In this talk, we investigate the sensitivity of optimal trading strategies and consumption streams with respect to the current level of wealth. It turns out that both sensitivities can be expressed via the so-called risk tolerance process. They appear quite naturally in various expansions of portfolio optimisation problems. Existence and several dynamic characterisations are established in a general semimartingale setting, building on earlier results of Kramkov and Sirbu (2006, 2007).

The talk is based on joint work with Jan Kallsen and Johannes Muhle-Karbe.
Speaker(s): Christoph Czichowsky (London School of Economics)