In the online search problem, a sequence of asset prices appears in an online manner. A trader needs to trade an asset in "one-shot". In doing so, the trader's objective is to select the maximum price from the online sequence. Clearly, when the trader settles for a price (makes a trade), it cannot change its decision and the trade is final. The objective is to select a value that is as large as possible from an online sequence of prices. The problem is previously studied under a "purely online" setting, where the trader only knows rough lower and upper bounds for the prices, as well as under an "advice setting", where the trader is given some "short" advice about the best price that is fully accurate.

In this thesis, we study the online search problem under a setting where certain predictions about the input sequence are provided that are not fully trusted and may contain some error. We consider two types of predictions: first, we study predictions about the best (the largest) price in the input sequence. Second, we study query-based predictions that provide answers to binary questions asked by the trader. For both settings, we introduce efficient algorithms for the trader. The performance of these strategies is measured under the worst-case competitive analysis. We show that the competitive ratio of our algorithms degrades smoothly as a function of error. To study the typical performance of our algorithms, we run them on real-world data on exchange prices for fiat currencies and cryptocurrencies. Our experimental results confirm our findings in the theoretical study of the problems.

Finally, we study an alternative search problem in which the goal is to find the longest interval, that is, to select a price that is as small as possible and a price that is as large as possible, from an online sequence of asset prices. For this problem also, we present efficient algorithms and test our algorithms experimentally on the real-world data.