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In the paper we develop mathematical tools of quantile hedging in incompletemarket. 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 themarket and non-market risk is present in insurance company. We show hot to findthe minimal capital $V_0$ to provide with the one-year hedging strategy forinsurance company satisfying $E\left[{\mathbf 1}_{\{V_1 \geqD\}}\right]=0.995$, where $V_1$ denotes the value of insurance company in oneyear time and $D$ is the payoff of the contract.  o finding a hedging strategy for derivative not using underlying but an assetwith 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 optionson nontradable asset.

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