Abstract
This paper is concerned with a problem on optimization in stock price
model that allows for jumps in the stochastic processes. We show that the problem
is formulated into the optimal stochastic control problem under the criterion of mean
square tracking error at the end of the planning horizon. The optimal control and the
optimal proportion invested in the index fund which are specified by the product of
the market value of risk and the discounted terminal value of bench mark portfolio are
derived by the solution to ordinary differential equations associated with an adjoint
equation.
