Previous

Next we look at a "previous" prior. The previous prior uses the marginal action probabilities from the previous time step as priors to the current timestep. This means at time *t*, *ft*[*a*] plays the role of a posterior probability of making a decision, however, at time *t* + 1 *ft*[*a*] now serves as the empirical prior. This is the example introduced in Section 4.4. This corresponds to *pt*[*a*] = *ft*−<sup>1</sup>[*a*] for *t* > 0, and *pt*[*a*] = 0.5 for *t* = 0. The previous prior represents an empirical prior where the decision is conditioned on previous market information, where *T* controls the level of influence from the previous market stage (in our case, each year). A high *T* means high influence from the past market state, whereas low *T* means focusing on current market conditions alone (as measured by *U*). In the extreme case of *T* = <sup>∞</sup>, a backward looking expectations [55] approach is recovered where decisions are assumed to be a function purely of past decisions, however, in the more general case with *T* < <sup>∞</sup>, *U* adjusts the decisions based on the current market state.
