ON STOCHASTIC ANALYSIS WITH SOME APPLICATIONS IN MATHEMATICAI FINANCE

Abstract

ABSTRACT The aim of this thesis is to study and using stochastic analysis techniques in solving some problems in mathematical finance . Option and their pricing formulae for the European and Asian considered .The pricing formulae are considered only for complete markets . We deal with and study some mathematical problems in mathematics finance such that minimizing consumption and finance portfolio which corresponding to the market that described by mathematical models which sign in chapter 2 and chapter 3 of this thesis . Therefore this thesis study some problems and showing the machineries which solve it , by using machineries stochastic analysis with two methods ,the first describe, in chapter , the stochastic optimal consumption portfolio processes and apply to some problems in this method . In chapter 5 of this thesis showing that given method which is called stochastic control and then explain optimal consumption problems can put in manner stochastic control problem. Some problem to be treatment in this matter .