Long-term strategic asset allocation with inflation risk and regime switching

Long-term strategic asset allocation is an important problem in both finance and actuarial science. There are two key issues in long-term strategic asset allocation, namely, the presence of inflation risk and the impact of changes in (macro)-economic conditions on model dynamics. In this article, we take into account the two key issues in our model formulation and develop a quantitative model for long-term strategic asset allocation. A continuous-time, regime-switching market with the presence of inflation risk is considered. There are three tradeable assets in the market, namely, a fixed interest security, an ordinary share and an inflation-linked bond. We assume that the nominal rate of interest on the fixed interest security, the expected rate of return from the ordinary share and the appreciation rate of inflation are modulated by a continuous-time, finite-state, hidden Markov chain. The states of the chain represent different states of an economy. With knowledge about the price of the ordinary share and the price index level, an investor wishes to maximize the expected utility of real terminal wealth. By making use of the separation principle, we solve the optimal portfolio selection problem and the estimation problem independently. We derive a robust estimate of the hidden state of the chain and develop a robust, filter-based, EM algorithm for the on-line recursive estimates of the key model parameters.