Factors at Risk 部分内容如下： Abstract
Fctors at Risk
G. Studer
Prof. H.-J. Luthi
RiskLab: Technical Report, January 1997
Abctract:
The identification of scenarios which have a particularly low or high P&L helps to
get a better understanding of the portfolio's risk exposure. Therefore, the notions of
safe (resp. dangerous) regions are introduced, which represent sets where the P&L
is greater (resp. less) than a given critical level. In order to describe such sets in
an easily interpretable way, one-dimensional intervals are used. Such intervals can be
determined by solving a sequence of restricted maximum loss problems.
Keywords: Risk Management - Maximum Loss Optimization
1 Introd.uction
Maximum Loss (ML) was introduced as a method for measuring market risks of
nonlinear portfolios (cf. [Studer]). The basic idea of ML is to determine the worst
case out of a specific set A of scenariosFcalled "trust region". Maximum Loss is
a coheren,t risk measure (cf. [Artzner et al.]) and it is always more conservative
than the corresponding VAR (for a more detailed discussion of VAR refer to
[Beckstrom and Campbell] and [RiskMetrics]).
Mathematically, the ML problem can be formulated as follows: the risk factors
w= (w 1, . . . , w M) represent shifted market rates (e.g. commodity prices Fforeign
exchange rates, equity indices, interest rates), such that wi= 0 corresponds to
the actual value of market rate i. The profit and loss (P&L) function v : IRM→IR；w→v(w)
gives the change in portfolio value (satisfying v(0) = 0). If A ⊂IRM denotes the trust region,then ML is defined as:
ML= min v(w) s.t. w∈ A(1) |