Dresden 2006 – wissenschaftliches Programm
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AKSOE: Physik sozio-ökonomischer Systeme
AKSOE 10: Poster Session (posters are expected to be displayed the full day 8:30-18:00)
AKSOE 10.15: Poster
Mittwoch, 29. März 2006, 16:00–18:00, P2
A subjective approach to the risk measurement — •Piotr Jaworski — Institute of Mathematics, Warsaw University, ul.Banacha 2, 02-097 Warszawa, Poland
Decision making in finance is decision making under uncertainity. A natural question is how to measure risk. In my talk I would like to present a subjective point of view on risk measurement.
If a financial institution has a risky position then it has to prepare some reserves to secure its position. It is natural to consider the optimal level of reserves as a risk measure of the position. Furthermore we assume that the "risk-bearers" are "rational". Their decisions depend on their subjective preferences. In our model these preferences are described by two non-decreasing, weakly convex functions L1 and L2. The first one measures the cost of keeping reserves, and the second the loss when the reserves are not sufficient. Let the random variable X describe the liabilities, and the function
| L( X, r)=L1(r)+L2(( X−r)+) |
costs. The risk-bearer, whom we assume to be rational, chooses the optimal level of reserves r∗, i.e. such that no other level r gives better outcome
| ∀ r V(r ,r∗)=E(L( X,r)−L( X ,r∗)) ≥ 0. |
The optimal r∗ becomes a measure of the risk associated with X. Note, that for any fixed r such r∗ is a minimizer of the expected relative costs V( ·, r ).