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Portfolio management under drawdown constraint in discrete-time financial markets

Part of: Mathematical finance

Published online by Cambridge University Press:  09 December 2022

Diego Hernández-Bustos  and
Daniel Hernández-Hernández
Diego Hernández-Bustos*
Affiliation:
Instituto de Investigaciones en Matemáticas Aplicadas y Sistemas U.N.A.M.
Daniel Hernández-Hernández*
Affiliation:
Research Center for Mathematics (CIMAT)
*
*Postal address: Circuito Escolar 3000, C.U., Ciudad de México, Coyoacán, 04510, México. Email address: diego.hernandez@iimas.unam.mx
**Postal address: Apartado postal 402, Guanajuato, GTO, 36000, México. Email address: dher@cimat.mx
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Abstract

Considering a representative agent in the market, we study the long-term optimal investment problem in a discrete-time financial market, introducing a set of restrictions in the admissible strategies. The drawdown constraints limit the size of possible losses of the portfolio and impose a floor-based performance measure. The optimal growth rate is characterized, and under suitable hypotheses it is proved that an optimal strategy exists. The approach to solving this problem is based on dynamic programming techniques and a fixed point argument adapted from the theory of Markov decision processes.

Keywords

Risk-sensitive controloptimal growth ratedrawdown constraint

MSC classification

Secondary: 91G10: Portfolio theory
Type
Original Article
Information
Journal of Applied Probability , Volume 60 , Issue 1 , March 2023 , pp. 127 - 147
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Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of Applied Probability Trust

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