Dependence Properties of Exit Times with Applications to Risk Management

We investigate the dependence structure of d -dimensional Ito processes which are not necessarily timehomogeneous. Sufficient conditions are given which imply that the processes are associated, i.e. show a certain kind of positive dependence. We also prove that associated processes have associated hitting times. Some applications in risk management are given.

[1]  Risk management in credit risk portfolios with correlated assets , 2002 .

[2]  Alfred Müller,et al.  Dependence properties and comparison results for Lévy processes , 2008, Math. Methods Oper. Res..

[3]  L. Pitt,et al.  Diffusion equation techniques in stochastic monotonicity and positive correlations , 1991 .

[4]  Jan Bergenthum,et al.  Comparison of semimartingales and Lévy processes , 2007 .

[5]  Y. L. Tong The multivariate normal distribution , 1989 .

[6]  L. Rüschendorf On a Comparison Result for Markov Processes , 2008 .

[7]  N. Bäuerle,et al.  Stochastic Orders and Risk Measures: Consistency and Bounds , 2006 .

[8]  R. Szekli Stochastic Ordering and Dependence in Applied Probability , 1995 .

[9]  Richard E. Barlow,et al.  Statistical Theory of Reliability and Life Testing: Probability Models , 1976 .

[10]  Michel Denuit,et al.  Does Positive Dependence between Individual Risks Increase Stop-Loss Premiums? , 2001 .

[11]  B. Øksendal,et al.  Applied Stochastic Control of Jump Diffusions , 2004, Universitext.

[12]  A. Müller,et al.  Comparison Methods for Stochastic Models and Risks , 2002 .

[13]  N. Ebrahimi On the Dependence Structure of Certain Multi-dimensional Ito Processes and Corresponding Hitting Times , 2002 .

[14]  Susan A. Murphy,et al.  Monographs on statistics and applied probability , 1990 .

[15]  T. Liggett Interacting Particle Systems , 1985 .

[16]  D. Walkup,et al.  Association of Random Variables, with Applications , 1967 .