Abstract:
The problem of dealing with claims on asset which is not traded has attracted
a lot of interests recently. Naturally the approach consist of choosing
a related traded asset or index to use for hedging purposes. In this thesis,
we consider a model for which the non-traded asset is driven by a Ornstein-
Uhlenbeck process. We introduce it into a consumption-investment problem
with factor model under recursive utility of Epstein-Zin type. Due to the second
Brownian motion, we are working in an incomplete market in which the
objective of an agent is pricing and hedging this random payoff. Making use
of the maximum principle method, we solve our forward-backward system and
find the optimal consumption and investment strategies and a relation given
the indifference price. Since a closed form formula for the indifference price
is not obtained, a finite difference method is applied to estimate its value.
For numerical purpose, we consider a one period model. We perform some
numerical analysis on the optimal investment in presence of a claim and on
the indifference price. In general, we observe that, for the parameters specification
considered, the optimal investment becomes an increasing function
with regard to initial wealth of the agent so as to be higher than its value in
the no claim case. However, it is rather a decreasing function with respect
to the correlation between non-traded and traded assets and is always net off
the investment with zero claim. Regarding the indifference price, we observe
that it increases when the traded asset becomes more and more correlated to
the non-traded one. Then, analysing also the dependency of the indifference
price to the risk aversion, we obtain that an agent is willing to pay less for
the non-traded asset when he/she becomes less tolerant of risk. Finally, we
notice from the indifference price versus the initial wealth that an agent is less
willing to take on more risk.
