Large deviations for interacting Bessel-like processes and applications to systemic risk

We establish a process level large deviation principle for systems of interacting Bessel-like diffusion processes. By establishing weak uniqueness for the limiting non-local SDE of McKean-Vlasov type, we conclude that the latter describes the process level hydrodynamic limit of such systems and obtain a propagation of chaos result. This is the first instance of results of this type in the context of interacting diffusion processes under explicit assumptions on the coefficients, where the diffusion coefficients are allowed to be both non-Lipschitz and degenerate. In the second part of the paper, we explain how systems of this type naturally arise in the study of stability of the interbank lending system and describe some financial implications of our results.

[1]  A. Dembo,et al.  Large Deviations for Diffusions Interacting Through Their Ranks , 2012, 1211.5223.

[2]  Mykhaylo Shkolnikov.  Large volatility-stabilized markets , 2011, 1102.3461.

[3]  P. Dupuis,et al.  Large deviation properties of weakly interacting processes via weak convergence methods , 2010, 1009.6030.

[4]  Xiongzhi Chen.  Brownian Motion and Stochastic Calculus , 2008 .

[5]  Richard Mateosian,et al.  Old and New , 2006, IEEE Micro.

[6]  M. Yor,et al.  A survey and some generalizations of Bessel processes , 2003 .

[7]  M. Zani.  Large deviations for squared radial Ornstein–Uhlenbeck processes , 2002 .

[8]  R. Bass,et al.  Degenerate stochastic differential equations with Hölder continuous coefficients and super-Markov chains , 2002 .

[9]  M. Yor,et al.  The importance of strictly local martingales; applications to radial Ornstein–Uhlenbeck processes , 1999 .

[10]  École d'été de probabilités de Saint-Flour,et al.  Ecole d'été de probabilités de Saint-Flour XIX, 1989 , 1991 .

[11]  A. Sznitman.  Topics in propagation of chaos , 1991 .

[12]  M. Yor,et al.  Continuous martingales and Brownian motion , 1990 .

[13]  J. Gärtner.  On the McKean‐Vlasov Limit for Interacting Diffusions , 1988 .

[14]  J. Gärtner,et al.  Large deviations from the mckean-vlasov limit for weakly interacting diffusions , 1987 .

[15]  Huang Zhiyuan,et al.  A COMPARISON THEOREM FOR SOLUTIONS OF STOCHASTIC DIFFERENTIAL EQUATIONS AND ITS APPLICATIONS , 1984 .

[16]  D. W. Stroock,et al.  Multidimensional Diffusion Processes , 1979 .