The paper shows how to combine (historical) statistical data and (current) market prices to form conservative trading strategies for options. This gives rise to a “worst case” state price distribution, which provides sharp price bounds for all convex European options. 1 This research was supported in part by National Science Foundation grant DMS 02-04639. Some key words and phrases : Incomplete...

Some classical results on risk bounds as the Fréchet bounds, the Hoeffding–Fréchet bounds and the extremal risk property of the comonotonicity dependence structure are used to describe worst case dependence structures for portfolios of real risks. An extension of the worst case dependence structure to portfolios of risk vectors is given. The bounds are used to (re-)derive and extend some result...

An asymmetric multivariate generalization of the recently proposed class of normal mixture GARCH models is developed. Issues of parametrization and estimation are discussed. Conditions for covariance stationarity and the existence of the fourth moment are derived, and expressions for the dynamic correlation structure of the process are provided. In an application to stock market returns, it is ...

In this paper we consider the robust portfolio selection problem involving two types of uncertainties; the uncertainty in the distribution of exit time and the uncertainty in the distribution of portfolio return conditional on exit time. To deal with these uncertainties, we propose a tractable approach by applying worst-case VaR strategy to the case where partial information on the exit time di...

Simulation is widely used to measure credit risk in portfolios of loans, bonds, and other instruments subject to possible default. This analysis requires performing the difficult modeling task of capturing the dependence between obligors adequately. Current methods assume a form for the joint distribution of the obligors and match its parameters to given dependence specifications, usually corre...

Research related to aggregation, robustness, and model uncertainty of regulatory risk measures, for instance, Value-at-Risk (VaR) and Expected Shortfall (ES), is of fundamental importance within quantitative risk management. In risk aggregation, marginal risks and their dependence structure are often modeled separately, leading to uncertainty arising at the level of a joint model. In this paper...

This paper develops a bi-objective portfolio selection problem that maximizes returns and minimizes a risk measure called conditional Drawdown (CDD). The drawdown measures include the maximal Drawdown and Average Drawdown as its limiting case. The CDD family of risk functional is similar to conditional value at Risk (CVaR). In this paper, the fuzzy method has been used to solve the bi-objec...

in today’s competitive business environment, the design and management of supply chainnetwork is one of the most important challenges that managers encounter. the supply chain network shouldbe designed for satisfying of customer demands as well as minizing the total system costs. this paper presentsa multi-period multi-stage supply chain network design problem under demand uncertainty. the prob...

This paper considers the worst-case CVaR in situation where only partial information on the underlying probability distribution is given. It is shown that, like CVaR, worst-case CVaR remains a coherent risk measure. The minimization of worst-case CVaR under mixture distribution uncertainty, box uncertainty and ellipsoidal uncertainty are investigated. The application of worst-case CVaR to robus...

Despite significant advances in risk management, routing hazardous materials (hazmat) has relied on relatively simpler methods. In this paper, we formally introduce an advanced risk measure, called conditional valueat-risk (CVaR), applied to truck routing problems for hazmat transportation. We find that CVaR offers a flexible, risk-averse, and computationally tractable routing method that is ad...