Sensitivity of Optimal Comsumption Streams

Martin Herdegen (ETH Zürich)
Thursday, April 16, 2015 - 4:00pm
TU Berlin, Straße des 17. Juni 136, 10623 Berlin, Raum MA 041

We study the sensitivity of optimal consumption streams with respect to perturbations of the random endowment. We show that to the leading order, any consumption correction for the perturbed endowment is still optimal as long as the budget constraint is binding. More importantly, we also establish the optimal correction at the next-to-leading order. This can be computed in two steps. First, one has to find the optimal correction for a deterministic perturbation. This only involves the risk-tolerance process of the unperturbed problem and yields a "risk-tolerance martingale". If the risk-tolerance process is deterministic, e.g. in the case of a deterministic unperturbed endowment, the latter is constant. In a second step, one can then calculate the optimal correction for any random perturbation. This is given by an explicit formula containing only the conditional expectation of the terminal cumulative perturbation under an equivalent measure induced by the "risk tolerance martingale", the "risk-tolerance martingale" and the risk-tolerance process itself.
Talk based on a joint work with Johannes Muhle-Karbe (ETH Zürich).