How to customise subcaptions with `\documentclass{scrartcl}` that work inside no-float environments?

Question

DISCLAIMER: Yesterday, I posted this question about subcaptions numbering. The question received an excellent answer that works perfect for \documentclass{article}, but that fails whenever using \documentclass{scrartcl}. I posted a MWE with \documentclass{article} because I did not know that the package subcaption fails with scrartcl. Hence, I was suggested to either edit my question or ask a new one. Because the question already has an accepted answer that I think may be useful to other readers, I have left the other question as it is and I ask here a new one.

Consider the following (now correct) MWE:

\documentclass[a4paper]{scrartcl}

\usepackage{subcaption}
\usepackage[demo]{graphicx}

\captionsetup[figure]{labelsep=period}
\renewcommand{\thefigure}{\Roman{figure}}
\DeclareCaptionSubType*[alph]{figure}
\captionsetup[subfigure]{labelformat=simple,labelsep=period}

\begin{document}

\begin{center}
\captionof{figure}{Optimal Claims}\label{optimalclaims}
\medbreak
\begin{subfigure}[H]{0.49\textwidth}
    \includegraphics[width=\textwidth]{Resources/Plot1.pdf}
    \medbreak
    \captionof{figure}{Our Game}\label{our}
\end{subfigure}
\hfill
\begin{subfigure}[H]{0.49\textwidth}
    \includegraphics[width=\textwidth]{Resources/Plot2.pdf}
    \medbreak
    \captionof{figure}{mascu}\label{mascu}
\end{subfigure}
\end{center}

\end{document}

Which generates the following output:

As you can see, I get II.a and II.b, and what I would get is I.a. and I.b. instead. Therefore, my question is: how can I get I.a. and I.b. with \documentclass[a4paper]{scrartcl} (that is, without subcaption)?

IMPORTANT: I need a solution that works inside environments that allow no floats or, at least, a solution that is easy to adapt to such environments (as the accepted solution by Mico in my original question). I'm namely thinking about mdframed environments, in which I'm writing my proofs.

Thank you all very much in advanced for your time and effort. I'm sorry for the confusion with my first question.

Answer 1

If the caption is set above the pictures use \captionabove. For explanations see the comments by Axel Sommerfeldt at the end of this answer.

In a non-float environment you have to add \captionsetup{type=figure}.

\documentclass[a4paper]{scrartcl}

\usepackage{subcaption}
\usepackage[demo]{graphicx}
\usepackage{mdframed}

\captionsetup[figure]{labelsep=period}
\renewcommand{\thefigure}{\Roman{figure}}
\DeclareCaptionSubType*[alph]{figure}
\captionsetup[subfigure]{labelformat=simple,labelsep=period}

\begin{document}

\begin{figure}[!htb]
  \captionabove{Optimal Claims}\label{optimalclaims}
  \centering
  \begin{subfigure}{0.49\textwidth}
    \includegraphics[width=\textwidth]{Plot1.pdf}
    \medbreak
    \subcaption{X}\label{our}
  \end{subfigure}%
  \hfill
  \begin{subfigure}{0.49\textwidth}
    \includegraphics[width=\textwidth]{Plot2.pdf}
    \medbreak
    \subcaption{Y}\label{mascu}
  \end{subfigure}
\end{figure}

\begin{mdframed}
  \begin{center}
    \begin{minipage}{\linewidth}
      \centering
      \captionsetup{type=figure}
      \captionabove{Optimal Claims}\label{optimalclaims2}
      \begin{subfigure}{0.49\textwidth}
        \includegraphics[width=\textwidth]{Plot1.pdf}
        \medbreak
        \subcaption{X}\label{our2}
      \end{subfigure}%
      \hfill
      \begin{subfigure}{0.49\textwidth}
        \includegraphics[width=\textwidth]{Plot2.pdf}
        \medbreak
        \subcaption{Y}\label{mascu2}
      \end{subfigure}
    \end{minipage}
  \end{center}
\end{mdframed}
\end{document}