An explicit solution for optimal investment problems with autoregressive prices and exponential utility

Tom 42 / 2015

Sándor Deák, Miklós Rásonyi Applicationes Mathematicae 42 (2015), 379-401 MSC: Primary 93E20; Secondary 91G10. DOI: 10.4064/am2267-12-2015 Opublikowany online: 21 January 2016


We calculate explicitly the optimal strategy for an investor with exponential utility function when the price of a single risky asset (stock) follows a discrete-time autoregressive Gaussian process. We also calculate its performance and analyse it when the trading horizon tends to infinity. Dependence of the asymptotic performance on the autoregression parameter is determined. This provides, to the best of our knowledge, the first instance of a theorem linking directly the memory of the asset price process to the attainable satisfaction level of investors trading in the given asset.


  • Sándor DeákEötvös Loránd University
    Pázmány Péter sétány 1/C
    Budapest, Hungary
  • Miklós RásonyiAlfréd Rényi Institute of Mathematics
    Hungarian Academy of Sciences
    Reáltanoda utca 13-15
    Budapest, Hungary

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