The second set of challenges: As seen, a common assumption is that financial decision makers act rationally; see Homo economicus. Recently, however, researchers in experimental economics and experimental finance have challenged this assumption empirically. These assumptions are also challenged theoretically, by behavioral finance, a discipline primarily concerned with the limits to rationality of economic agents.
Consistent with, and complementary to these findings, various persistent market anomalies have been documented, these being price and/or return distortions—e.g. size premiums—which appear to contradict the efficient-market hypothesis; calendar effects are the best known group here. Related to these are various of the economic puzzles, concerning phenomena similarly contradicting the theory. The equity premium puzzle, as one example, arises in that the difference between the observed returns on stocks as compared to government bonds is consistently higher than the risk premium rational equity investors should demand, an "abnormal return". For further context see Random walk hypothesis § A non-random walk hypothesis, and sidebar for specific instances.
More generally, and particularly following the financial crisis of 2007–2010, financial economics and mathematical finance have been subjected to deeper criticism; notable here is Nassim Nicholas Taleb, who claims that the prices of financial assets cannot be characterized by the simple models currently in use, rendering much of current practice at best irrelevant, and, at worst, dangerously misleading; see Black swan theory, Taleb distribution. A topic of general interest studied in recent years has thus been financial crises, and the failure of financial economics to model these. (A related problem is systemic risk: where companies hold securities in each other then this interconnectedness may entail a "valuation chain"—and the performance of one company, or security, here will impact all, a phenomenon not easily modeled, regardless of whether the individual models are correct; see Systemic risk § Inadequacy of classic valuation models.)
Areas of research attempting to explain (or at least model) these phenomena, and crises, include noise trading, market microstructure, and Heterogeneous agent models. The latter is extended to agent-based computational economics, where price is treated as an emergent phenomenon, resulting from the interaction of the various market participants (agents). The noisy market hypothesis argues that prices can be influenced by speculators and momentum traders, as well as by insiders and institutions that often buy and sell stocks for reasons unrelated to fundamental value; see Noise (economic). The adaptive market hypothesis is an attempt to reconcile the efficient market hypothesis with behavioral economics, by applying the principles of evolution to financial interactions. An information cascade, alternatively, shows market participants engaging in the same acts as others ("herd behavior"), despite contradictions with their private information. See also Hyman Minsky's "financial instability hypothesis", as well as George Soros' approach, § Reflexivity, financial markets, and economic theory.
Note however, that on the obverse, various studies have shown that despite these departures from efficiency, asset prices do typically exhibit a random walk and that one cannot therefore consistently outperform market averages ("alpha").  The practical implication, therefore, is that passive investing (e.g. via low-cost index funds) should, on average, serve better than any other active strategy. Burton Malkiel's A Random Walk Down Wall Street—first published in 1973, and in its 11th edition as of 2015—is a widely read popularization of these arguments. (See also John C. Bogle's Common Sense on Mutual Funds; but compare Warren Buffett's The Superinvestors of Graham-and-Doddsville.) Note also that institutionally inherent limits to arbitrage—as opposed to factors directly contradictory to the theory—are sometimes proposed as an explanation for these departures from efficiency.