Sub- and Supersolution Approach to Accuracy Analysis of Portfolio Optimization Asymptotics in Multiscale Stochastic Factor Markets

Jean Pierre Fouque, Ruimeng Hu, Ronnie Sircar

Research output: Contribution to journalArticlepeer-review

Abstract

The problem of portfolio optimization when stochastic factors drive returns and volatilities has been studied in previous works by the authors. In particular, they proposed asymptotic approximations for value functions and optimal strategies in the regime where these factors are running on both slow and fast timescales. However, the rigorous justification of the accuracy of these approximations has been limited to power utilities and a single factor. In this paper, we provide an accurate analysis for cases with general utility functions and two timescale factors by constructing sub- and supersolutions to the fully nonlinear problem so that their difference is at the desired level of accuracy. This approach will be valuable in various related stochastic control problems.

Original languageEnglish (US)
Pages (from-to)109-128
Number of pages20
JournalSIAM Journal on Financial Mathematics
Volume13
Issue number1
DOIs
StatePublished - 2022

All Science Journal Classification (ASJC) codes

  • Numerical Analysis
  • Finance
  • Applied Mathematics

Keywords

  • portfolio optimization
  • rigorous asymptotics
  • stochastic volatility
  • subsolution
  • supersolution
  • utility maximization

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