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Viscosity Solution of Mean‐Variance Portfolio Selection of a Jump Markov Process with No‐Shorting Constraints

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  • Moussa Kounta

Abstract

We consider the so‐called mean‐variance portfolio selection problem in continuous time under the constraint that the short‐selling of stocks is prohibited where all the market coefficients are random processes. In this situation the Hamilton‐Jacobi‐Bellman (HJB) equation of the value function of the auxiliary problem becomes a coupled system of backward stochastic partial differential equation. In fact, the value function V often does not have the smoothness properties needed to interpret it as a solution to the dynamic programming partial differential equation in the usual (classical) sense; however, in such cases V can be interpreted as a viscosity solution. Here we show the unicity of the viscosity solution and we see that the optimal and the value functions are piecewise linear functions based on some Riccati differential equations. In particular we solve the open problem posed by Li and Zhou and Zhou and Yin.

Suggested Citation

  • Moussa Kounta, 2016. "Viscosity Solution of Mean‐Variance Portfolio Selection of a Jump Markov Process with No‐Shorting Constraints," Journal of Applied Mathematics, John Wiley & Sons, vol. 2016(1).
    • Handle: RePEc:wly:jnljam:v:2016:y:2016:i:1:n:4543298
    DOI: 10.1155/2016/4543298
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    References listed on IDEAS

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    1. Merton, Robert C., 1972. "An Analytic Derivation of the Efficient Portfolio Frontier," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 7(4), pages 1851-1872, September.
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