Credit risk is the distribution of financial losses due to unexpected changes in the credit quality of a counterparty in a financial agreement. We review the structural, reduced form and incomplete information approaches to estimating joint default probabilities and prices of credit sensitive securities.

Two methods are frequently used for modeling the choice among uncertain outcomes: stochastic dominance and mean–risk approaches. The former is based on an axiomatic model of risk-averse preferences but does not provide a convenient computational recipe. The latter quantifies the problem in a lucid form of two criteria with possible tradeoff analysis, but cannot model all risk-averse preferences...

Determining contributions to overall portfolio risk is an important topic in risk management. For positions (instruments and sub-portfolios), this problem has been well studied, and a significant theory built, around the calculation of marginal contributions. We consider the problem of determining the contributions to portfolio risk of risk factors. This cannot be addressed through an immediate...

This paper introduces the Risk Visualization as a Service (RVaaS) and presents the motivation, rationale, methodology, Cloud APIs used, operations and examples of using RVaaS. Risks can be calculated within seconds and presented in the form of Visualization to ensure that unexploited areas are ex-posed. RVaaS operates in two phases. The first phase includes the risk modeling in Black Scholes Mo...

We consider the problem of optimizing a portfolio of n assets, whose returns are described by a joint discrete distribution. We formulate the mean–risk model, using as risk functionals the semideviation, deviation from quantile, and spectral risk measures. Using the modern theory of measures of risk, we derive an equivalent representation of the portfolio problem as a zero-sum matrix game, and ...

This paper introduces a Value-at-Risk (VaR) model to generate route choices for a hazmat shipment based on a specified risk confidence level. The objective is to determine a route which minimizes the likelihood that the risk will be greater than a set threshold. Several properties of the VaR model are established. An exact solution procedure is proposed and tested to solve the single-trip probl...

This paper introduces the Risk Visualization as a Service (RVaaS) and presents the motivation, rationale, methodology, Cloud APIs used, operations and examples of using RVaaS. Risks can be calculated within seconds and presented in the form of Visualization to ensure that unexploited areas are exposed. RVaaS operates in two phases. The first phase includes the risk modeling in Black Scholes Mod...

Often, construction projects fail to achieve their time, budget, and quality goals. This is frequently due to the failure of the contractor to analyze and assess unanticipated risks. The analytic hierarchy process (AHP) is a new approach that can be used to analyze and assess project risks during the bidding stage of a construction project and to overcome the limitations of the traditional appr...

When dealing with market risk under the Basel II Accord, variation pays in the form of lower capital requirements and higher profits. Typically, GARCH type models are chosen to forecast Value-at-Risk (VaR) using a single risk model. In this paper we illustrate two useful variations to the standard mechanism for choosing forecasts, namely: (i) combining different forecast models for each period,...