Super-Diffusive Noise Source in Asset Dynamics


Given an asset with value St, we revisit the Black and Scholes dynamics  when the driving noise ξt is a non-Gaussian super-diffusive stochastic process with variance of the type . This super-diffusive quadratic variance behavior, synthesizes a ballistic component which would occur in strongly fluctuating environments. When , the assets can, with high probability, be driven towards the bankruptcy . This extra dynamic feature significantly affects the management of an optimal portfolio. In this context, we focus on basic decisions like: 1) determine the optimal level to sell the asset; 2) determine how to balance a portfolio which incorporates such a high volatility asset; and 3) when facing incertitudes on the assets growth rate μ, construct an optimal adaptive portfolio control. In all mentioned cases and despite the presence of this highly non-Gaussian noise source, we are able to deliver simple exact and fully explicit optimal control rules.


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M. Hongler, "Super-Diffusive Noise Source in Asset Dynamics," Journal of Mathematical Finance, Vol. 3 No. 1, 2013, pp. 53-58. doi: 10.4236/jmf.2013.31004.

Conflicts of Interest

The authors declare no conflicts of interest.


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