Beyond Value-at-Risk : GlueVaR Distortion Risk Measures

We propose a new family of risk measures, called GlueVaR, within the class of distortion risk measures. Analytical closed-form expressions are shown for the most frequently used distribution functions in financial and insurance applications. The relationship between Glue-VaR, Value-at-Risk (VaR) and Tail Value-at-Risk (TVaR) is explained. Tail-subadditivity is investigated and it is shown that some GlueVaR risk measures satisfy this property. An interpretation in terms of risk attitudes is provided and a discussion is given on the applicability in non-financial problems such as health, safety, environmental or catastrophic risk management

Variational inequalities in Hilbert spaces with measures and optimal stopping problems

We study the existence theory for parabolic variational inequalities in weighted L2 spaces with respect to excessive measures associated with a transition semigroup. We characterize the value function of optimal stopping problems for finite and infinite dimensional diffusions as a generalized solution of such a variational inequality. The weighted L2 setting allows us to cover some singular cases, such as optimal stopping for stochastic equations with degenerate diffusion coeficient. As an application of the theory, we consider the pricing of American-style contingent claims. Among others, we treat the cases of assets with stochastic volatility and with path-dependent payoffs.

Solvency Capital estimation and Risk Measures

This paper examines why a financial entity’s solvency capital estimation might be underestimated if the total amount required is obtained directly from a risk measurement. Using Monte Carlo simulation we show that, in some instances, a common risk measure such as Value-at-Risk is not subadditive when certain dependence structures are considered. Higher risk evaluations are obtained for independence between random variables than those obtained in the case of comonotonicity. The paper stresses, therefore, the relationship between dependence structures and capital estimation.

Comparison of quality of life after stereotactic body radiotherapy and surgery for early-stage prostate cancer

Background: As the long-term efficacy of stereotactic body radiation therapy (SBRT) becomes established and other prostate cancer treatment approaches are refined and improved, examination of quality of life (QOL) following prostate cancer treatment is critical in driving both patient and clinical treatment decisions. We present the first study to compare QOL after SBRT and radical prostatectomy, with QOL assessed at approximately the same times pre- and post-treatment and using the same validated QOL instrument. Methods: Patients with clinically localized prostate cancer were treated with either radical prostatectomy (n = 123 Spanish patients) or SBRT (n = 216 American patients). QOL was assessed using the Expanded Prostate Cancer Index Composite (EPIC) grouped into urinary, sexual, and bowel domains. For comparison purposes, SBRT EPIC data at baseline, 3 weeks, 5, 11, 24, and 36 months were compared to surgery data at baseline, 1, 6, 12, 24,and 36 months. Differences in patient characteristics between the two groups were assessed using Chi-squared tests for categorical variables and t-tests for continuous variables. Generalized estimating equation (GEE) models were constructed for each EPIC scale to account for correlation among repeated measures and used to assess the effect of treatment on QOL. Results: The largest differences in QOL occurred in the first 16 months after treatment, with larger declines following surgery in urinary and sexual QOL as compared to SBRT, and a larger decline in bowel QOL following SBRT as compared to surgery. Long-term urinary and sexual QOL declines remained clinically significantly lower for surgery patients but not for SBRT patients. Conclusions: Overall, these results may have implications for patient and physician clinical decision making which are often influenced by QOL. These differences in sexual, urinary and bowel QOL should be closely considered in selecting the right treatment, especially in evaluating the value of non-invasive treatments, such as SBRT.

Comparison of quality of life after stereotactic body radiotherapy and surgery for early-stage prostate cancer

