Market risk modelling in Solvency II regime and hedging options not using underlying

In the paper we develop mathematical tools of quantile hedging in incomplete market. Those could be used for two significant applications: \begin{enumerate} \item 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. \item 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 genaralisation of the work of Klusik and Palmowski \cite{KluPal}. \end{enumerate} \medskip {\it Keywords:} quantile hedging, solvency II, capital modelling, hedging options on nontradable asset. \medskip