Related papers: Capital allocation and tail central moments for th…
We show how to reduce the problem of computing VaR and CVaR with Student T return distributions to evaluation of analytical functions of the moments. This allows an analysis of the risk properties of systems to be carefully attributed…
Using the framework of factor models, we establish the general expression of the coefficient of tail dependence between the market and a stock (i.e., the probability that the stock incurs a large loss, assuming that the market has also…
The Capital Asset Pricing Model (CAPM) relates a well-diversified stock portfolio to a benchmark portfolio. We insert size effect in CAPM, capturing the observation that small stocks have higher risk and return than large stocks, on…
A novel forecast combination and weighted quantile based tail-risk forecasting framework is proposed, aiming to reduce the impact of modelling uncertainty in tail-risk forecasting. The proposed approach is based on a two-step estimation…
Conditional Value-at-Risk (CVaR) is a widely used risk metric in applications such as finance. We derive concentration bounds for CVaR estimates, considering separately the cases of light-tailed and heavy-tailed distributions. In the…
In this paper we propose a problem-driven scenario generation approach to the single-period portfolio selection problem which use tail risk measures such as conditional value-at-risk. Tail risk measures are useful for quantifying potential…
Tail risk protection is in the focus of the financial industry and requires solid mathematical and statistical tools, especially when a trading strategy is derived. Recent hype driven by machine learning (ML) mechanisms has raised the…
This paper investigates an optimal investment problem under the tail Value at Risk (tail VaR, also known as expected shortfall, conditional VaR, average VaR) and portfolio insurance constraints confronted by a defined-contribution pension…
At high levels, the asymptotic distribution of a stationary, regularly varying Markov chain is conveniently given by its tail process. The latter takes the form of a geometric random walk, the increment distribution depending on the sign of…
We introduce a new actuarial tail-shape index, the $\theta$-index, based on a probability equal level relationship between Value at Risk and Expected Shortfall. The index is defined at each tail probability level as the parameter value for…
The study of loss function distributions is critical to characterize a model's behaviour on a given machine learning problem. For example, while the quality of a model is commonly determined by the average loss assessed on a testing set,…
We propose a novel framework of estimating systemic risk measures and risk allocations based on Markov chain Monte Carlo (MCMC) methods. We consider a class of allocations whose jth component can be written as some risk measure of the jth…
Capital allocation principles are used in various contexts in which a risk capital or a cost of an aggregate position has to be allocated among its constituent parts. We study capital allocation principles in a performance measurement…
For measuring tail risk with scarce extreme events, extreme value analysis is often invoked as the statistical tool to extrapolate to the tail of a distribution. The presence of large datasets benefits tail risk analysis by providing more…
Measures of tail dependence between random variables aim to numerically quantify the degree of association between their extreme realizations. Existing tail dependence coefficients (TDCs) are based on an asymptotic analysis of relevant…
Expected risk minimization (ERM) is at the core of many machine learning systems. This means that the risk inherent in a loss distribution is summarized using a single number - its average. In this paper, we propose a general approach to…
Estimating the probability of extreme events involving multiple risk factors is a critical challenge in fields such as finance and climate science. This paper proposes a semi-parametric approach to estimate the probability that a…
This article proposes a new class of risk-sharing rules by exploring the relationship between capital allocation and risk sharing. While the former is concerned with ex-ante allocating capitals to different lines of business within a…
Recent financial disasters emphasised the need to investigate the consequence associated with the tail co-movements among institutions; episodes of contagion are frequently observed and increase the probability of large losses affecting…
Risk management is very important for individual investors or companies. There are many ways to measure the risk of investment. Prices of risky assets vary rapidly and randomly due to the complexity of finance market. Random interval is a…