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We discuss and extend a powerful, geometric framework to represent the set of portfolios, which identifies the space of asset allocations with the points lying in a convex polytope. Based on this viewpoint, we survey certain state-of-the-art tools from geometric and statistical computing in order to handle important and difficult problems in digital finance. Although our tools are quite general, in this paper we focus on two specific questions. The first concerns crisis detection, which is of prime interest for the public in general and for policy makers in particular because of the significant impact that crises have on the economy. Certain features in stock markets lead to this type of anomaly detection: Given the assets' returns, we describe the relationship between portfolios' return and volatility by means of a copula, without making any assumption on investor strategies. We examine a recent method relying on copulae to construct an appropriate indicator that allows us to automate crisis detection. On real data, the indicator detects all past crashes in the cryptocurrency market, whereas from the DJ600-Europe index, from 1990 to 2008, the indicator identifies correctly 4 crises and issues one false positive for which we offer an explanation. Our second contribution is to introduce an original computational framework to model asset allocation strategies, which is of independent interest for digital finance and its applications. Our approach addresses the crucial question of evaluating portfolio management, and is relevant to individual managers as well as financial institutions. To evaluate portfolio performance, we provide a new portfolio score, based on the aforementioned framework and concepts. In particular, our score relies on the statistical properties of portfolios, and we show how they can be computed efficiently.