Financial prediction with constrained tail risk

Trindade, A. Alexandre; Uryasev, Stan; Shapiro, Alexander; Zrazhevsky, Grigory

doi:10.1016/j.jbankfin.2007.04.014

Cited by 53 publications

(45 citation statements)

References 21 publications

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“…Let L be the random loss of interest and F(y) = Pr{L ≤ y} be the cumulative distribution function (CDF) of L. Then, the inverse CDF of L can be defined as F −1 (γ ) = inf {y : F(y) ≥ γ }. Following the definitions of Trindade et al [2007], for any α ∈ (0, 1), we define the α-VaR of L as v α = F −1 (α), and define the α-CVaR of L as…”

Section: Estimations Of Var and Cvarmentioning

confidence: 99%

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Monte Carlo Methods for Value-at-Risk and Conditional Value-at-Risk

Liu

2014

ACM Trans. Model. Comput. Simul.

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Value-at-risk (VaR) and conditional value-at-risk (CVaR) are two widely used risk measures of large losses and are employed in the financial industry for risk management purposes. In practice, loss distributions typically do not have closed-form expressions, but they can often be simulated (i.e., random observations of the loss distribution may be obtained by running a computer program). Therefore, Monte Carlo methods that design simulation experiments and utilize simulated observations are often employed in estimation, sensitivity analysis, and optimization of VaRs and CVaRs. In this article, we review some of the recent developments in these methods, provide a unified framework to understand them, and discuss their applications in financial risk management.

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Section: Estimations Of Var and Cvarmentioning

confidence: 99%

“…Let T be the set of optimal solutions to the stochastic program defined in Equation (2). Then it can be shown that T = [v α , u α ], where u α = sup{t : F(t) ≤ α} (see, e.g., Rockafellar and Uryasev [2002] and Trindade et al [2007]). In particular, note that v α ∈ T .…”

Section: Estimations Of Var and Cvarmentioning

confidence: 99%

Monte Carlo Methods for Value-at-Risk and Conditional Value-at-Risk

Liu

2014

ACM Trans. Model. Comput. Simul.

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“…Results for v p (μ) are similar in nature and hence are omitted. As explained in Hong and Liu [2009] and Trindade et al [2007], the estimator c p (μ) has an asymptotic variance of the form Var( c p − E[ c p ]) ≈ A p n −1 s , with A p being some constant, which corresponds to the asymptotic variance of the simulation errors, say ε(μ i ; n s ) as in (7). In addition, Trindade et al [2007] prove that the asymptotic bias of c p (μ) has an order of O(n −1 s ).…”

Section: Numerical Experimentsmentioning

confidence: 99%

Stochastic kriging with biased sample estimates

Chen

Kim

2014

ACM Trans. Model. Comput. Simul.

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Stochastic kriging has been studied as an effective metamodeling technique for approximating response surfaces in the context of stochastic simulation. In a simulation experiment, an analyst typically needs to estimate relevant metamodel parameters and further do prediction; therefore, the impact of parameter estimation on the performance of the metamodel-based predictor has drawn some attention in the literature. However, how the standard stochastic kriging predictor is affected by the presence of bias in finite-sample estimates has not yet been fully investigated. In this article, we study the predictive performance and investigate optimal budget allocation rules subject to a fixed computational budget constraint. Furthermore, we extend the analysis to two-level or nested simulation, which has been recently documented in the risk management literature, with biased estimators.

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“…Another relevant feature of this risk measure, which will be fundamental in defining selection criteria for our portfolio strategies, is that it can be minimized over the set of decision variables. These results are based on [41,42] and are summarized below. Proposition 1.…”

Section: Risk Measures and Performance Indicators For An Insurance Comentioning

confidence: 99%

Multi-Objective Stochastic Optimization Programs for a Non-Life Insurance Company under Solvency Constraints

Kaucic¹,

Daris²

2015

Risks

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In the paper, we introduce a multi-objective scenario-based optimization approach for chance-constrained portfolio selection problems. More specifically, a modified version of the normal constraint method is implemented with a global solver in order to generate a dotted approximation of the Pareto frontier for bi-and tri-objective programming problems. Numerical experiments are carried out on a set of portfolios to be optimized for an EU-based non-life insurance company. Both performance indicators and risk measures are managed as objectives. Results show that this procedure is effective and readily applicable to achieve suitable risk-reward tradeoff analysis.

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Financial prediction with constrained tail risk

Cited by 53 publications

References 21 publications

Monte Carlo Methods for Value-at-Risk and Conditional Value-at-Risk

Monte Carlo Methods for Value-at-Risk and Conditional Value-at-Risk

Stochastic kriging with biased sample estimates

Multi-Objective Stochastic Optimization Programs for a Non-Life Insurance Company under Solvency Constraints

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