Now showing items 3-22 of 39

• Centering, Trust Region, Reflective Techniques for Nonlinear Minimization Subject to Bounds ﻿

(Cornell University, 1993-09)
Bound-constrained nonlinear minimization problems occur frequently in practice. Most existing methods belong to an active set type which can be slow for large scale problems. Recently, we proposed a new approach [7,6,8] ...
• Combining Trust Region and Affine Scaling Linearly ConstrainedNonconvex Minimization ﻿

(Cornell University, 1997-07)
An interior point method is proposed for a general nonlinear (nonconvex) minimization with linear inequality constraints. This method is a combination of the trust region idea for nonlinearity and affine scaling technique ...
• The Computational Structure and Characterization of Nonlinear Discrete Chebyshev Problems ﻿

(Cornell University, 1988-12)
We present the generalisation of some concepts in linear Chebyshev theory to the nonlinear case. We feel these generalisations capture the inherent structure and characteristics of the best Chebyshev approximation and ...
• Discrete Hedging Under Piecewise Linear Risk Management ﻿

(Cornell University, 2003-01-22)
In an incomplete market it is usually impossible to eliminate the intrinsic risk of an option. In this case quadratic risk-minimization is often used to determine a hedging strategy. However, it may be more natural to use ...
• Dynamic Hedging in a Volatile Market ﻿

(Cornell University, 2003-01-23)
In financial markets, errors in option hedging can arise from two sources. First, the option value is a nonlinear function of the underlying; therefore, hedging is instantaneous and hedging with discrete rebalancing gives ...
• Dynamic Hedging with a Deterministic Local Volatility Function Model ﻿

(Cornell University, 2003-01-23)
We compare the dynamic hedging performance of the deterministic local volatility function approach with the implied/constant volatility method. Using an example in which the underlying price follows an absolute diffusion ...
• An Efficient Algorithm for Nonlinear Minimax Problems ﻿

(Cornell University, 1990-03)
We present a new method for solving a nonlinear minimax problem. This new algorithm exploits the structure and characterisation of the solution whenever possible. The exploitation is based on the results that have been ...
• A Global and Quadratic Affine Scaling Method for Linear $L_{1}$ Problems. ﻿

(Cornell University, 1989-07)
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 Quadratically-Convergent Method for Linear $L_{\infty}$ Problems ﻿

(Cornell University, 1990-04)
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 ﻿

(Cornell University, 1991-06)
The $l_p$ norm discrete estimation problem $min_{x \epsilon \Re}{n}$ $\|b-A^{T}x\|_{p}$ 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 ﻿

(Cornell University, 2003-01-19)
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 ﻿

(Cornell University, 2003-01-22)
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 ill-posed. ...
• Hedging guarantees in variable annuities (under both market and interest rate risks) ﻿

(Cornell University, 2004-05-21)
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 ﻿

(Cornell University, 1993-05)
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 ﻿

(Cornell University, 2004-05-21)
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 ﻿

(Cornell University, 1995-11)
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 ﻿

(Cornell University, 1995-11)
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 ﻿

(Cornell University, 2003-01-23)
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 ﻿

(Cornell University, 1994-11)
(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 ﻿

(Cornell University, 1994-11)
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 ...