  Kyle (1985) builds a pioneering and influential model, in which an insider
with long-lived private information submits an optimal order in each period
given the market maker's pricing rule. An inconsistency exists to some extent
in the sense that the ``constant pricing rule " actually assumes an adaptive
expected price with pricing rule given before insider making the decision, and
the ``market efficiency" condition, however, assumes a rational expected price
and implies that the pricing rule can be influenced by insider's strategy. We
loosen the ``constant pricing rule " assumption by taking into account
sufficiently the insider's strategy has on pricing rule. According to the
characteristic of the conditional expectation of the informed profits, three
different models vary with insider's attitudes regarding to risk are presented.
Compared to Kyle (1985), the risk-averse insider in Model 1 can obtain larger
guaranteed profits, the risk-neutral insider in Model 2 can obtain a larger ex
ante expectation of total profits across all periods and the risk-seeking
insider in Model 3 can obtain larger risky profits. Moreover, the limit
behaviors of the three models when trading frequency approaches infinity are
given, showing that Model 1 acquires a strong-form efficiency, Model 2 acquires
the Kyle's (1985) continuous equilibrium, and Model 3 acquires an equilibrium
with information released at an increasing speed.
