The following seminars have been jointly organised by the Risk and Stochastics Group and the Department of Mathematics. The Seminar normally takes place on Thursdays from 12.00 - 13.00 in room NAB.1.09 (New Academic Building, LSE), unless stated below. Follow this link for a map of the School.
The series aims to promote communication and discussion of research in the mathematics of insurance and finance and their interface, to encourage interaction between practice and theory in these areas, and to support academic students in related programmes at postgraduate level. All are welcome to attend. ***If you are not an LSE member of staff or LSE student please email firstname.lastname@example.org with details of the Joint Risk and Stochastics and Financial Mathematics seminar(s) you would like to attend so that we can notify the security reception desks to facilitate your access into the New Academic Building***
Please contact the seminar administrator on email@example.com for further information about any of these seminars.
Joint Risk & Stochastics and Financial Mathematics Seminars are not intended to take place during the Summer Term. Ad hoc Summer Term seminars will be listed below:
Thursday 28 May 2015: 12pm - 1pm, Room OLD 3.28, Old Building
Martin Herdegen (ETH Zürich)
Sensitivity of optimal consumption streams
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 and a corresponding risk-tolerance measure. If the risk-tolerance process and the interest rate are deterministic, 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 whose key ingredients are the conditional expectations of the terminal cumulative perturbation and the integrated risk-tolerance process under the risk-tolerance measure.
Joint work with Johannes Muhle-Karbe.