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426
Conditional value-at-risk for general loss distributions
- Journal of Banking and Finance
, 2002
"... Abstract. Fundamental properties of conditional value-at-risk, as a measure of risk with significant advantages over value-at-risk, are derived for loss distributions in finance that can involve discreetness. Such distributions are of particular importance in applications because of the prevalence o ..."
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Cited by 386 (28 self)
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Abstract. Fundamental properties of conditional value-at-risk, as a measure of risk with significant advantages over value-at-risk, are derived for loss distributions in finance that can involve discreetness. Such distributions are of particular importance in applications because of the prevalence of models based on scenarios and finite sampling. Conditional value-at-risk is able to quantify dangers beyond value-at-risk, and moreover it is coherent. It provides optimization shortcuts which, through linear programming techniques, make practical many large-scale calculations that could otherwise be out of reach. The numerical efficiency and stability of such calculations, shown in several case studies, are illustrated further with an example of index tracking. Key Words: Value-at-risk, conditional value-at-risk, mean shortfall, coherent risk measures, risk sampling, scenarios, hedging, index tracking, portfolio optimization, risk management
Optimization of Convex Risk Functions
, 2004
"... We consider optimization problems involving convex risk functions. By employing techniques of convex analysis and optimization theory in vector spaces of measurable functions we develop new representation theorems for risk models, and optimality and duality theory for problems involving risk functio ..."
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Cited by 103 (14 self)
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We consider optimization problems involving convex risk functions. By employing techniques of convex analysis and optimization theory in vector spaces of measurable functions we develop new representation theorems for risk models, and optimality and duality theory for problems involving risk functions.
Facility Location under Uncertainty: A Review
- IIE Transactions
, 2004
"... Plants, distribution centers, and other facilities generally function for years or decades, during which time the environment in which they operate may change substantially. Costs, demands, travel times, and other inputs to classical facility location models may be highly uncertain. This has made th ..."
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Cited by 77 (7 self)
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Plants, distribution centers, and other facilities generally function for years or decades, during which time the environment in which they operate may change substantially. Costs, demands, travel times, and other inputs to classical facility location models may be highly uncertain. This has made the development of models for facility location under uncertainty a high priority for researchers in both the logistics and stochastic/robust optimization communities. Indeed, a large number of the approaches that have been proposed for optimization under uncertainty have been applied to facility location problems. This paper reviews the literature...
Portfolio Value-atRisk with Heavy-Tailed Risk Factors,” Mathematical Finance 12
, 2002
"... This paper develops efficient methods for computing portfolio value-at-risk (VAR) when the underlying risk factors have a heavy-tailed distribution. In modeling heavy tails, we focus on multivariate t distributions and some extensions thereof. We develop two methods for VAR calculation that exploit ..."
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Cited by 67 (2 self)
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This paper develops efficient methods for computing portfolio value-at-risk (VAR) when the underlying risk factors have a heavy-tailed distribution. In modeling heavy tails, we focus on multivariate t distributions and some extensions thereof. We develop two methods for VAR calculation that exploit a quadratic approximation to the portfolio loss, such as the delta-gamma approximation. In the first method, we derive the characteristic function of the quadratic approximation and then use numerical transform inversion to approximate the portfolio loss distribution. Because the quadratic approximation may not always yield accurate VAR estimates, we also develop a low variance Monte Carlo method. This method uses the quadratic approximation to guide the selection of an effective importance sampling distribution that samples risk factors so that large losses occur more often. Variance is further reduced by combining the importance sampling with stratified sampling. Numerical results on a variety of test portfolios indicate that large variance reductions are typically obtained. Both methods developed in this paper overcome difficulties associated with VAR calculation with heavy-tailed risk factors. The Monte Carlo method also extends to the problem of estimating the conditional excess, sometimes known as the conditional VAR.
Distributionally Robust Optimization under Moment Uncertainty with Application to Data-Driven Problems
"... Stochastic programs can effectively describe the decision-making problem in an uncertain environment. Unfortunately, such programs are often computationally demanding to solve. In addition, their solutions can be misleading when there is ambiguity in the choice of a distribution for the random param ..."
