FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W2527864306> ?p ?o ?g. }

• W2527864306 abstract "This thesis develops the numerical methods and their mathematical analysis for solving nonlinear partial and integral-partial differential equations and inequalities arising from the valuation of European and American option with transaction costs. The models can hardly be solvable analytically. Therefore, in practice, approximate solutions to such a model are always sought. In this thesis, we discuss two models for the asset price movements: the geometric Brownian motion and jump diffusion process. For the valuation of European options with transaction costs when the underlying asset price follows a geometric Brownian motion, the classical Black-Scholes model becomes a nonlinear partial differential equation. To approximately solve this, we use an upwind finite difference scheme for the spatial discretization and a fully implicit time-stepping scheme. We prove that the system matrix from this scheme is an M -matrix and that the approximate solution converges unconditionally to the exact one by proving that the scheme is consistent, monotone and unconditionally stable. The discretized nonlinear system is then solved using a Newton iterative algorithm. For the valuation of American options with transaction costs when the underlying asset follows geometric Brownian motion, we propose a power penalty method for a finite-dimensional Nonlinear Complementarity Problem (NCP) arising from the discretization of the continuous American option pricing model. We show that the mapping involved in the system is continuous and strongly monotone. Thus, the unique solvability of both the NCP and the penalty equation and the exponential convergence of the solution to the penalty equation to that of the NCP are guaranteed by an existing theory. In the presence of transaction costs and when the underlying asset price follows a jump diffusion process, the problem becomes a nonlinear partial integro-differential equation (PIDE). Since exact solutions can hardly be found, numerical approximations to the nonlinear PIDE are always sought. This is challenging as the PIDE involves a nonlocal integration term. The method we propose is based on an upwind finite difference scheme for the spatial discretization and a fully implicit time stepping scheme. The fully discretized system is solved by a Newton iterative method coupled with a Fast Fourier Transform (FFT) for the computation of the discretized integral term. The constraint in the American option model is imposed by adding a penalty term to the original partial integro-differential complementarity problem. We also perform some numerical experiments to illustrate the usefulness and accuracy of the method." @default.
• W2527864306 created "2016-10-14" @default.
• W2527864306 creator A5044412240 @default.
• W2527864306 date "2014-01-01" @default.
• W2527864306 modified "2023-09-25" @default.
• W2527864306 title "Numerical methods for nonlinear partial differential equations and inequalities arising from option valuation under transaction costs" @default.
• W2527864306 cites W109754632 @default.
• W2527864306 cites W130211666 @default.
• W2527864306 cites W134645927 @default.
• W2527864306 cites W1489605740 @default.
• W2527864306 cites W1499969990 @default.
• W2527864306 cites W1503295912 @default.
• W2527864306 cites W1507795625 @default.
• W2527864306 cites W1508405709 @default.
• W2527864306 cites W1543439990 @default.
• W2527864306 cites W1573587806 @default.
• W2527864306 cites W158727854 @default.
• W2527864306 cites W1600624394 @default.
• W2527864306 cites W1966119267 @default.
• W2527864306 cites W1968546292 @default.
• W2527864306 cites W2002182424 @default.
• W2527864306 cites W2006465918 @default.
• W2527864306 cites W2009758399 @default.
• W2527864306 cites W2014001084 @default.
• W2527864306 cites W2015726575 @default.
• W2527864306 cites W2031293992 @default.
• W2527864306 cites W2040394324 @default.
• W2527864306 cites W2041015802 @default.
• W2527864306 cites W2043375786 @default.
• W2527864306 cites W2048956060 @default.
• W2527864306 cites W2054756613 @default.
• W2527864306 cites W2064978316 @default.
• W2527864306 cites W2076959590 @default.
• W2527864306 cites W2077791698 @default.
• W2527864306 cites W2087092441 @default.
• W2527864306 cites W2087099404 @default.
• W2527864306 cites W2115086321 @default.
• W2527864306 cites W2132967688 @default.
• W2527864306 cites W2134572726 @default.
• W2527864306 cites W2136287637 @default.
• W2527864306 cites W2136364195 @default.
• W2527864306 cites W2142278738 @default.
• W2527864306 cites W2148080284 @default.
• W2527864306 cites W2151065060 @default.
• W2527864306 cites W2156690247 @default.
• W2527864306 cites W2159074954 @default.
• W2527864306 cites W2175456627 @default.
• W2527864306 cites W2323282084 @default.
• W2527864306 cites W2588081979 @default.
• W2527864306 cites W2621537150 @default.
• W2527864306 cites W2971371059 @default.
• W2527864306 cites W3035235874 @default.
• W2527864306 cites W3121209513 @default.
• W2527864306 cites W3122167020 @default.
• W2527864306 cites W3124062437 @default.
• W2527864306 cites W3125465369 @default.
• W2527864306 cites W63424562 @default.
• W2527864306 cites W69750804 @default.
• W2527864306 cites W2265683391 @default.
• W2527864306 hasPublicationYear "2014" @default.
• W2527864306 type Work @default.
• W2527864306 sameAs 2527864306 @default.
• W2527864306 citedByCount "0" @default.
• W2527864306 crossrefType "journal-article" @default.
• W2527864306 hasAuthorship W2527864306A5044412240 @default.
• W2527864306 hasConcept C10138342 @default.
• W2527864306 hasConcept C101615488 @default.
• W2527864306 hasConcept C121332964 @default.
• W2527864306 hasConcept C126255220 @default.
• W2527864306 hasConcept C134306372 @default.
• W2527864306 hasConcept C149782125 @default.
• W2527864306 hasConcept C158622935 @default.
• W2527864306 hasConcept C162324750 @default.
• W2527864306 hasConcept C194483076 @default.
• W2527864306 hasConcept C2524010 @default.
• W2527864306 hasConcept C2834757 @default.
• W2527864306 hasConcept C28826006 @default.
• W2527864306 hasConcept C3017618536 @default.
• W2527864306 hasConcept C33923547 @default.
• W2527864306 hasConcept C41008148 @default.
• W2527864306 hasConcept C56739046 @default.
• W2527864306 hasConcept C62520636 @default.
• W2527864306 hasConcept C68710425 @default.
• W2527864306 hasConcept C73000952 @default.
• W2527864306 hasConcept C93373587 @default.
• W2527864306 hasConcept C93779851 @default.
• W2527864306 hasConceptScore W2527864306C10138342 @default.
• W2527864306 hasConceptScore W2527864306C101615488 @default.
• W2527864306 hasConceptScore W2527864306C121332964 @default.
• W2527864306 hasConceptScore W2527864306C126255220 @default.
• W2527864306 hasConceptScore W2527864306C134306372 @default.
• W2527864306 hasConceptScore W2527864306C149782125 @default.
• W2527864306 hasConceptScore W2527864306C158622935 @default.
• W2527864306 hasConceptScore W2527864306C162324750 @default.
• W2527864306 hasConceptScore W2527864306C194483076 @default.
• W2527864306 hasConceptScore W2527864306C2524010 @default.
• W2527864306 hasConceptScore W2527864306C2834757 @default.
• W2527864306 hasConceptScore W2527864306C28826006 @default.
• W2527864306 hasConceptScore W2527864306C3017618536 @default.
• W2527864306 hasConceptScore W2527864306C33923547 @default.

• next