Physics of Risk

Working on Physics of Risk is very interesting and useful experience. This experience provides valuable insights into the mechanics behind various complex systems, well modeled by macroscopic models. Using our experience we are able to obtain qualitative and quantitative agreements between varying models. In our newest publication 1 we have used one-step formalism 2 to obtain macroscopic treatments of Kirman model 3.

One part of this work is dedicated to the transition between original Kirman model (was previously discussed on this website) and stochastic Kirman’s model for return. Previously Alfarano et al. have attempted to obtain stochastic treatment of Kirman’s model, though they stopped after obtaining stochastic model for population fraction 4 (we have discussed their derivation on Physics of Risk). We derive analogous equation for population fraction by using one-step formalism and further use Ito variable substitution formula 5 to obtain stochastic model for return.

Another important part of this work is dedicated to Bass diffusion model 6 (this model and it’s variations were discussed on Models of business section of this website), which we find to be ideologically similar to the very same Kirman’s model. Indeed as we show in 1, Bass diffusion is actually analogous to unidirectional Kirman’s model (see discussion on our website).

References

• V. Daniunas, V. Gontis, A. Kononovicius. Agent-based versus macroscopic modeling of competition and business processes in economics. ICCGI 2011, The Sixth International Multi-Conference on Computing in the Global Information Technology, pp. 84-88. Luxembourg, 2011. Note: Received IARIA Best Paper Award (see http://www.iaria.org/conferences2011/AwardsICCGI11.html). thinkmind: iccgi_2011_4_40_10188. arXiv: 1104.2895 [physics.soc-ph]. Download.
• N. G. van Kampen. Stochastic process in Physics and Chemistry. North Holland, Amsterdam, 2007.
• A. P. Kirman. Ants, rationality and recruitment. Quarterly Journal of Economics 108, 1993, pp. 137-156.
• S. Alfarano, T. Lux, F. Wagner. Estimation of Agent-Based Models: The Case of an Asymmetric Herding Model. Computational Economics 26 (1), 2005, pp. 19-49.
• C. W. Gardiner. Handbook of stochastic methods. Springer, Berlin, 2009.
• F. M. Bass. A New Product Growth Model for Consumer Durables. Management Science 15, 1969, pp. 215-227.