Vladimir Norkin of the Glushkov Institute of Cybertronics in Kiev gave a very interesting (and very equation based) seminar on mixed integer approaches in stochastic optimisation on Friday afternoon. Norkin has been a visitor in IME for the last week. Titled "Safety First Class of Stochastic Decision Problems: Mixed Integer Approach" he explored examples of portfolios with critical thresholds.
Portfolio selection is a relatively new area for me, something I have learnt since arriving at IIASA. Its interesting to see how the idea is used in a variety of sectors and the philosophy of risk minimisation by selecting a diverse portfolio. Safety first means the minimisation of the probability of bad events.
Norkin started the seminar with a quote from Ulrich Beck (1986) that "society starts to realise its exposure to changes including those that appear due to its own development..." and then moved on to AD Roy's (1952) paper on "Safety first and the holding of assets". Its interesting to note that while mathematical techniques and computational capabilities have increased since then, the idea and fundamental theory still holds true.
Norkin also discussed techniques associated with a finite scenario set that relates directly to my YSSP project. He intimated that all finite scenario set probability optimisation problems can be reduced to a mixed Boolean programming problem building on Korbut and Finkelstein (1969).