A0786
Title: Duality in optimal consumption-investment problems with alternative data
Authors: Kexin Chen - The Hong Kong Polytechnic University (Hong Kong) [presenting]
Hoi Ying Wong - The Chinese University of Hong Kong (Hong Kong)
Abstract: An optimal consumption-investment problem is investigated when the expected return of a risky asset is modulated by a hidden Markov chain, representing different unobserved economic regimes. While the classical approach estimates the hidden state from historical asset prices, the technology nowadays enables investors to make decisions using alternative data as a complementary source of observations. Social media commentary, expert opinion, pandemic data, and GPS data are a part of ``alternative data'', that is, data that originate outside of the standard repertoire of market data but are considered useful for predicting stock trends. We model the asset price and alternative data series as a diffusion process and a marked point process, respectively. We, therefore, incorporate the alternative data into the filtering process that extends the Wonham filter to a degenerate jump diffusion with L\'{e}vy type jumps. This introduces a remarkable analytical challenge to the corresponding stochastic control problem. We resolve the difficulties with a novel duality approach. We link the dual problem to an optimization problem over a set of equivalent local martingale measures and devise a methodology to obtain the optimal solution with the alternative data filtering technique. We show that the dual problem admits a unique smooth solution for hyperbolic absolute risk aversion (HARA) utility functions. In addition, we obtain an explicit feedback on optimal consumption-investment strategy.
