Research On Multi-period Portfolio Model Based On Entropy

Since Markowitz put forward the portfolio theory in 1952,the benefits and risks of the portfolio have evolved from qualitative analysis to quantitative research.With the development of modern portfolio theory,some scholars have found that: in the complex securities market only study the random situation is no longer applicable to the real investment environment;there are some defects in the risk measurement index established by Markowitz(computational complexity,overestimation of the risk and return distribution can only be normal distribution);the real investors are in a long-term investment situation,then they need to adjust their investment strategies as the market changes.Based on the above reasons,this paper studies the multi period portfolio model based on entropy in random,fuzzy and fuzzy random.The main contents of this paper are as follows:(1)In the random situation,this paper first makes a simple comparison on several classical risk measures,so as to construct a new risk measure index of entropy and semi variance,and verify that the new index is relatively better,then the model is extended to a multi period model.The traditional mathematical method can’t be used to solve our model,so we design a hybrid intelligent algorithm combining wavelet neural network and genetic algorithm,and use the method of reverse dynamic programming to do.(2)In the fuzzy case,we add the riskless asset and increase the transaction cost in to our model,then,a multi period portfolio model with riskless asset and transaction cost is constructed.We give a concrete example of verifying our approach.The results show that the model we construct is reasonable and the algorithm we designed is valid,then we can give investors more investment strategy.(3)In a mixture of random uncertainty and fuzzy uncertainty situation,the mathematical expressions of continuous fuzzy random entropy is proposed,and we verify the rationality of this formula.Then we use the continuous fuzzy random entropy in the portfolio model,and a specific example is used to solve the effective frontier of the model.And extend the model to the case of multi period investment.In summary,in this paper we propose a semi variance entropy risk measurement index,and put forward the concept of continuous fuzzy random entropy according to the stochastic entropy and fuzzy entropy,and construct the corresponding portfolio model.These research results not only enrich the research content of the portfolio model but also reduce the complexity of the calculation,and provide investors with a better investment strategy.Therefore,the research on the multi period portfolio model based on entropy has certain theoretical and practical significance.