The Application Of Equivalent Martingale Measure In Asset Pricing

One of the important theoretical basis of financial mathematics is: in a finitenumber of assets and the limited period assumption, the absence of arbitrage isequivalent to the existence of equivalent martingale measure, so that the discountedasset price process is a martingale(the first fundamental theorem of asset pricing).Further more, if the market is complete, no arbitrage assumption is equivalent tothe existence of the unique equivalent martingale measure(the second fundamentaltheorem of asset pricing). A series of methods developed from this result is calledthe martingale method. The martingale approach makes many problems in financialtheory relatively simple.In the framework of complete market, the main work is as follows:The section1, we reveal the inner mechanism of the risk neutral probabilitymeasure through the three assets pricing, and give the reasonable explanation;The section2, we first discuss the measure transformation of finite state modelso that illustrate the risk neutral pricing is essentially a conversion process. Inother words, through correcting the expected probability of future cash flows, wetransform the pricing problem of assets into the risk-free interest rate discountedproblem.Second the risk neutral pricing methods put all the pricing problem intoa unified theoretical framework: all asset pricing will obtain payof in according tothe risk-free rate. Finally, we give the application of the measure transformation ondynamic optimal portfolio selection in an complete market;The section3, we study a optimal investment problem and optimal investment-consumption problem in an complete market for utility maximizing criteria, extenddeterministic function coefcient of the market to the random function, and estab- lish the mathematical model; And further according to the reality of investors fordiferent aspects of the consumer can make a diference in satisfaction and happiness,we divide consumption into three parts and draw some conclusions.