Robust portfolio allocation for a bank under inflation

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In this study, we develop a robust portfolio allocation model for a bank in an incomplete market with inflation (a non-tradeable stochastic factor). The optimality criterion of the investments is established on a functional via a modified version of the monotone mean-variance preferences. An increase in anticipated inflation will increase the interest rate, while reducing the expected net stream of dollar receipts in the loan portfolio. Eventually whilst existing loans mature and are re-negotiated (at the higher interest rate), the interest rate is earned by the bank on existing loans are locked up. Under such explicit risk aggregation paradigm, we formulate this problem as a stochastic differential game (SDG) and apply the Hamilton-Jacobi-Bellman-Isaacs (HJBI)-equation to derive the optimal investment strategy. We discuss the dynamics of myopic optimal portfolio and the intertemporal hedging demand portfolio of the optimal portfolio holdings. We describe the dynamics of the total capital ratio under Basel III regulations. Finally, we show that our solution coincides with the solution to classical Markowitz optimization problem with risk aversion coefficient depends on stochastic factor. Our results confirm that the banker’s optimal holdings and the trade-off between holding a myopically optimal portfolio and intertemporal hedging demand are determined by the derivatives of marginal utility with respect to the state variable.
Original languageEnglish
Article number88738
Pages (from-to)3361-3394
Number of pages34
JournalTheoretical Economics Letters
Issue number15
Publication statusPublished - 26 Nov 2018

Bibliographical note

Copyright 2018 by author and Scientific Research Publishing Inc. Version archived for private and non-commercial use with the permission of the author/s and according to publisher conditions. For further rights please contact the publisher.


  • Basel III Capital Accord
  • Capital adequacy Ratio (CAR)
  • HJBI Equation
  • Monotone Preferences
  • Inflation
  • Stochastic Differential Game

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