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CreditRisk Model with Dependent Risk Factors
CreditRisk + model conditional independence dependent risk factors Panjer’s recursion multivariate copulas
2016/1/26
The CreditRisk + model is widely used in industry for computing the loss of a credit port-folio. The standard CreditRisk + model assumes independence among a set of common risk factors, a simplified a...
Jackknife Empirical Likelihood Method for Some Risk Measures and Related Quantities
Confidence interval jackknife empirical likelihood risk measure
2016/1/20
Quantifying risks is of importance in insurance. In this paper, we employ the jackknife empirical likelihood method to construct confidence intervals for some risk measures and related quantities stud...
Minimax Risk: Pinsker Bound
COMMUNICATION THEORY, STATISTICAL DENSITY ESTIMATION FISHER INFORMATION KERNEL ESTIMATORS LINEAR ESTIMATORS, BAYES LOCAL ASYMPTOTIC NORMALITY METHOD OF SIEVES MINIMAX ESTIMATION NOISE (SIGNAL PROCESSING IN THE PRESENCE OF ) PREDICTION AND FILTERING LINEAR SIEVES, METHOD OF SPECTRAL ANALYSIS SHRINKAGE ESTIMATORS SMOOTHNESS PRIORS SOBOLEV SPACES SPLINE FUNCTIONS STATIONARY PROCESSES STEIN EFFECT
2015/8/25
We give an account of the Pinsker bound describing the exact asymptotics of the minimax risk in a class of nonparametric smoothing problems. The parameter spaces are Sobolev classes or ellipsoids, and...
The LASSO risk: asymptotic results and real world examples
Coefficient vector linear observation construct sparse the lasso matrix sequence
2015/8/21
We consider the problem of learning a coefficient vector x0 ∈ RN from noisy linear observation y = Ax0 + w ∈ Rn. In many contexts (ranging from model
selection to image processing) it is desirable to...
Consider estimating the mean vector from data Nn(; 2I ) with lq norm loss,
q 1, when is known to lie in an n-dimensional lp ball, p 2 (0; 1). For large
n, the ratio of minimax linear risk to...
Wavelets have motivated development of a host of new ideas in nonparametric
regression smoothing. Here we apply the tool of exact risk analysis, to understand the
small sample behavior of wavelet es...
The LASSO risk for gaussian matrices
Noisy linear observation vector image processing the matrix sequence
2015/8/20
We consider the problem of learning a coecient vector x0 2 R N from noisy linear observation y = Ax0 + w 2 R n. In many contexts (ranging from model selection to image processing) it is desirable to ...
Unbiased Risk Estimates for Singular Value Thresholding and Spectral Estimators
Singular value thresholding Stein’s unbiased risk estimate (SURE) differentiability of eigenvalues and eigenvectors magnetic resonance cardiac imaging
2015/6/17
In an increasing number of applications, it is of interest to recover an approximately low-rank data matrix from noisy observations. This paper develops an unbiased risk estimate—holding in a Gaussian...
On the Gerber-Shiu discounted penalty function for the ordinary renewal risk model with constant interest
Surplus immediately prior to ruin Deficit at ruin
2011/11/7
In this paper, we study the Gerber-Shiu discounted penalty function for the ordinary renewal risk model modified by the constant interest on the surplus. The time of ruin is analyzed in terms of it$\&...
Exponential and non-exponential upper bounds for the ruin probabilities for the double Cox processes risk models
Probability Double Cox processes Martingale method
2011/11/4
In this paper, we consider a general insurance risk model in which the premium income process and the claim process are based on Cox processes. Exponential upper bounds for ruin probabilities are obta...
Conditional Value-at-Risk for Random Immediate Reward Variables in Markov Decision Processes
Markov Decision Processes Conditional Value-at-Risk Risk Optimal Policy Inventory Model
2013/1/30
We consider risk minimization problems for Markov decision processes. From a standpoint of making the risk of random reward variable at each time as small as possible, a risk measure is introduced usi...
From Smile Asymptotics to Market Risk Measures
dynamic convex risk measures volatility skew stochastic volatility models indifference pricing backward stochastic differential equations
2011/10/9
Abstract: The left tail of the implied volatility skew, coming from quotes on out-of-the-money put options, can be thought to reflect the market's assessment of the risk of a huge drop in stock prices...
BSDEs in Utility Maximization with BMO Market Price of Risk
Quadratic BSDEs BMO Market Price of Risk Power Utility Maximization Dynamic Exponential Moments
2011/8/22
Abstract: This article studies quadratic semimartingale BSDEs arising in power utility maximization when the market price of risk is of BMO type. In a Brownian setting we provide a necessary and suffi...
Ordinal Discriminant Analysis: A new approach to the construction of optimal linear scores for ordinal risk categories
construction optimal linear scores ordinal risk categories
2011/3/4
Most classification methods provide either a prediction of group membership or an assessment of class membership probability. In the case of two-group classifica-tion the predicted probability can be ...
Dynamic risk measuring under model uncertainty: taking advantage of the hidden probability measure
Dynamic risk model uncertainty hidden probability measure
2011/2/28
We study dynamic risk measures in a very general framework enabling to model uncertainty and processes with jumps. We previously showed the existence of a canonical equivalence class of probability me...