Robust Optimal Portfolio Choice Under Markovian Regime-switching Model

Abstract

We investigate an optimal portfolio selection problem in a continuous-time Markov-modulated financial market when an economic agent faces model uncertainty and seeks a robust optimal portfolio strategy. The key market parameters are assumed to be modulated by a continuous-time, finite-state Markov chain whose states are interpreted as different states of an economy. The goal of the agent is to maximize the minimal expected utility of terminal wealth over a family of probability measures in a finite time horizon. The problem is then formulated as a Markovian regime-switching version of a two-player, zero-sum stochastic differential game between the agent and the market. We solve the problem by the Hamilton-Jacobi-Bellman approach.

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Correspondence to Robert J. Elliott.

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Elliott, R.J., Siu, T.K. Robust Optimal Portfolio Choice Under Markovian Regime-switching Model. Methodol Comput Appl Probab 11, 145–157 (2009). https://doi.org/10.1007/s11009-008-9085-3

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Keywords

  • Robust optimal portfolio
  • Utility maximization
  • Model uncertainty
  • Stochastic differential game
  • Change of measures

AMS 2000 Subject Classification

  • 91A15
  • 91A40
  • 91B28
  • 93E20