30 research outputs found
Utility Maximization with a Stochastic Clock and an Unbounded Random Endowment
We introduce a linear space of finitely additive measures to treat the
problem of optimal expected utility from consumption under a stochastic clock
and an unbounded random endowment process. In this way we establish existence
and uniqueness for a large class of utility-maximization problems including the
classical ones of terminal wealth or consumption, as well as the problems that
depend on a random time horizon or multiple consumption instances. As an
example we explicitly treat the problem of maximizing the logarithmic utility
of a consumption stream, where the local time of an Ornstein-Uhlenbeck process
acts as a stochastic clock.Comment: Published at http://dx.doi.org/10.1214/105051604000000738 in the
Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute
of Mathematical Statistics (http://www.imstat.org
Stability of utility-maximization in incomplete markets
The effectiveness of utility-maximization techniques for portfolio management
relies on our ability to estimate correctly the parameters of the dynamics of
the underlying financial assets. In the setting of complete or incomplete
financial markets, we investigate whether small perturbations of the market
coefficient processes lead to small changes in the agent's optimal behavior
derived from the solution of the related utility-maximization problems.
Specifically, we identify the topologies on the parameter process space and the
solution space under which utility-maximization is a continuous operation, and
we provide a counterexample showing that our results are best possible, in a
certain sense. A novel result about the structure of the solution of the
utility-maximization problem where prices are modeled by continuous
semimartingales is established as an offshoot of the proof of our central
theorem.Comment: to appear in Stochastic Processes and Application