Dynamic Asset Allocation With Ambiguous Belief

The development of asset allocation in modern financial economics mentions two relative realms: the decision maker's belief and the utility model which the belief is built on.Intrinsically speaking, the decision maker's belief focuses on the forecasting of the future return of the risk assets. In the framework of the classical financial economics, under the restriction of the rational person, the decision maker's belief in most theories includes few irrational factors. However, more and more market anomalies prove the existence of the irrational belief from the decision makers' behaviors. Our paper focus on two market anomalies: underreaction and overreaction. Following the analysis of BSV, we take the underreaction as the behavior from conservatism, overreaction as the behavior from representativeness heuristic. To put these two thinking into asset allocation, we represent them as two return regime simultaneously acting in the decision maker's belief: mean-reverting regime and trending regime. The weights of these two regime in the decision maker's belief could be updated based on the new market information, which is called learning process. To guarantee the behavior of underreaction and overreaction, the probability of regime-switching is set ahead following the number from BSV.To represent the ambiguous belief of the decision maker, we take the recursive ambiguity model as the utility model of the decision maker. Under the setting of the exact form of the model, we work out the decision maker's optimal asset allocation plan. From the transformation of the pricing kernel formula, we get the distorted belief weight under different ambiguity aversion level and analyze the influence factors to it.Finally, the decision maker's optimal asset allocation is simulated under different utility model setting, original belief weight and market condition. Through the comparison among Bayes strategy, mean-reverting strategy and trending strategy, we get some guiding conclusion about the ambiguity aversion decision maker.