Optimal investment and consumption for financial markets with jumps under transaction costs

Sergei Egorov () and Serguei Pergamenchtchikov ()
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Sergei Egorov: Normandie Univ, LMRS UMR 6085
Serguei Pergamenchtchikov: Normandie Univ, LMRS UMR 6085

Finance and Stochastics, 2024, vol. 28, issue 1, No 4, 123-159

Abstract: Abstract We consider a portfolio optimisation problem for financial markets described by semimartingales with independent increments and jumps defined through Lévy processes. First, for power utility functions, we show a corresponding verification theorem and then find optimal consumption/investment strategies in an explicit form. Moreover, on the basis of the strategies constructed using the Leland–Lépinette approach, we develop an asymptotic optimal investment and consumption method for financial markets with proportional transaction costs when the number of portfolio revisions tends to infinity. Finally, we provide Monte Carlo simulations to numerically illustrate the obtained results in practice.

Keywords: Financial markets; Optimal investment/consumption problem; Stochastic control; Dynamic programming; Hamilton–Jacobi–Bellman equation; 91G10; 91G80; 93E20 (search for similar items in EconPapers)
JEL-codes: G11 G23 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s00780-023-00521-1

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