We consider the economic problem of optimal consumption and investment with
power utility. We study the optimal strategy as the relative risk aversion
tends to infinity or to one. The convergence of the optimal consumption is
obtained for general semimartingale models while the convergence of the optimal
trading strategy is obtained for continuous models. The limits are related to
exponential and logarithmic utility. To derive these results, we combine
approaches from optimal control, convex analysis and backward stochastic
differential equations (BSDEs).Comment: 45 page
