Merton Consumption-Investment Problem under Different Stochastic Integral Conventions

This study examines the Merton consumption-investment problem under the Itô, Stratonovich, and Hänggi-Klimontovich conventions, corresponding to stochastic integral convention parameter α = 0, 1/2, and 1, respectively. The study finds that if the drift term is transformed synchronously, the optimal investment strategy is unaffected by the choice of convention; if the drift coefficient value is fixed, the investor's opportunity set will change. Under logarithmic utility, consumption decisions are unaffected, but the optimal portfolio weights shift, and the stochastic integral convention cannot be identified using return data alone.