Analysis of optimal strategies for a competing stock market portfolio model with a polyvariant profit function
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ANALYSIS OF OPTIMAL STRATEGIES FOR A COMPETING STOCK MARKET PORTFOLIO MODEL WITH A POLYVARIANT PROFIT FUNCTION B. Yu. Kyshakevych,a A. K. Prykarpats’kyi,a† and I. P. Tverdokhlibb
UDC 330:519 (447)
Abstract. A competitive market model with a polyvariant profit function is investigated as applied to the competing banking portfolio medium under conditions of “zeitnot” stock behavior of clients with a view to devising optimal strategies. The method of associated Markov processes is developed with a view to finding an optimal strategy for choosing the most valuable share package for monovariant and bivariant profit functions. Under certain constraints on the so-called bank “promotional” parameter with respect to the “fee” for a missed share package transaction in the case of an asymptotically large portfolio size, universal transcendental equations are obtained that determine the optimal share package choice among competing strategies with monovariant and bivariant profit functions. Keywords: stock market, share portfolio, profit function, competition, Markov process, optimal strategy. 1. ANALYSIS OF OPTIMAL STRATEGIES FOR A COMPETING STOCK MARKET PORTFOLIO MODEL As is well known, the market of shares accumulated in the banking medium exerts influence on the efficiency of a national economy. This portfolio medium can have a considerable amount of share packages of various business and industrial structures ordered according to their financial and economic indices or values for potential buyer clients. Under the conditions of the current “zeitnot” stock exchange mechanism of realization of shares, which implies both a fixed time interval and a constraint on the access to complete information on their financial and economic value, an optimal strategy of the choice [1, 2] of the most valuable share package out of a proposed bank portfolio is important from the viewpoint of client buyers. The situation is essentially more complicated when several buyers compete with one another, and, as a result, a nontrivial problem arises that lies in the choice of the potentially most valuable share package within a portfolio by a client buyer before other client buyers. In this case, as has been noted above, in view of the zeitnot stock behavior of market transactions of this type, the share market offers only dynamic comparative information on share prices to the buyer during his choice, namely, if the client buyer has chosen some share package from the bank portfolio for the sake of acquaintance, then, after the acquaintance with its basic characteristics, he can purchase it immediately or return the request to the portfolio and begin to acquaint himself with another share package. If its value characteristic turns out to be worse than that of values of the packages considered earlier, then he immediately passes to the analysis of the next share package and so on until a share package is chosen whose value characteristic exceeds those of all the considered share packages. In this case, the buyer must make a decision whether he consi
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