We consider the online problems of time series search and one-way trading with interrelated prices. We derive two algorithms PUND and PDIV which extend the solutions found in literature with profit functions, derive the competitive ratio and prove optimality. For the new as well as for the established online algorithms, we give a numerical example. For the time series search problem with interrelated prices, we present another algorithm UND∗. This algorithm has constant time complexity and an explicit formula for the competitive ratio and selected period to sell. The current solution in literature has linear time complexity and no such explicit formulas.

We consider Cover’s universal portfolio and the problem of risk management in a distribution-free setting when learning from experts. We aim to find optimal portfolios without modelling the financial market at the outset. Although it exists, the price distribution of the constituent assets is neither known nor given as part of the input. We consider the portfolio selection problem from the perspective of online algorithms that process input piece-by-piece in a serial fashion. Under the minimax regret criterion, we propose two risk-adjusted algorithms that track the expert with the lowest maximum drawdown. We obtain upper bounds on the worst-case performance of our algorithms that equal the bounds obtained by Cover (Math Finance 1(1):1–29, 1991). We also present computational evidence using NYSE data over a 22-year period, which shows superior performance of investment strategies that take risk management into account.

Automated credit rating prediction (ACRP) algorithms are used to predict the ratings of bonds without having to trust one rating agency, like Moody's, Fitch or S&P. Nevertheless, for the moment, the accuracy of ACRP algorithms is investigated by empirical tests. In this paper, the framework for a competitive analysis is set and afterwards in this framework, the definition of competitive ACRP algorithms and its demonstration is given. In this way, for a competitive ACRP algorithm, a worst-case guarantee concerning the misclassification error is offered. Furthermore, several ACRP algorithms from the literature are compared according their competitiveness.

The objective of on-line portfolio selection is to design provably good algorithms with respect to some on-line or offline benchmark. Existing algorithms do not consider ‘trading risk’. We present a novel risk-adjusted portfolio selection algorithm (RAPS). RAPS incorporates the ‘trading risk’ in terms of the maximum possible loss. We show that RAPS performs provably ‘as well as’ the Universal Portfolio (UP) [4] in the worst-case. We empirically evaluate RAPS on historical NYSE data. Results show that RAPS is able to beat BCRP as well as several ‘follow-the-winner’ algorithms from the literature, including UP. We conclude that RAPS outperforms in case the assets in the portfolio follow a positive trend.

Credit rating prediction using clustering algorithms has become more and more important in the financial literature. Expanding the ideas of [4] and [5], we propose an approach to generate models for automated credit rating prediction based on support vector domain description (SVDD) and linear regression (LR). The models include the prediction for sovereign and corporate bonds. Another advantage is, the prediction models contain as many groups as rating grades exist, given by rating agencies like S&P, Fitch and Moody's. Our approach is formulated as a step-by-step procedure and all steps are illustrated by an example with artificial data. A numerical example with real data demonstrates the practical usability of our approach.

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