Statistically Optimal Strategy Analysis of a Competing Portfolio Market with a Polyvariant Profit Function

TL;DR

This paper develops a Markov process-based method to analyze and determine optimal strategies in a competitive banking portfolio market with complex profit functions, considering client behavior and large portfolio volumes.

Contribution

It introduces a novel Markov process approach for optimizing strategies in a market with polyvariant profit functions and derives universal transcendental equations for optimal share selection.

Findings

Universal transcendental equations for optimal strategies derived

Optimal strategies depend on specific market parameters and portfolio size

Method applicable to both monovariant and bivariant profit functions

Abstract

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.