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R. C. Dalang and M.-O. Hongler, “The Right Time to Sell a Stock Whose Price Is Driven by Markovian Noise,” Annals of Applied Probability, Vol. 14, No. 4, 2004, pp. 2176-2201. doi:10.1214/105051604000000747

has been cited by the following article:

• TITLE: Super-Diffusive Noise Source in Asset Dynamics

  AUTHORS: Max-Olivier Hongler

  KEYWORDS: Black-Scholes Dynamics; Non-Gaussian Volatility; Optimal Stopping; Adaptive Optimal Control; Exact Solutions

  JOURNAL NAME: Journal of Mathematical Finance, Vol.3 No.1, February 26, 2013

  ABSTRACT: Given an asset with value St, we revisit the Black and Scholes dynamicswhen the driving noise ξtis 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 asset’s 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.