### abstract ###
Assuming that the loss function is convex in the prediction, we construct a prediction strategy universal for the class of Markov prediction strategies, not necessarily continuous
Allowing randomization, we remove the requirement of convexity
### introduction ###
This paper belongs to the area of research known as universal prediction of individual sequences (see  CITATION  for a review): the predictor's goal is to compete with a wide benchmark class of prediction strategies
In the previous papers  CITATION  and  CITATION  we constructed prediction strategies competitive with the important classes of Markov and stationary, respectively, continuous prediction strategies
In this paper we consider competing against possibly discontinuous strategies
Our main results assert the existence of prediction strategies competitive with the Markov strategies
This paper's idea of transition from continuous to general benchmark classes was motivated by Skorokhod's topology for the space  SYMBOL  of ``c\`adl\`ag'' functions, most of which are discontinuous
Skorokhod's idea was to allow small deformations not only along the vertical axis but also along the horizontal axis when defining neighborhoods
Skorokhod's topology was metrized by Kolmogorov so that it became a separable space ( CITATION , Appendix III;  CITATION , p ~913), which allows us to apply one of the numerous algorithms for prediction with expert advice (Kalnishkan and Vyugin's Weak Aggregating Algorithm in this paper) to construct a universal algorithm
In Section  we give the main definitions and state our main results, Theorems  and ; their proofs are given in Sections  and , respectively
