Evolutionary Finance: Models with Short-Lived Assets

Evolutionary Finance explores the "survival and extinction" questions of investment strategies (portfolio rules) in the market selection process. It studies the stochastic dynamics of ?nancial markets, where asset prices are determined endogenously by short-run equilibrium between supply and demand, which is formed each period as a result of the interaction of strategies employed by competing market participants. This paper focuses on "short-lived" risky securities that are traded at the beginning of each period and yield payo¤s at the end of it (which live only one period), with the cycle then repeating. We review some key models developed in this area, which address the following problems in order: 1) introducing the central results that we are primarily interested in under substantially more general assumptions; 2) exploring the Nash equilibrium properties of survival strategies and the single survivor problem within the framework of independent and identically distributed states of the world and fixed-mix portfolio rules; 3) extending the discussion on the single survivor problem to a considerably broader scope, emphasizing its Markovian nature; 4) including a risk-free asset into the market; 5) allowing for short-selling in the market. The two main results of these studies are: i) the existence of survival strategies that can be expressed by explicit formulas, i.e., Kelly's rule of "betting one's beliefs"; and, ii) the asymptotic uniqueness (within a speci?c class of strategies called basic) of such survival strategies.