  In this paper, we consider a dynamic asset pricing model in an approximate
fractional economy to address empirical regularities related to both investor
protection and past information. Our newly developed model features not only in
terms with a controlling shareholder who diverts a fraction of the output, but
also good (or bad) memory in his budget dynamics which can be well-calibrated
by a pathwise way from the historical data. We find that poorer investor
protection leads to higher stock holdings of controlling holders, lower gross
stock returns, lower interest rates, and lower modified stock volatilities if
the ownership concentration is sufficiently high. More importantly, by
establishing an approximation scheme for good (bad) memory of investors on the
historical market information, we conclude that good (bad) memory would
increase (decrease) aforementioned dynamics and reveal that good (bad) memory
strengthens (weakens) investor protection for minority shareholder when the
ownership concentration is sufficiently high, while good (bad) memory inversely
weakens (strengthens) investor protection for minority shareholder when the
ownership concentration is sufficiently low. Our model's implications are
consistent with a number of interesting facts documented in the recent
literature.
