Pré-Publication, Document De Travail Année : 2020

Optimal investment and consumption for financial markets with jumps

Résumé

We consider a portfolio optimization problem for financial markets described by exponential Lévy processes with jumps. For this problem we obtain and study the Hamilton-Jacobi-Bellman (HJB) equation which is an integral and partial differential equation of the second order. For this problem we show the corresponding verification theorem and construct the optimal consumption/investment strategies. For the power utility function for find the optimal strategies in the explicit form. Finally, we do the Monte Carlo simulations to illustrate numerically the obtained theoretical results.

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Dates et versions

hal-02422880 , version 1 (23-12-2019)
hal-02422880 , version 2 (24-06-2020)

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  • HAL Id : hal-02422880 , version 2

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Sergei Egorov, Serguei Pergamenshchikov. Optimal investment and consumption for financial markets with jumps. 2020. ⟨hal-02422880v2⟩
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