Traders buy and sell financial instruments in hopes of making profit, and brokers are responsible for the transaction. Some brokers, known as market-makers, take the position opposite to the trader's. If the trader buys, they sell; if the trader sells, they buy. Said differently, brokers make money whenever their traders lose money. From this somewhat strange mechanism emerge various conspiracy theories, notably that brokers manipulate prices in order to maximize their traders' losses. In this paper, our goal is to perform this evil task optimally. Assuming total control over the price of an asset (ignoring the usual aspects of finance such as market conditions, external influence or stochasticity), we show how in cubic time, given a set of trades specified by a stop-loss and a take-profit price, a broker can find a maximum loss price movement. We also study the same problem under a model of probabilistic trades. We finally look at the online trade setting, where broker and trader exchange turns, each trying to make a profit. We show that the best option for the trader is to never trade.
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