Background: As the long-term efficacy of stereotactic body radiation therapy (SBRT) becomes established and other prostate cancer treatment approaches are refined and improved, examination of quality of life (QOL) following prostate cancer treatment is critical in driving both patient and clinical treatment decisions. We present the first study to compare QOL after SBRT and radical prostatectomy, with QOL assessed at approximately the same times pre- and post-treatment and using the same validated QOL instrument. Methods: Patients with clinically localized prostate cancer were treated with either radical prostatectomy (n = 123 Spanish patients) or SBRT (n = 216 American patients). QOL was assessed using the Expanded Prostate Cancer Index Composite (EPIC) grouped into urinary, sexual, and bowel domains. For comparison purposes, SBRT EPIC data at baseline, 3 weeks, 5, 11, 24, and 36 months were compared to surgery data at baseline, 1, 6, 12, 24,and 36 months. Differences in patient characteristics between the two groups were assessed using Chi-squared tests for categorical variables and t-tests for continuous variables. Generalized estimating equation (GEE) models were constructed for each EPIC scale to account for correlation among repeated measures and used to assess the effect of treatment on QOL. Results: The largest differences in QOL occurred in the first 1-6 months after treatment, with larger declines following surgery in urinary and sexual QOL as compared to SBRT, and a larger decline in bowel QOL following SBRT as compared to surgery. Long-term urinary and sexual QOL declines remained clinically significantly lower for surgery patients but not for SBRT patients. Conclusions: Overall, these results may have implications for patient and physician clinical decision making which are often influenced by QOL. These differences in sexual, urinary and bowel QOL should be closely considered in selecting the right treatment, especially in evaluating the value of non-invasive treatments, such as SBRT.

The connection between distortion risk measures and ordered weighted averaging operators

Distortion risk measures summarize the risk of a loss distribution by means of a single value. In fuzzy systems, the Ordered Weighted Averaging (OWA) and Weighted Ordered Weighted Averaging (WOWA) operators are used to aggregate a large number of fuzzy rules into a single value. We show that these concepts can be derived from the Choquet integral, and then the mathematical relationship between distortion risk measures and the OWA and WOWA operators for discrete and finite random variables is presented. This connection offers a new interpretation of distortion risk measures and, in particular, Value-at-Risk and Tail Value-at-Risk can be understood from an aggregation operator perspective. The theoretical results are illustrated in an example and the degree of orness concept is discussed.

A Methodology to measure shareholder value orientation and shareholder value creation aimed at providing a research basis to investigate the link between both magnitudes

Does shareholder value orientation lead to shareholder value creation? This article proposes methods to quantify both, shareholder value orientation and shareholder value creation. Through the application of these models it is possible to quantify both dimensions and examine statistically in how far shareholder value orientation explains shareholder value creation. The scoring model developed in this paper allows quantifying the orientation of managers towards the objective to maximize wealth of shareholders. The method evaluates information that comes from the companies and scores the value orientation in a scale from 0 to 10 points. Analytically the variable value orientation is operationalized expressing it as the general attitude of managers toward the objective of value creation, investment policy and behavior, flexibility and further eight value drivers. The value creation model works with market data such as stock prices and dividend payments. Both methods where applied to a sample of 38 blue chip companies: 32 firms belonged to the share index IBEX 35 on July 1st, 1999, one company represents the “new economy” listed in the Spanish New Market as per July 1st, 2001, and 5 European multinational groups formed part of the EuroStoxx 50 index also on July 1st, 2001. The research period comprised the financial years 1998, 1999, and 2000. A regression analysis showed that between 15.9% and 23.4% of shareholder value creation can be explained by shareholder value orientation.

Implementation of the ordinal shapley value for a three-agent economy

We propose a simple mechanism that implements the Ordinal Shapley Value (Pérez-Castrillo and Wettstein [2005]) for economies with three or less agents.

An ordinal shapley value for economic environments (Revised version)

We propose a new solution concept to address the problem of sharing a surplus among the agents generating it. The problem is formulated in the preferences-endowments space. The solution is defined recursively, incorporating notions of consistency and fairness and relying on properties satisfied by the Shapley value for Transferable Utility (TU) games. We show a solution exists, and call it the Ordinal Shapley value (OSV). We characterize the OSV using the notion of coalitional dividends, and furthermore show it is monotone and anonymous. Finally, similarly to the weighted Shapely value for TU games, we construct a weighted OSV as well.

An ordinal shapley value for economic environments

We propose a new solution concept to address the problem of sharing a surplus among the agents generating it. The sharing problem is formulated in the preferences-endowments space. The solution is defined in a recursive manner incorporating notions of consistency and fairness and relying on properties satisfied by the Shapley value for Transferable Utility (TU) games. We show a solution exists, and refer to it as an Ordinal Shapley value (OSV). The OSV associates with each problem an allocation as well as a matrix of concessions ``measuring'' the gains each agent foregoes in favor of the other agents. We analyze the structure of the concessions, and show they are unique and symmetric. Next we characterize the OSV using the notion of coalitional dividends, and furthermore show it is monotone in an agent's initial endowments and satisfies anonymity. Finally, similarly to the weighted Shapley value for TU games, we construct a weighted OSV as well.