State Space Approach to Adaptive Fuzzy Modeling for Financial Investment

This paper proposes a new adaptive learning framework for fuzzy system under dynamically changing environment. Especially, a state space model with filtering algorithm, traditionally used for the estimation of unobservable state variables, is applied to online non-linear optimization problems by reinterpreting control variables and objective function as state variables and observation model, respectively. Our proposed methodology substantially improves the flexibility of the objective function, which enables to construct the adaptive fuzzy system achieving arbitrarily designed user's objective. In addition, time-series structure is actively introduced into the parameter transition, whose proper modeling is expected to enhance the performance. Particularly, the introduction of mean-reversion process makes it possible to adaptively learn model parameters around specific predetermined levels obtained by existing learning methodologies. As an application of adaptive learning fuzzy system for financial investment, the current work focuses on the construction of the target return replication portfolio. Concretely, the target return is specified as zero floored market index considering investor's great demand to construct a portfolio with restricted downside risk. The validity of our framework is shown by out-of-sample numerical experiments with the data of well-known high liquid instruments such as S&P500 and TOPIX, which indicates the robustness and reliability of our proposed method in practice.