The analysis of many complex problems and complex dynamic systems suggests that there are dependencies between high complexity and properties of the underlying structures, as the existence of large grids, non-regularities and inhomogeneous structures and irregular flows of information. These observations indicate the existence of a unified criterion that defines structural elements of complex entities. We present the idea of such a criterion basing on concepts from computational and parametric complexity theory and analyse its impact in financial risk management. It is shown that selected real-world problems in risk managements are complex in the sense of NP-completeness. Here the criterion is used to analyse the structural reasons for the proved complexity. We show how selected risk management methods fit into the picture of our complexity criterion and derive some implications for the future generation of risk management methods from the viewpoint of complexity. 1.
|
789
|
The Pricing of Options and Corporate Liabilities
– Black, Scholes
- 1973
|
|
404
|
Introduction to graph theory
– West
- 2001
|
|
374
|
Combinatorial Algorithms for Integrated Circuits
– Lengauer
- 1990
|
|
307
|
On a theory of computation and complexity over the real numbers
– Blum, Shub, et al.
- 1989
|
|
278
|
Human Error
– Reason
- 1990
|
|
200
|
Complexity and Real Computation
– Blum, Cucker, et al.
- 1997
|
|
194
|
Easy Problems for Tree-Decomposable Graphs
– Arnborg, Lagergren, et al.
- 1991
|
|
175
|
Capital asset prices: A theory of market equilibrium under conditions of risk
– SHARPE
- 1964
|
|
165
|
On the pricing of corporate debt: The risk structure of interest rates
– Merton
- 1974
|
|
72
|
Graph Minors V. Excluding a planar graph
– Robertson, Seymour
- 1986
|
|
70
|
Linear Time Solvable Optimization Problems on Graphs of Bounded Clique Width
– Courcelle, Makowsky, et al.
- 2000
|
|
64
|
Modeling term structures of defaultable bonds
– Duffie, Singleton
- 1999
|
|
60
|
Handle-rewriting hypergraph grammars
– Courcelle, Engelfriet, et al.
- 1993
|
|
50
|
Deciding first-order properties of locally tree-decomposable structures
– Frick, Grohe
|
|
50
|
Graph minors III. Planar tree-width
– Robertson, Seymour
- 1984
|
|
38
|
Communication Complexity and Parallel Computing
– Hromkovič
- 1997
|
|
32
|
Some Remarks on the Value-at-Risk and the Conditional Value-at-Risk
– Pflug
- 2000
|
|
29
|
A Simplified Model for Portfolio Analysis
– Sharpe
- 1963
|
|
27
|
The boundedness of all products of a pair of matrices is undecidable
– Blondel, Tsitsiklis
|
|
20
|
Efficient solution of connectivity problems on hierarchically defined graphs
– Lengauer, Wanke
- 1988
|
|
20
|
Linear time computable problems and first-order descriptions
– Seese
- 1996
|
|
18
|
Business Dynamics
– Sterman
- 2000
|
|
18
|
1997a): Portfolio Credit Risk I
– Wilson
|
|
15
|
Hamiltonian cycles in solid grid graphs
– Umans, Lenhart
- 1997
|
|
14
|
Rational Theory of Option Pricing
– Merton
- 1973
|
|
13
|
The Gödel incompleteness theorem and decidability over a ring, From Topology to Computation
– BLUM, SMALE
- 1990
|
|
13
|
Modelling, Measuring and Hedging Operational Risk
– Cruz
- 2002
|
|
12
|
Nonrecursive tilings of the plane
– Hanf
- 1974
|
|
11
|
Risk-Neutral Valuation: Pricing and Hedging of Financial Derivatives
– Bingham, Kiesel
- 2004
|
|
10
|
Committee on Banking Supervision, 2001, The New Basel Capital Accord, consultative document
– Basel
|
|
8
|
The complexity of problems concerning graphs with regularities
– Wagner
- 1984
|
|
6
|
Saddlepoint approximation of CreditRisk
– Gordy
- 2002
|
|
6
|
2001, Measuring and Managing Operational Risk
– Marshall
- 2001
|
|
5
|
Parameterized Complexity Theory
– Downey
- 1999
|
|
5
|
Rethinking risk-adjusted returns, in
– Lehrbass
- 1999
|
|
5
|
Computational Complexity
– Papamiditriou
- 1994
|
|
5
|
A hybrid genetic-quantitative method for riskreturn optimisation of credit portfolios, Quantitative Methods in Finance 2001 conference abstracts
– Seese
|
|
5
|
Large grids and local information flow as a reason for high complexity
– Schlottmann
- 2002
|
|
5
|
2001, Structural reasons for high complexity: A survey on results and problems, working paper
– Seese
- 2001
|
|
4
|
Axiomatising tree-interpretable structures
– Blumensath
- 2002
|
|
4
|
Graph classes: A survey
– unknown authors
|
|
4
|
On Cox processes and credit risky securities, Review of Derivatives Research
– Lando
- 1998
|
|
4
|
The complexity of compacting hierarchically specified layouts of integrated circuits
– Lengauer
- 1982
|
|
3
|
2000: ‘The risk profile problem for stock portfolio optimization’ (extended abstract) STOC 2000
– Kao, Nolte
- 1993
|
|
3
|
Operational Risk
– King
- 2001
|
|
3
|
Loan portfolio value
– Vasicek
- 2002
|
|
2
|
Hybrid multi-objective evolutionary computation of constrained downside risk-return efficient sets for credit portfolios’, presented at Computing in Economics and Finance 2002 conference, Aix-en-Provence, France, full paper: www.cepremap.ens.fr/sce2002/pa
– Seese
|
|
2
|
The Key to Risk Management
– Tschoegl
- 1976
|
|
2
|
Limiting loan loss probability distribution
– Vasicek
- 1991
|
|
1
|
Towards support for complexity in mechanical products and processes
– Barnes
- 2000
|
