  We consider a Black-Scholes type equation arising on a pricing model for a
multi-asset option with general transaction costs. The pioneering work of
Leland is thus extended in two different ways: on the one hand, the problem is
multi-dimensional since it involves different underlying assets; on the other
hand, the transaction costs are not assumed to be constant (i.e. a fixed
proportion of the traded quantity). In this work, we generalize Leland's
condition and prove the existence of a viscosity solution for the corresponding
fully nonlinear initial value problem using Perron method. Moreover, we develop
a numerical ADI scheme to find an approximated solution. We apply this method
on a specific multi-asset derivative and we obtain the option price under
different pricing scenarios.
