We investigate wealth-driven strategy selection in a complete market
with risky assets paying stochastic dividends, when traders investment
strategies are based on both dividends and past realized prices. We
are interested in assessing whether investment strategies can be
ordered with respect to their relative profitability, or, in other
terms, if a dominance relation can be established.

At this purpose, we study the random dynamical system describing
market dynamics and, using local stability analysis for steady-state
solutions, we identify the conditions under which one single investor
dominates the market.

The general result depends on whether, due to traders investment
behaviors, a price feedback mechanism between expected and realized
price is at work. When agents look only at dividends, confirming
previous results, we find that an order relation can always be
established. Conversely, when agents base their investment decisions
on past realized prices, our new results show that an order relation
can be established only when the market is stable, and only
conditionally on the ecology of active investors. Existence of an
order relation turns out to depend on the strength of the feedback
mechanism.

We also show that, irrespectively of the traders’ investment behavior,
allocating wealth proportionally to expected relative dividends is the
strategy which dominates the market in the long run.