Theoretical Research And Some Applications Of Portfolio Model

Portfolio theory is an indispensable theoretical study theory in finance.It has an unshakable decisive position in modern finance.Its main purpose is to obtain a specific investment portfolio,that is,when the investment income is given,how to minimize the investment,,or how to maximize the investor's investment income under specific investment risks.In real life,financial investment is unpredictable,with risks and benefits both exist.From the Asian financial crisis in 1997,to the US subprime mortgage crisis in 2006,as well as the global financial crisis in 2007,each of such examples reminds every investor that,investment has risk,which needs to be cautious when entering the market.This paper mainly studies the asymptotically optimal growth rate of funds using the empirical logarithmic optimal portfolio under the sliding portfolio model,and explains that to get the capital's asymptotically optimal growth rate,it can be achieved through the choice of constructed portfolios.At the same time,the Markov process is used to establish a stock price analysis model,also the stock price and operating cycle are predicted.Finally,based on the Markowitz mean-variance model,the concept of mutual information is introduced to further optimize the model.The paper is divided into five chapters.The first chapter introduces the background of the topic,such as the domestic and international research progress,together with research purposes and research methods.The second chapter obtains the large sample nature between the average return and the expected return of the broker under the sliding portfolio model,and uses the empirical logarithmic optimal portfolio to study the asymptotically optimal growth rate of funds.The third chapter uses the Markov process to establish a stock price analysis model.Through the analysis and solution of the model,the stock price operation cycle and stock price trend are analyzed and predicted.In the fourth chapter,based on the Markowitz mean-variance model,the concept of mutual information in Shannon entropy is introduced,and the entropy optimization portfolio model is obtained and analyzed.The fifth chapter is the conclusion.