Abstract:
We consider a standard problem of maximizing expected utility for the
terminal value of a portfolio’s capital in the case where the asset
price process is a stochastic exponential of the Levy process.
Situations where utility has a logarithmic, power and exponential form
are studied. The aim of the paper is to in at most possible general
assumptions solve the main and the dual problems and obtain answers in
rather explicit form in terms of the Levy triplet. Using it in
logarithmic case we calculate the conditions which determine if the
solution to the dual problem is an equivalent martingale measure, a
martingale or a supermartingale.
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