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    Saddle points for maximin investment problems with observable but non-predictable parameters: solution via heat equation.

    168884_168884.pdf (160.4Kb)
    Access Status
    Open access
    Authors
    Dokuchaev, Nikolai
    Date
    2006
    Type
    Journal Article
    
    Metadata
    Show full item record
    Citation
    Dokuchaev, Nikolai. 2006. Saddle points for maximin investment problems with observable but non-predictable parameters: solution via heat equation. IMA Journal of Management Mathematics. 17 (3): pp. 257-276.
    Source Title
    IMA Journal of Management Mathematics
    DOI
    10.1093/imaman/dpi041
    ISSN
    1471-678X
    School
    Department of Mathematics and Statistics
    Remarks

    This is a pre-copy-editing, author produced PDF of an article accepted for publication in IMA Journal of Management Mathematics following peer review. The definitive publisher-authenticated version: Dokuchaev, Nikolai. 2006. Saddle points for maximin investmentproblems with observable but non-predictable parameters: solutionvia heat equation. IMA Journal of Management Mathematics. 17 (3): pp. 257-276. is available online at http://dx.doi.org/10.1093/imaman/dpi041

    URI
    http://hdl.handle.net/20.500.11937/41201
    Collection
    • Curtin Research Publications
    Abstract

    We study optimal investment problem for a market model where the evolution of risky assets prices is described by Itoˆs equations. The risk-free rate, the appreciation rates, and the volatility of the stocks are all random; they depend on a random parameter that is not adapted to the driving Brownian motion. The distribution of this parameter is unknown. The optimal investment problem is stated in a mazimin setting to ensure that a strategy is found such that the minimum of expected utility over all possible distributions of parameters is maximal. We show that a saddle point exists and can be found via solution of the standard one-dimensional heat equation with a Cauchy condition defined via one-dimensional minimization. This solution even covers models with unknown solution for a given distribution of the market parameters.

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