An evolutionary finance model with a risk-free asset

The purpose of this work is to develop an evolutionary finance model with a risk-free asset playing the role of a numeraire. The model describes a market where one risk-free and several “short-lived” risky assets (securities) are traded in discrete time. The risky securities live one period, yield random payoffs at the end of it, and then are re-born at the beginning of the next period. The main goal of the study is to identify investment strategies that make it possible for an investor to “survive” in the market selection process. It is shown that a strategy of this kind exists, is in a sense asymptotically unique and can be described by a simple explicit formula amenable for quantitative investment analysis.