This week's speaker is Arne Bang Huseby from University of Oslo with the talk: 

Optimal reinsurance contracts in the multivariate case 

Abstract: An insurance contract implies that risk is ceded from ordinary policy holders to companies.  However, companies do the same thing between themselves.  This is known as reinsurance, and the ceding company is known as the cedent.  The rationale could be the same; i.e., that a financially weaker agent is passing risk to a stronger one. In reality even the largest companies do this to diversify risk, and financially the cedent may be as strong as the reinsurer.  The problem of determining re­in­su­rance contracts which are optimal with respect to some reasonable criterion has been studied extensively within actuarial science.  Different contact types are considered such as stop-loss contracts where the reinsurance company covers risk above a certain level, and insurance layer contracts where the reinsurance company covers risk within an interval.  The contracts are then optimized with respect to some risk measure, such as value-at risk (VaR) or conditional tail expectation (CTE). In this seminar we consider the problem of minimizing VaR in the case of multiple insurance layer contracts.  Such contracts are known to be optimal in the univariate case, and the optimal contract is easily determined.  In the multivariate case, however, finding the optimal set of contracts is not easy.  In fact the optimal contract is not even unique in this case.  Still by considering solutions where the risk is balanced between the contracts, a solution can be found using an iterative Monte Carlo method.