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Optimal portfolio for a small investor in a market model with discontinuous prices

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Abstract

A consumption-investment problem is considered for a small investor in the case of a market model in which prices evolve according to a stochastic equation with a jump-process component. The techniques we use include the martingale representation theorem, Lagrange multiplier methods, and Markovian methods for the resolution of stochastic differential equations. We establish a Black-Scholes formula.

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Authors and Affiliations

  1. E.N.S. de CACHAN, LA.M.M./C.M.L.A., 61 Avenue du Président Wilson, 94235, Cachan, Cedex, France

    Monique Jeanblanc-Picqué

  2. Département Maths-Info, Univérsité d'Orléans, B.P. 6759, 45067, Orléans Cedex 2, France

    Monique Pontier

Authors
  1. Monique Jeanblanc-Picqué
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  2. Monique Pontier
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Communicated by A. Bensoussan

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Jeanblanc-Picqué, M., Pontier, M. Optimal portfolio for a small investor in a market model with discontinuous prices. Appl Math Optim 22, 287–310 (1990). https://doi.org/10.1007/BF01447332

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  • DOI: https://doi.org/10.1007/BF01447332

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