\documentclass{standalone}
\usepackage{pgfplots, tikz}
\pgfmathdeclarefunction{poiss}{1}{%
  \pgfmathparse{(#1^x)*exp(-#1)/(x!)}%
  }
\begin{document}
        \begin{tikzpicture}
            \begin{axis}[
            declare function={
            C=4;
            risk(\t,\a) = exp(\a*\t)-0.5;
            cost(\t,\a) = \a*\t^2;
            },
              axis x line=center,
              axis y line=center,
              xtick={0,2,...,19},
              ytick={0.1,0.2,...,0.6},
                domain = 0:18,
                samples = 19,
                xlabel={$t$},
                ylabel={$ $},
                xlabel style={right},
                ylabel style={above left},
                ymax=0.5,
                xmax=20,
                x post scale=1.4
                ]
                \addplot+[smooth,blue] {risk(x,-0.03)};
                \addlegendentry{$\lambda = 1$}
                \addplot+[smooth,orange] {cost(x,0.001)};
                \addlegendentry{$\lambda = 1$}
            \end{axis}
        \end{tikzpicture}
\end{document}
