liability, to obtain a cost-of-capital margin. In such approaches, the preferences represented by the regulatory risk measure are not reflected in the hedging process. We address this issue by an alternative two-step hedging procedure, based on generalised regression arguments, which leads to portfolios that are neutral with respect to a risk measure, such as Value-at-Risk or the expectile. First, a portfolio of traded assets aimed at replicating the liability is determined by local quadratic hedging. Second, the residual liability is hedged using an alternative objective function. The risk margin is then defined as the cost of the capital required to hedge the residual liability. In the case quantile regression is used in the second step, yearly solvency constraints are naturally satisfied; furthermore, the portfolio is a risk minimiser among all hedging portfolios that satisfy such constraints. We present a neural network algorithm for the valuation and hedging of insurance liabilities based on a backward iterations scheme. The algorithm is fairly general and easily applicable, as it only requires simulated paths of risk drivers

A new strategy against peri-implantitis: Antibacterial internal coating

The bacterial biofilm formation in the oral cavity and the microbial activity around the implant tissue represent a potential factor on the interface between bone and implant fixture that could induce an inflammatory phenomenon and generate an increased risk for mucositis and peri-implantitis. The aim of the present clinical trial was to investigate the bacterial quality of a new antibacterial coating of the internal chamber of the implant in vivo at six months. The PIXIT implant (Edierre srl, Genova Italy) is prepared by coating the implant with an alcoholic solution containing polysiloxane oligomers and chlorhexidine gluconate at 1%. A total of 15 healthy patients (60 implants) with non-contributory past medical history (nine women and six men, all non-smokers, mean age of 53 years, ranging from 45–61 years) were scheduled to receive bilateral fixed prostheses or crown restorations supported by an implant fixture. No adverse effects and no implant failure were reported at four months. All experimental sites showed a good soft tissue healing at the experimental point times and no local evidence of inflammation was observed. Real-Time Polymerase Chain Reaction (PCR) analysis on coated and uncoated implants showed a decrease of the bacterial count in the internal part of the implant chamber. The mean of total bacteria loading (TBL) detected in each PCR reaction was lower in treated implants (81,038 units/reaction) compared to untreated implants (90,057 units/reaction) (p < 0.01). The polymeric chlorhexydine coating of the internal chamber of the implant showed the ability to control the bacterial loading at the level of the peri-implant tissue. Moreover, the investigation demonstrated that the coating is able to influence also the quality of the microbiota, in particular on the species involved in the pathogenesis of peri-implantitis that are involved with a higher risk of long-term failure of the dental implant restoration