A competing market model with a polyvariant profit function that assumes "zeitnot" stock behavior of clients is formulated within the banking portfolio medium and then analyzed from the perspective of devising optimal strategies. An associated Markov process method for finding an optimal choice strategy for monovariant and bivariant profit functions is developed. Under certain conditions on the bank "promotional" parameter with respect to the "fee" for a missed share package transaction and at an asymptotically large enough portfolio volume, universal transcendental equations - determining the optimal share package choice among competing strategies with monovariant and bivariant profit functions - are obtained.
Ever since the pioneering work of Markowitz [20], the statistical analysis of numerous types of portfolio markets -especially from the perspective of formulating optimal choice strategies -has become an increasingly active area of research.
Moreover, many of the fruits of this research have been adopted and standardized in a variety of influential financial treatises such as Berezovsky & Gnedin [4] and Brealy & Myers [6]. With the recent successes of financial mathematics and the keen interest (some would say obsession) fueled by the uncertainty and volatility of current economic markets, it is not surprising that there has been something of an explosion in statistically optimal market strategy papers such as Blanchet-Scalliet et al. [5], Bronshtein & Zav’yalova [7], Chan & Yung [8], Davis et al. [9,10], Gollier [16], Kyshakevych et al. [18,19], Maslov [21], Okui [25], Reidel [29], Sun et al. [30], and Ye & Peng [31], to name just a few. Here we adapt and extend some of the techniques developed in [18,19] in order to add another piece to the puzzle of optimal strategy formulation: one that treats “zeitnot” markets with polyvariant profit functions. The zeitnot (not enough time) assumption imposes a strong time-horizon dependence on our model, and establishes a certain commonality with the work in [5], but our work also has some striking differences with this and the other research appearing in the literature.
It is a well known that stock markets within the banking medium have a regulative influence on a country’s economic well being. This medium may have within its portfolio large share packages of diverse business-industrial structures, ordered by means of some natural indices of their financial-economic attractiveness or worth to a potential client-buyer.
For modern zeitnot stock market processes, both at the fixed time constraint and bounded access to the full resource information about share financial-economic value, an optimal choice strategy [9,4,26,17, ?] , identifying the most desirable share package from a particular bank portfolio, assumes a great deal of importance for clients.
The situation becomes much more complicated when many client-buyers are in competition, and then a nontrivial fast choice problem arises subject to the most worth share package within the portfolio. For, as was already mentioned above, the “zeitnot” market character of such share market operations provides a client with only comparative information data about their worth during the choice process. Namely, if a client-buyer chooses some share package from the bank portfolio, he or she can after learning its basic characteristics buy it right away, or return the request back to the portfolio and pass ahead to become familiar with a next share package. If its worth characteristic proves to be equal or lower than those previously considered, the client-buyer will right away pass on to choosing a next share packages until he or she finds a share package with a worth characteristic higher than all those considered previously. In this case the client-buyer should make a decision as to whether this package is potentially the most valuable among all the possible choices and stops the process by purchasing it. If the client-buyer decides not to buy this share package, then he or she should proceed to analyzing the worth characteristics of the next packages, taking into account that the portfolio volume is finite and the market time is fixed.
If there are two or more clients-buyers, a similar choice strategy subject to the most valuable share package is followed, and based on an analysis of the relative characteristics, both decide to buy the package, then the client-buyer who acts fastest will acquire the package and be most successful. The edge in speed will go to the client-buyer able to evaluate the potential share package in the fewest number of steps. At the same time, the choice process for identifying the most valuable share package is definitely affected by certain additional Financial constraints, which essentially influence the number of steps-requests to the portfolio data base. So, in a “zeitnot” market, a client buyer ought to be charged a progressive amount of money (fee) when using the request procedure subject to the portfolio data base for each share package considered and then returned to the portfolio share package. If, at last, the client-buyer stops at some potentially most valuable share package (from his or her point of view) and buys it, the bank, as a financial promotional-active institution, reimburses some money (gift) for the successful commercial operation, thereby stimulating clients to engage in active cooperation with the bank.
The competing stock market model within a bank portfolio medium under the “zeitnot” market scheme delineated above, which governs the relationships among clients-buyers, represents a fairly typical situation [9,10,4] in a modern financial-economical context. As the whole
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