scholarly journals A semi-smooth Newton method for an inverse problem in option pricing

PAMM ◽  
2007 ◽  
Vol 7 (1) ◽  
pp. 1081105-1081106
Author(s):  
Bertram Düring
Keyword(s):  
Inverse Problem ◽  
Option Pricing ◽  
Newton Method

scholarly journals The Adjoint Method for the Inverse Problem of Option Pricing

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Shou-Lei Wang ◽  
Yu-Fei Yang ◽  
Yu-Hua Zeng
Keyword(s):  
Inverse Problem ◽  
Option Pricing ◽  
Implied Volatility ◽  
Adjoint Method ◽  
Numerical Examples ◽  
Limited Memory ◽  
Minimization Procedure ◽  
Volatility Function ◽  
The Cost ◽  
Quasi Newton

The estimation of implied volatility is a typical PDE inverse problem. In this paper, we propose theTV-L1model for identifying the implied volatility. The optimal volatility function is found by minimizing the cost functional measuring the discrepancy. The gradient is computed via the adjoint method which provides us with an exact value of the gradient needed for the minimization procedure. We use the limited memory quasi-Newton algorithm (L-BFGS) to find the optimal and numerical examples shows the effectiveness of the presented method.

scholarly journals On local regularization for an inverse problem of option pricing

2011 ◽  
Vol 24 (9) ◽  
pp. 1481-1485
Author(s):  
Cynthia Lester ◽  
Xiaoyue Luo ◽  
Ruya Huang
Keyword(s):  
Inverse Problem ◽  
Option Pricing ◽  
Local Regularization

scholarly journals An inexact Gauss-Newton method for inversion of basal sliding and rheology parameters in a nonlinear Stokes ice sheet model

2012 ◽  
Vol 58 (211) ◽  
pp. 889-903 ◽  
Author(s):  
Noemi Petrat ◽  
Hongyu Zhu ◽  
Georg Stadler ◽  
Thomas J.R. Hughes ◽  
Omar Ghattas
Keyword(s):  
Inverse Problem ◽  
Newton Method ◽  
Ice Sheet ◽  
Nonlinear Least Squares ◽  
Surface Velocity ◽  
Inexact Newton Method ◽  
Observation Error ◽  
Nonlinear Rheology ◽  
Cost Functional ◽  
Basal Sliding

AbstractWe propose an infinite-dimensional adjoint-based inexact Gauss-Newton method for the solution of inverse problems governed by Stokes models of ice sheet flow with nonlinear rheology and sliding law. The method is applied to infer the basal sliding coefficient and the rheological exponent parameter fields from surface velocities. The inverse problem is formulated as a nonlinear least-squares optimization problem whose cost functional is the misfit between surface velocity observations and model predictions. A Tikhonov regularization term is added to the cost functional to render the problem well-posed and account for observational error. Our findings show that the inexact Newton method is significantly more efficient than the nonlinear conjugate gradient method and that the number of Stokes solutions required to solve the inverse problem is insensitive to the number of inversion parameters. The results also show that the reconstructions of the basal sliding coefficient converge to the exact sliding coefficient as the observation error (here, the noise added to synthetic observations) decreases, and that a nonlinear rheology makes the reconstruction of the basal sliding coefficient more difficult. For the inversion of the rheology exponent field, we find that horizontally constant or smoothly varying parameter fields can be reconstructed satisfactorily from noisy observations.

scholarly journals Identification of Flexural Rigidity in a Kirchhoff Plates Model Using a Convex Objective and Continuous Newton Method

2015 ◽  
Vol 2015 ◽  
pp. 1-11
Author(s):  
B. Jadamba ◽  
R. Kahler ◽  
A. A. Khan ◽  
F. Raciti ◽  
B. Winkler
Keyword(s):  
Inverse Problem ◽  
Newton Method ◽  
Fourth Order ◽  
Flexural Rigidity ◽  
Numerical Study ◽  
Variable Parameter ◽  
Kirchhoff Plates ◽  
Estimation Problems ◽  
Output Least Squares ◽  
Continuous Newton Method

This work provides a detailed theoretical and numerical study of the inverse problem of identifying flexural rigidity in Kirchhoff plate models. From a mathematical standpoint, this inverse problem requires estimating a variable coefficient in a fourth-order boundary value problem. This inverse problem and related estimation problems associated with general plates and shell models have been investigated by numerous researchers through an optimization framework using the output least-squares (OLSs) formulation. OLS yields a nonconvex framework and hence it is suitable for investigating only the local behavior of the solution. In this work, we propose a new convex framework for the inverse problem of identifying a variable parameter in a fourth-order inverse problem. Existence results, optimality conditions, and discretization issues are discussed in detail. The discrete inverse problem is solved by using a continuous Newton method. Numerical results show the feasibility of the proposed framework.

scholarly journals A Lagrange-Newton Method for EIT/UT Dual-Modality Image Reconstruction

Sensors ◽  
2019 ◽  
Vol 19 (9) ◽  
pp. 1966 ◽  
Author(s):  
Guanghui Liang ◽  
Shangjie Ren ◽  
Shu Zhao ◽  
Feng Dong
Keyword(s):  
Inverse Problem ◽  
Image Reconstruction ◽  
Newton Method ◽  
Constraint Equation ◽  
Reconstruction Method ◽  
Ultrasound Tomography ◽  
Impedance Tomography ◽  
Dual Modality ◽  
Mesh Model ◽  
Image Reconstruction Method

An image reconstruction method is proposed based on Lagrange-Newton method for electrical impedance tomography (EIT) and ultrasound tomography (UT) dual-modality imaging. Since the change in conductivity distribution is usually accompanied with the change in acoustic impedance distribution, the reconstruction targets of EIT and UT are unified to the conductivity difference using the same mesh model. Some background medium distribution information obtained from ultrasound transmission and reflection measurements can be used to construct a hard constraint about the conductivity difference distribution. Then, the EIT/UT dual-modality inverse problem is constructed by an equality constraint equation, and the Lagrange multiplier method combining Newton-Raphson iteration is used to solve the EIT/UT dual-modality inverse problem. The numerical and experimental results show that the proposed dual-modality image reconstruction method has a better performance than the single-modality EIT method and is more robust to the measurement noise.

Sign in / Sign up

Export Citation Format

Share Document