Consumption/Investment problems with transaction costs

David Hobson, University of Warwick. Part of the probability, stochastic modelling and financial mathematics seminar series.

In this talk we will discuss the Merton problem with transaction costs.

In the classical Merton problem an investor with power-law utility maximises his discounted expected utility of consumption over the infinite horizon. The investor can put his wealth in either a bank account or a risky asset, and the problem is to find the optimal consumption rate and the optimal proportion of wealth to be invested in the risky asset.

The optimal strategy involves an infinite amount of trading and is not robust to including market frictions. Under proportional transaction costs the intuition is clear: trade in a minimal fashion to keep the fraction of wealth in the risky asset in an interval.

We revisit this classical problem and show how many salient features of the problem can be reduced considering the behaviour of quadratic whose coefficients depend on the parameters of the problem.

David Hobson, University of Warwick