JavaScript is disabled for your browser. Some features of this site may not work without it.
Browsing by Author "Li, Yuying"
Now showing items 1029 of 39

A Global and Quadratic Affine Scaling Method for Linear $L_{1}$ Problems.
Coleman, Thomas F.; Li, Yuying (Cornell University, 198907)Recently, various interior point algorithms  related to the Karmarkar algorithm  have been developed for linear programming. In this paper, we first show how this "interior point" philosophy can be adapted to the ... 
A Global and QuadraticallyConvergent Method for Linear $L_{\infty}$ Problems
Coleman, Thomas F.; Li, Yuying (Cornell University, 199004)We propose a new global and quadratically convergent algorithm for the linear $l_{\infty}$ problem. This method works on the piecewise $l_{\infty}$ problem directly by generating descent directions  via a sequence of ... 
A Globally Convergent Method for Lp Problems
Li, Yuying (Cornell University, 199106)The $l_p$ norm discrete estimation problem $min_{x \epsilon \Re}{n}$ $\bA^{T}x\_{p}$ is troblesome when $p$ is close to unity because the objective function approaches a discontinuous form. In this paper, we present ... 
Hedging a Portfolio of derivatives by Modeling Cost
Boyle, Katharyn A.; Coleman, Thomas F.; Li, Yuying (Cornell University, 20030119)We consider the problem of hedging the loss of a given portfolio of derivatives using a set of more liquid derivative instruments. We illustrate why the typical mathematical formulation for this hedging problem is ... 
Hedging a Portfolio of Derivatives by Modeling Cost
Boyle, Katharyn A.; Coleman, Thomas F.; Li, Yuying (Cornell University, 20030122)We consider the problem of hedging the loss of a given portfolio of derivatives using a set of more liquid derivative instruments. We illustrate why the typical mathematical formulation for this hedging problem is illposed. ... 
Hedging guarantees in variable annuities (under both market and interest rate risks)
Coleman, Thomas F; Li, Yuying; Patron, MariaCristina (Cornell University, 20040521)In order to prevent possibly very large losses, insurance companies have to devise risk management strategies for the guarantees provided by variable annuities. When hedging the options embedded in these guarantees, due ... 
An Interior Trust Region Approach for Nonlinear Minimization Subject to Bounds
Coleman, Thomas F.; Li, Yuying (Cornell University, 199305)We propose a new trust region approach for minimizing a nonlinear function subject to simple bounds. By choosing an appropriate quadratic model and scaling matrix at each iteration, we show that it is not necessary to ... 
Minimizing CVaR and VaR for a portfolio of derivatives
alexander, siddharth; coleman, thomas f.; Li, Yuying (Cornell University, 20040521)Value at risk (VaR) and conditional value at risk (CVaR) are the most frequently used risk measures in current risk management practice. As an alternative to VaR, CVaR is attractive since it is a coherent risk measure. ... 
A Newton Acceleration of the Weiszfeld Algorithm for Minimizing the Sum of Euclidean Distances
Li, Yuying (Cornell University, 199511)The Weiszfeld algorithm for continuous location problems can be considered as an iteratively reweighted least squares method. It exhibits linear convergence. In this paper, a Newton type algorithm with similar simplicity ... 
A Newton Acceleration of the Weiszfeld Algorithm for Minimizing the Sum ofEuclidean Distances
Li, Yuying (Cornell University, 199511)The Weiszfeld algorithm for continuous location problems can be considered as an iteratively reweighted least squares method. It exhibits linear convergence. In this paper, a Newton type algorithm with similar simplicity ... 
A Newton Method for American Option Pricing
Coleman, Thomas F.; Li, Yuying; Verma, Arun (Cornell University, 20030123)The variational inequality formulation provides a mechanism to determine both the option value and the early exercise curve implicitly [17]. Standard finite difference approximation typically leads to linear complementarity ... 
On Global Convergence of a Trust Region and Affine Scaling Method for Nonlinearly Constrained Minimization
Li, Yuying (Cornell University, 199411)(The following contains mathematical formulae and symbols that may become distorted in ASCII text.) A nonlinearly constrained optimization problem can be solved by the exact penalty approach involving non differentiable ... 
On Global Convergence of A Trust Region and Affine Scaling Methodfor Nonlinearly Constrained Minimization
Li, Yuying (Cornell University, 199411)A nonlinearly constrained optimization problem can be solved by the exact penalty approach involving nondifferentiable functions $\sum_{i} c_i(x)$ and $\sum_{i}\max(0,c_i(x))$. In \cite{Li94a}, a trust region affine ... 
On The Convergence of Reflective Newton Methods for LargeScale Nonlinear Minimization Subject to Bounds
Coleman, Thomas F.; Li, Yuying (Cornell University, 199211)We consider a new algorithm, a reflective Newton method, for the problem of minimizing a smooth nonlinear function of many variables, subject to upper and/or lower bounds on some of the variables. This approach generates ... 
On the Convergence of Reflective Newton Methods for Largescale Nonlinear Minimization Subject to Bounds
Coleman, Thomas F.; Li, Yuying (Cornell University, 199211)We consider a new algorithm, a reflective Newton method, for the problem of minimizing a smooth nonlinear function of many variables, subject to upper and/or lower bounds on some of the variables. This approach ... 
Piecewise Differentiable Minimization for Illposed Inverse Problems
Li, Yuying (Cornell University, 199608)Based on minimizing a piece wise differentiable lp function subject to a single inequality constraint, this paper discusses algorithms for a discretized regularization problem for illposed inverse problems. We examine ... 
A QuadraticallyConvergent Algorithm for the Linear Programming Problem with Lower and Upper Bounds
Coleman, Thomas F.; Li, Yuying (Cornell University, 199004)We present a new algorithm to solve linear programming problems with finite lower and upper bounds. This algorithm generates an infinite sequence of points guaranteed to converge to the solution; the ultimate convergence ... 
Reconstructing the Unknown Local Volatility Function
Coleman, Thomas F.; Li, Yuying; Verma, Arun (Cornell University, 20030123)Using market European option prices, a method for computing a smooth local volatility function in a 1factor continuous diffusion model is proposed. Smoothness is introduced to facilitate accurate approximation of the ... 
Reconstructing the unknown volatility function
Coleman, Thomas F; Li, Yuying; Verma, Arun (Cornell University, 199809)Using market European option prices, a method for computing a {\em smooth} local volatility function in a 1factor continuous diffusion model is proposed. Smoothness is introduced to facilitate accurate approximation of ... 
A Reflective Newton Method for Minimizing a Quadratic Function Subject to Bounds on Some of the Variables
Coleman, Thomas F.; Li, Yuying (Cornell University, 199211)We propose a new algorithm, a reflective Newton method, for the minimization of a quadratic function of many variables subject to upper and lower bounds on some of the variables. This method applies to a general ...