Abstract
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.
Highlights
The banking sector has been subject to constant changes in the economic environment over the past two decades
We examine the dynamics of myopic optimal portfolio and the intertemporal hedging demand portfolio of the optimal portfolio holdings
In this study we examined continuous time optimization incorporating inflation, assuming that the preference criterion is based on a modification of a monotone mean-variance functional introduced by Maccheroni et al [27]
Summary
The banking sector has been subject to constant changes in the economic environment over the past two decades. This article makes the following contributions to the literature: 1) Introducing banker’s provision capital risk process as a controllable diffusion process, we extend [31] analysis into robust portfolio allocation/management framework with inflation This allows the banker to deal with the issue of bank capital adequacy and risk management in an incomplete market within a stochastic dynamic setting. This empowers the banker to regulate his/her provision capital risk process by controlling the amount of wealth invested in the loan portfolio as well as the amount of wealth invested in the stock index.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