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Cited by 60 (4 self)
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Stochastic programs can effectively describe the decision-making problem in an uncertain environment. Unfortunately, such programs are often computationally demanding to solve. In addition, their solutions can be misleading when there is ambiguity in the choice of a distribution for the random parameters. In this paper, we propose a model describing one’s uncertainty in both the distribution’s form (discrete, Gaussian, exponential, etc.) and moments (mean and covariance). We demonstrate that for a wide range of cost functions the associated distributionally robust stochastic program can be solved efficiently. Furthermore, by deriving new confidence regions for the mean and covariance of a random vector, we provide probabilistic arguments for using our model in problems that rely heavily on historical data. This is confirmed in a practical example of portfolio selection, where our framework leads to better performing policies on the “true” distribution underlying the daily return of assets.
Optimization with stochastic dominance constraints
- SIAM Journal on Optimization
"... We consider the problem of constructing a portfolio of finitely many assets whose returns are described by a discrete joint distribution. We propose a new portfolio optimization model involving stochastic dominance constraints on the portfolio return. We develop optimality and duality theory for the ..."
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Cited by 55 (6 self)
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We consider the problem of constructing a portfolio of finitely many assets whose returns are described by a discrete joint distribution. We propose a new portfolio optimization model involving stochastic dominance constraints on the portfolio return. We develop optimality and duality theory for these models. We construct equivalent optimization models with utility functions. Numerical illustration is provided.
Conditional Risk Mappings
, 2004
"... We introduce an axiomatic definition of a conditional convex risk mapping and we derive its properties. In particular, we prove a representation theorem for conditional risk mappings in terms of conditional expectations. We also develop dynamic programming relations for multistage optimization probl ..."
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Cited by 54 (12 self)
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We introduce an axiomatic definition of a conditional convex risk mapping and we derive its properties. In particular, we prove a representation theorem for conditional risk mappings in terms of conditional expectations. We also develop dynamic programming relations for multistage optimization problems involving conditional risk mappings.
Credit risk optimization with Conditional Value-at-Risk criterion
, 2001
"... This paper examines a new approach for credit risk optimization. The model is based on the Conditional Value-at-Risk (CVaR) risk measure, the expected loss exceeding Value-at-Risk. CVaR is also known as Mean Excess, Mean Shortfall, or Tail VaR. This model can simultaneously adjust all positions i ..."
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Cited by 53 (7 self)
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This paper examines a new approach for credit risk optimization. The model is based on the Conditional Value-at-Risk (CVaR) risk measure, the expected loss exceeding Value-at-Risk. CVaR is also known as Mean Excess, Mean Shortfall, or Tail VaR. This model can simultaneously adjust all positions in a portfolio of financial instruments in order to minimize CVaR subject to trading and return constraints.
Making and evaluating point forecasts
- Journal of the American Statistical Association
"... iv ..."
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Generalized Deviations in Risk Analysis
- FINANCE AND STOCHASTICS
"... General deviation measures are introduced and studied systematically for their potential applications to risk management in areas like portfolio optimization and engineering. Such measures include standard deviation as a special case but need not be symmetric with respect to ups and downs. Their pro ..."
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Cited by 43 (2 self)
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General deviation measures are introduced and studied systematically for their potential applications to risk management in areas like portfolio optimization and engineering. Such measures include standard deviation as a special case but need not be symmetric with respect to ups and downs. Their properties are explored with a mind to generating a large assortment of examples and assessing which may exhibit superior behavior. Connections are shown with coherent risk measures in the sense of Artzner, Delbaen, Eber and Heath, when those are applied to the difference between a random variable and its expectation, instead of to the random variable itself. However, the correspondence is only one-to-one when both classes are restricted by properties called lower range dominance, on the one hand, and strict expectation boundedness on the other. Dual characterizations in terms of sets called risk envelopes are fully provided.
