Application of Matching Theory in Finance; Market Design with the Purpose of Corporate Finance at Different Stages of Life CycleBased on the Matching Theory

Many markets do not act like commodity markets. in commodity allocations, the price does all the work (clears the market) and the market's task is to discover the price; but even in parts of the financial markets where the price clears the market, the market's task goes beyond price discovery. this study answers the key question "how can market design theory (with emphasis on matching theory) helps to solve corporate finance issues?" firstly, market failures and missing market in the field of financing are identified in accordance with the firms’ life cycle (based on the classification of organization for economic cooperation and development (2013): start-up, early stage, expantion and stabilisation). then, through combination of the theoretical foundations in the field of matching theory with the realities of financing, the theoretical model for problem-solving is presented. in the next step, this theoretical model is presented in the form of conceptual models to determine how to use the capabilities of market design theory and matching theory in solving problems in the field of corporate finance.

Matching theory can be considered as the most important part of market design theory. this theory, which is used in different markets, requires the presence of two elements of supply and demand, each of which presents a list of preferences in different ways, and then the theory of matching and its mechanism enters and brings the two parties in the market together by a matchmaker.

Considering that the subject of the research is under behavioral economics, the methodology of the present research is in the framework of market design theory. in a general context, the application of matching theory is the research method. for this purpose, firstly, market failures and missing market in the field of financing are identified in accordance with the firms’ life cycle. then, based on it, a theoretical model in the form of conceptual models is presented to determine how to use the capabilities of market design theory and matching theory in solving problems in the field of corporate finance. in this regard, the limitation of corporate financing methods in accordance with the life stages of companies in order to identify market participants, examination of the characteristics of financial allocations and also determination the assumptions of algorithms design have been considered.

The results show that there is "market failure" in cash financing of beginner companies (start-up and early stages) and "missing market" in non-cash financing of mature companies (expansion and stabilization stages). Therefore, based on it, three conceptual models including a conceptual model of cash financing (exchange of company with financial source or F-C model) and two conceptual models of barter (exchange of company with company or C-C model) - in terms of one-sided or two-sided market - are designed. the F-C model was designed to achieve matchmaker's goal of providing "cash" financing for beginner companies (start-up and early stages) to use as working capital or as financial support for the company's new and development projects. the C-C model was designed to achieve the matchmaker's goals of barter for developed companies (expansion and stabilization stages). these conceptual models differ significantly in the parties' goals for presenting in the market (cash financing or increasing the liquidity of the portfolio), the identity of the market parties (mature companies or beginner companies), the case of trade (assets or cash), and the type of trade (barter or cash). the limitations of financing methods and tools in the conceptual F-C model and its dependent algorithms, the study of the characteristics of financial allocations and their reflection as general and specific assumptions of the design and application of each algorithm, were also emphasized.

CONCLUSIONS & SUGGESTIONS:

With emphasis the stability of algorithm outputs, four algorithms were proposed to improve financial allocations in corporate financing:  1) decisive acceptance algorithm in one-to-one allocation (two-sided matching) for cash financing of beginner companies was presented. 2) deferred acceptance algorithm in many-to-many allocation (two-sided matching) for cash financing of beginner companies, based on the gale-shapley SMP algorithm and its developments with emphasis on the algorithm redesigned by roth in 2008 (as the basic algorithm), was suggested. 3) deferred acceptance algorithm in one-to-one allocation (two-sided matching) for barter financing of mature companies, which was proposed based on Gale-Shapley SMP algorithm and its developments. 4) SRP algorithm in one-to-one allocation (one-sided matching) for barter financing of mature companies, which irving’s 1985 SRP algorithm and its developments were proposed as the basic algorithm for redesign.