Modeling catastrophe claims with left-truncated severity distributions (extended version)

In this paper, we present a procedure for consistent estimation of the severity and frequency distributions based on incomplete insurance data and demonstrate that ignoring the thresholds leads to a serious underestimation of the ruin probabilities. The event frequency is modelled with a non-homogeneous Poisson process with a sinusoidal intensity rate function. The choice of an adequate loss distribution is conducted via the in-sample goodness-of-fit procedures and forecasting, using classical and robust methodologies.Natural catastrophe; Property insurance; Loss distribution; Truncated data; Ruin probability;

Estimation of operational value-at-risk in the presence of minimum collection threshold: An empirical study

The recently finalized Basel II Capital Accord requires banks to adopt a procedure to estimate the operational risk capital charge. Under the Advanced Measurement Approaches, that are currently mandated for all large internationally active US banks, require the use of historic operational loss data. Operational loss databases are typically subject to a minimum recording threshold of roughly $10,000. We demonstrate that ignoring such thresholds leads to biases in corresponding parameter estimates when the threshold is ignored. Using publicly available operational loss data, we analyze the effects of model misspecification on resulting expected loss, Value-at-Risk, and Conditional Value-at-Risk figures and show that underestimation of the regulatory capital is a consequence of such model error. The choice of an adequate loss distribution is conducted via in-sample goodness-of-fit procedures and backtesting, using both classical and robust methodologies. --

Modelling catastrophe claims with left-truncated severity distributions (extended version)

In this paper, we present a procedure for consistent estimation of the severity and frequency distributions based on incomplete insurance data and demonstrate that ignoring the thresholds leads to a serious underestimation of the ruin probabilities. The event frequency is modelled with a non-homogeneous Poisson process with a sinusoidal intensity rate function. The choice of an adequate loss distribution is conducted via the in-sample goodness-of-fit procedures and forecasting, using classical and robust methodologies. This is an extended version of the article: Chernobai et al. (2006) Modelling catastrophe claims with left-truncated severity distributions, Computational Statistics 21(3-4): 537-555.Natural Catastrophe, Property Insurance, Loss Distribution, Truncated Data, Ruin Probability

Implementing Loss Distribution Approach for Operational Risk

To quantify the operational risk capital charge under the current regulatory framework for banking supervision, referred to as Basel II, many banks adopt the Loss Distribution Approach. There are many modeling issues that should be resolved to use the approach in practice. In this paper we review the quantitative methods suggested in literature for implementation of the approach. In particular, the use of the Bayesian inference method that allows to take expert judgement and parameter uncertainty into account, modeling dependence and inclusion of insurance are discussed

Black swans or dragon kings? A simple test for deviations from the power law

We develop a simple test for deviations from power law tails, which is based on the asymptotic properties of the empirical distribution function. We use this test to answer the question whether great natural disasters, financial crashes or electricity price spikes should be classified as dragon kings or 'only' as black swans

Elliptic equations with a singular drift from a weak Morrey space

In this paper we prove the existence and uniqueness of weak solutions to the Dirichlet problem for an elliptic equation with a drift $b$ satisfying $\operatorname{div} b\le 0$ in $\Omega$. We assume $b$ belongs to some weak Morrey class which includes in the 3D case, in particular, drifts having a singularity along the axis $x_3$ with the asymptotic $b(x)\sim c/r$, where $r=\sqrt{x_1^2+x_2^2}$

On the existence and uniqueness of weak solutions to elliptic equations with a singular drift

In this paper we study the Dirichlet problem for a scalar elliptic equation in a bounded Lipschitz domain $\Omega \subset \mathbb R^3$ with a singular drift of the form $b_0= b-\alpha \frac {x'}{|x'|^2}$ where $x'=(x_1,x_2,0)$, $\alpha \in \mathbb R$ is a parameter and $b$ is a divergence free vector field having essentially the same regularity as the potential part of the drift. Such drifts naturally arise in the theory of axially symmetric solutions to the Navier-Stokes equations. For $\alpha <0$ the divergence of such drifts is positive which potentially can ruin the uniqueness of solutions. Nevertheless, for $\alpha<0$ we prove existence and H\"older continuity of a unique weak solution which vanishes on the axis $\Gamma:=\{ ~x\in \mathbb R^3:~|x'|=0~\}$.Comment: arXiv admin note: text overlap with arXiv:2208.1090

Scalar elliptic equations with a singular drift

We investigate the weak solvability and properties of weak solutions to the Dirichlet problem for a scalar elliptic equation -\Delta u + b^{(\al)}\cdot \nabla u= f in a bounded domain \Om\subset \Bbb R^2 containing the origin, where f\in W^{-1}_q(\Om) with $q>2$ and b^{(\al)}:=b-\al \frac{x}{|x|^2}, $b$ is a divergence--free vector field and \al\in \Bbb R is a parameter

Linking Operational IT Failures to IT Control Weaknesses

Operational IT failures have significant negative effects on firms but little is known about their origins. Building on accounting research linking adverse operational events to SOX-disclosed control weaknesses (CWs) over financial reporting, we study the origins of IT failures in relation to IT-CWs. We use a sample of 212 operational IT failures where the confidentiality, integrity or availability of data assets and functional IT assets (hardware, networks, etc.) has been compromised. We find that IT failures are linked to a relatively small set of IT-CWs, where each IT failure type is linked to distinctly different IT-CWs. Moreover, IT failures more harmful to the firm are found to be associated with IT-CWs that are more sever and difficult to remediate