We consider a utility-maximization problem in a general semimartingale financial market , subject to constraints on the number of shares held in each risky asset. These constraints are modeled by predictable convex-set-valued processes whose values do not necessarily contain the origin, i.e.,  no risky investment at all may be inadmissible . Such a setup subsumes the classical constrained utility-maximization problem, as well as the problem where illiquid assets or a random endowment are present. Our main result establishes existence of the optimal trading strategies in such markets under no smoothness requirements on the utility function , and relates them to the corresponding dual objects. Moreover, we show that the dual optimization problem can be posed over a set of countably-additive probability measures, thus eschewing the need for the usual finitely-additive enlargement.
We consider a utility-maximization problem in a general semimartingale financial model , subject to constraints on the number of shares held in each risky asset. These constraints are modeled by predictable convex-set-valued processes whose values do not necessarily contain the origin, i.e., it may be inadmissible for an investor to hold no risky investment at all . Such a setup subsumes the classical constrained utility-maximization problem, as well as the problem where illiquid assets or a random endowment are present. Our main result establishes the existence of optimal trading strategies in such models under no smoothness requirements on the utility function . The result also shows that, up to attainment, the dual optimization problem can be posed over a set of countably-additive probability measures, thus eschewing the need for the usual finitely additive enlargement.
R
market
model
A
it may be inadmissible for an investor to hold
D
may be inadmissible
R
existence of the
the existence of
R
markets
models
R
, and relates them to the corresponding dual objects. Moreover, we show that
. The result also shows that, up to attainment,
R
finitely-additive
finitely additive