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Optimal Reinsurance under Distortion Risk Measures
Distortion risk measure expected premium principle the optimal reinsurance strategy VaR TVaR
2016/1/25
In this paper, we discuss the optimal reinsurance strategy of minimizing the in-surer’s risk under the distortion risk measure. We assume that reinsurance premium is determined by the expected premium...
Bounds for the Sum of Dependent Risks and Worst Value-at-Risk with Monotone Marginal Densities
Complete mixability Monotone density Sum of dependent risks Value-at- Risk
2016/1/25
In quantitative risk management, it is important and challenging to find sharp bounds for the distribution of the sum of dependent risks with given marginal distributions, but an unspecified dependenc...
Optimal Reinsurance under Distortion Risk Measures
Distortion risk measure expected premium principle the optimal reinsurance strategy VaR TVaR
2016/1/20
In this paper, we discuss the optimal reinsurance strategy of minimizing the in-surer’s risk under the distortion risk measure. We assume that reinsurance premium is determined by the expected premium...
Risk Measure Estimation On Fiegarch Processes
Long Memory Models Volatility Risk Measure Estimation FIEGARCH Processes
2013/6/17
We consider the Fractionally Integrated Exponential Generalized Autoregressive Conditional Heteroskedasticity process, denoted by FIEGARCH(p,d,q), introduced by Bollerslev and Mikkelsen (1996). We pre...
Global risk bounds and adaptation in univariate convex regression
Global risk bounds adaptation univariate convex regression
2013/6/13
We consider the problem of nonparametric estimation of a convex regression function $\phi_0$. We study global risk bounds and adaptation properties of the least squares estimator (LSE) of $\phi_0$. Un...
Understanding Operational Risk Capital Approximations: First and Second Orders
Basel II/III Capital Approximation Loss Distributional Approach Capital Approximation Value-at-Risk Expected Shortfall Spectral Risk Measure Subexponential Regularly Varying
2013/5/2
We set the context for capital approximation within the framework of the Basel II / III regulatory capital accords. This is particularly topical as the Basel III accord is shortly due to take effect. ...
Spectral Risk Measures, With Adaptions For Stochastic Optimization
Spectral Risk Measures Adaptions Stochastic Optimization
2012/11/22
Stochastic optimization problems often involve the expectation in its objective. When risk is incorporated in the problem description as well, then risk measures have to be involved in addition to qua...
A CURE for noisy magnetic resonance images: Chi-square unbiased risk estimation
A CURE noisy magnetic resonance images Chi-square unbiased risk estimation
2011/7/5
In this article we derive an unbiased expression for the expected mean-squared error associated with continuously differentiable estimators of the noncentrality parameter of a chi-square random variab...
Coupled risk measures and their empirical estimation when losses follow heavy-tailed distributions
Risk measure Heavy-tailed distribution Distortion risk measure Weighted risk measure Proportional hazards transform Conditional tail expectation Premium calculation principle Index of economic inequality Statistical inference
2011/6/20
Considerable literature has been devoted to developing statistical
inferential results for risk measures, especially for those that are
of the form of L-functionals. However, practical and theoretic...
Unbiased risk estimation and scoring rules
scoring rules Unbiased risk estimation generalized twice Gaussian shift model
2011/6/17
Stein unbiased risk estimation is generalized twice, from the Gaussian shift model
to nonparametric families of smooth densities, and from the quadratic risk to more
general divergence type distance...
A Risk Comparison of Ordinary Least Squares vs Ridge Regression
Ridge Regression dimensional subspace
2011/6/16
We compare the risk of ridge regression to a simple variant of ordinary least squares, in which
one simply projects the data onto a finite dimensional subspace (as specified by a Principal
Component...
Sharper lower bounds on the performance of the empirical risk minimization algorithm
empirical risk minimization learning theory lower bound multidimensional central limit theorem uniform central limit theorem
2011/3/24
We present an argument based on the multidimensional and the uniform central limit theorems, proving that, under some geometrical assumptions between the target function $T$ and the learning class $F$...
Risk Quantification Associated with Wind Energy Intermittency in California
California renewable energy risk analysis systems engineering wind power generation
2010/3/10
As compared to load demand, frequent wind energy
intermittencies produce large short-term (sub 1-hr to 3-hr)
deficits (and surpluses) in the energy supply. These intermittent
deficits pose systemic...
Effect of Wind Intermittency on the Electric Grid：Mitigating the Risk of Energy Deficits
California renewable energy risk analysis systems engineering wind power generation
2010/3/10
Successful implementation of California’s
Renewable Portfolio Standard (RPS) mandating 33 percent
renewable energy generation by 2020 requires inclusion of a
robust strategy to mitigate increased r...
Lower bounds for the minimax risk using $f$-divergences and applications
Minimax lower bounds f-divergences Fano’sinequality Pinsker’s inequality Reconstruction from supportfunctions
2010/3/10
A new lower bound involving f-divergences between
the underlying probability measures is proved for the minimax
risk in estimation problems. The proof just uses the convexity
of the function f and ...