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Peer-reviewedCC BY 4.0Finance and Stochastics

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

  • Sergei Egorov
  • Serguei Pergamenchtchikov
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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.

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Cite

BibTeXRIS
BibTeX
@article{egorov2026optimal,
  title = {{Optimal investment and consumption for financial markets with jumps under transaction costs}},
  author = {Sergei Egorov and Serguei Pergamenchtchikov},
  journal = {Finance and Stochastics},
  year = {2026},
  month = sep,
  doi = {10.1007/s00780-023-00521-1},
  url = {https://hal.science/hal-05723577v1},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Optimal investment and consumption for financial markets with jumps under transaction costs
AU  - Sergei Egorov
AU  - Serguei Pergamenchtchikov
PY  - 2026
DA  - 2026/09/07
JO  - Finance and Stochastics
DO  - 10.1007/s00780-023-00521-1
UR  - https://hal.science/hal-05723577v1
AB  - 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.
SN  - 0949-2984
SN  - 1432-1122
ER  -