Optimal search with bounded daily returns

The `reservation price policy´ of [1] is based on the assumption that asset prices are arbitrary drawn from a pair of upper an lower bounds, that is, m and M. By defining a set of constants the maximum interday price fluctuation can be bounded in order to reduce market volatility. Arbitrary price movements like a sudden drop from M to m are excluded. We present and analyze online conversion algorithms under bounded daily returns. Results show that an investor solely requires the a-priori information whether the price function is symmetric or not to choose the algorithm with the smallest competitive ratio.