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Optimization for a Financial Market with Jumps by Lagrange’s Method
Author(s) -
Rong Situ
Publication year - 1999
Publication title -
pacific economic review
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.34
H-Index - 33
eISSN - 1468-0106
pISSN - 1361-374X
DOI - 10.1111/1468-0106.00077
Subject(s) - lagrange multiplier , multiplier (economics) , financial market , stochastic control , economics , mathematical economics , differential (mechanical device) , stochastic differential equation , optimal control , mathematical optimization , consumption (sociology) , mathematics , finance , macroeconomics , social science , sociology , engineering , aerospace engineering
A Lagrange multiplier was introduced by Chow in 1997 to give a set of necessary conditions for optimal control with respect to a general continuous stochastic differential system. Many applications to the continuous financial markets were derived. Inspired by Chow’s idea, this paper introduces a Lagrange multiplier to derive rigorously some necessary conditions for optimal control with respect to stochastic differential systems with jumps. The results reduce to Chow’s case for continuous systems. An application to optimal consumption for the financial market with jumps is provided.