Statistical Methods in Finance 2025

Portfolio Optimization using (Stochastic) Fuzzy Dynamic Programming

By:Pavan Saxena
IIT, Kanpur

In this study, problem of optimal portfolio allocation across multi-time periods is addressed. It is the process of determining the optimal combination of assets and their proportions with the objective of reducing risk and increasing profit in an investment. This model offers a steady state optimal asset allocation policy for a given portfolio for the investor across time-periods. As it is a multi-stage process, an attempt is being made to develop a stochastic dynamic programming model. Random nature of returns of assets was assumed to prespecified (for ease of computation). Two SDP models have been formulated - (1) One where only random nature of assets is considered and system performance measure (SPM) was based on the Markowitz mean-variance model which was eventually optimized as part of the SDP model. (2) In the second SDP model, responses of the investors/portfolio managers to portfolio returns and portfolio risks were treated as fuzzy sets and a combined fuzzy decision model was formulated as SPM which was eventually maximized as part of the SDP model. Demonstrated both the models with the sample historical weekly returns data of few stocks.