Hedging of equity-linked with maximal success factor

We consider an equity-linked contract whose payoff depends on the lifetime of policy holder and the stock price. We assume the limited capital for hedging and we provide with the best strategy for an insurance company in the meaning of so called succes factor $\IE^\IP\left[{\mathbf 1}_{\{V_T \geq D)}+{\mathbf 1}_{\{V_T < D\}}\frac{V_T}{D}\right ]$, where $V_T$ denotes the end value of strategy and $D$ is the payoff of the contract. The work is a genaralisation of the work of F\"{o}llmer and Schied \cite{FS2004} and Klusik and Palmowski \cite{KluPal}, but it considers much more general "incompletness" of the market, among others midterm nonmarket information signals and infitite nonmarket scenarios.