I plan to develop new constructive probabilistic methods for the risk-averse valuation and the optimal hedging of financial risks with respect to utility based preferences. The mathematical problem is well characterized by martingale and convex duality methods, but constructive and explicit solutions are limited so far. My thesis contributes such solutions for two innovative new classes of stochastic market models. In a discrete semi-complete model, a direct computation scheme is provided. In a continuous time Markovian model which allows for various mutual dependencies between tradable and further untradable factors of risk, both the utility-based valuation process and the hedging strategy are described by a semi- linear system of reaction diffusion equations. Using these results, I plan to analyze the asymptotic relation of the utility based approach to the valuation and hedging problem to related alternative approaches, and to develop approximative and asymptotic solution methods. More precisely , I want to study - the convergence of the solutions for discrete approximations of continuous models, - the dependence of the solution from the level of risk aversion, and - the asymptotic behavior of both the hedging strategy and the valuation process when the risk aversion tends to zero. The results should be used for a detailed qualitative and quantitative analysis of concrete application examples like weather derivatives or credit-risky securities. These have been studied only by related ( marginal - utility ) approaches so far - basically without addressing the crucial hedging problem.