Jin Ma
Impulse Control and Optimal Portfolio Selection with General
Transaction Costs
We study an optimal portfolio selection problem under general
transaction costs. We consider a simplified financial market that
consists of only a risk free asset and a risky asset, but the
admissible portfolios are only allowed to have piecewise constant
paths. We prove the existence of such optimal strategy for a fairly
large class of cost functionals, including the commonly used fixed
cost, proportional cost, and more general ones that are
H\"{o}lder-$\alpha$ continuous with $\alpha <1$. We show that the
number of trading times must have a finite expectation. This result
eventually lead to a direct construction of the optimal strategy,
without using the Quasilinear Variational Inequality. The sensitivity
of the value function on the parameters of the cost function is also
discussed.