Related papers: Calculation of aggregate loss distributions
This paper studies the application of the blended dynamics approach towards distributed optimization problem where the global cost function is given by a sum of local cost functions. The benefits include (i) individual cost function need…
We consider the class of risk measures associated with optimized certainty equivalents. This class includes several popular examples, such as CV@R and monotone mean-variance. Numerical schemes are developed for the computation of these risk…
The focus of this paper is the efficient computation of counterparty credit risk exposure on portfolio level. Here, the large number of risk factors rules out traditional PDE-based techniques and allows only a relatively small number of…
We consider the problem of estimating the probability of a large loss from a financial portfolio, where the future loss is expressed as a conditional expectation. Since the conditional expectation is intractable in most cases, one may…
Multivariate shortfall risk measures provide a principled framework for quantifying systemic risk and determining capital allocations prior to aggregation in interconnected financial systems. Despite their well established theoretical…
Splitting methods have emerged as powerful tools to address complex problems by decomposing them into smaller solvable components. In this work, we develop a general approach to forward-backward splitting methods for solving monotone…
Quantum Monte Carlo integration (QMCI) provides a quadratic speed-up over its classical counterpart, and its applications have been investigated in various fields, including finance. This paper considers its application to risk aggregation,…
We develop and analyze algorithms for distributionally robust optimization (DRO) of convex losses. In particular, we consider group-structured and bounded $f$-divergence uncertainty sets. Our approach relies on an accelerated method that…
The management of operational risk in the banking industry has undergone significant changes over the last decade due to substantial changes in operational risk environment. Globalization, deregulation, the use of complex financial products…
In this work we explore the Sibuya discrete probability distribution, which serves as the basis and the main instrument for numerical simulations of Grunwald--Letnikov fractional derivatives by the Monte Carlo method. We provide three…
As it is known in the finance risk and macroeconomics literature, risk-sharing in large portfolios may increase the probability of creation of default clusters and of systemic risk. We review recent developments on mathematical and…
The distribution of the sum of dependent risks is a crucial aspect in actuarial sciences, risk management and in many branches of applied probability. In this paper, we obtain analytic expressions for the probability density function (pdf)…
We examine numerical rounding errors of some deterministic solvers for systems of ordinary differential equations (ODEs). We show that the accumulation of rounding errors results in a solution that is inherently random and we obtain the…
Monte Carlo simulations are widely used in many areas including particle accelerators. In this lecture, after a short introduction and reviewing of some statistical backgrounds, we will discuss methods such as direct inversion, rejection…
Considerable literature has been devoted to developing statistical inferential results for risk measures, especially for those that are of the form of L-functionals. However, practical and theoretical considerations have highlighted quite a…
Monte Carlo simulations employed for the analysis of portfolios of catastrophic risk process large volumes of data. Often times these simulations are not performed in real-time scenarios as they are slow and consume large data. Such…
According to the Loss Distribution Approach, the operational risk of a bank is determined as 99.9% quantile of the respective loss distribution, covering unexpected severe events. The 99.9% quantile can be considered a tail event. As…
We formulate the statistics of the discrete multicomponent fragmentation event using a methodology borrowed from statistical mechanics. We generate the ensemble of all feasible distributions that can be formed when a single integer…
A general piecewise (including pointwise) probability distribution with space-saving notation and its hierarchical particular cases are considered. The explicit closed-form normalization, expectation, and variance formulas along with the…
A new approach is presented to evaluate multi-loop integrals, which appear in the calculation of cross-sections in high-energy physics. It relies on a fully numerical method and is applicable to a wide class of integrals with various mass…