Combinatorial Mathematics Problems In Financial Economics

The financial economics problems have a long history, each person or eacheconomic entity almost every day faces a combination decision-making problem.Facing the many uncertainty factors in life, and especially in recent years majorfinancial emergencies and many questions of financial reform, led to the research inthe field of financial economic environment is more and more complex, and the mainapplications of combinatorial mathematics is to find the optimal solution in variouscomplex relationships. Considering the combination of various financial problems inreal life, by suing combinatorial counting theory, combination optimization theory andcombinatorial design theory, respectively research combinatorial problem in themarket, and then reveals its significance in practical application.This article bases on the basic knowledge of combination and financial, and thendiscusses the application of combinatorial analysis theory in the market. The contentof this paper includes the following aspects: By using the combinatorial countingmethod, we analyze the general merchandise market, then get a simplified proof of themarket in the process of problem solving; By using the permutations principle, weprove the Beach,s original problem. In addition, we study on basic knowledgecombination investment in financial market and analyze the optimization problem ofportfolio investment in the financial market, construct a portfolio model ofstock in allowed short assumption by using the Markowitz Mean-Variance model.We through the example analysis, to help people build up the correct investmentconcept. Using case analysis，we explore the basic method through the capital assetpricing model, then we help people to correctly select portfolio. We analyze thearbitrage single factor pricing model and use the application of specific examples weuse in the stock market to help people to correctly choose the arbitrage portfolio.We derive and prove that the sufficient and necessary conditions of individual fundseparation phenomenon. Then we carriy on the example analysis. Finally, wesummarize the conclusions.