  In the paper we develop mathematical tools of quantile hedging in incomplete
market. Those could be used for two significant applications:
  o calculating the \textbf{optimal capital requirement imposed by Solvency II}
(Directive 2009/138/EC of the European Parliament and of the Council) when the
market and non-market risk is present in insurance company. We show hot to find
the minimal capital $V_0$ to provide with the one-year hedging strategy for
insurance company satisfying $E\left[{\mathbf 1}_{\{V_1 \geq
D\}}\right]=0.995$, where $V_1$ denotes the value of insurance company in one
year time and $D$ is the payoff of the contract.
  o finding a hedging strategy for derivative not using underlying but an asset
with dynamics correlated or in some other way dependent (no deterministically)
on underlying. The work is a generalisation of the work of Klusik and Palmowski
\cite{KluPal}.
  Keywords: quantile hedging, solvency II, capital modelling, hedging options
on nontradable asset.
