In practice this traded asset might be used as a proxy and hedging done with this asset. Thus some notion of an 'optimal' hedge with this traded asset is needed. However, the investor receives some of the untraded asset and the question is how to price and hedge this random payoff. Such frictions mean we are in the situation of incomplete markets. We propose an approximation to the solution for the 'optimal' price and hedge which is accurate when the position is small in comparison to wealth.
Logarithmic utility is considered as a special case.
It is hence very important to have reliable measures of risk for these portfolios. The development of a methodology that could be used for the measurement of strategic long-term financial risks is therefore an important task. Existing modelling instruments such as RiskMetrics allow a relatively good measurement of market risks of trading books. In this talk we primarily give an overview on models proposed for modelling the evolution of stochastic risk factors. Then, we present statistical techniques to estimate model parameters.