MULTI-PERIOD STOCHASTIC PROGRAMMING MODEL FOR STATE-DEPENDENT ASSET ALLOCATION WITH CVAR

• Published in: Journal of the Operations Research Society of Japan Vol. 58; no. 4; pp. 307 - 329
• Main Authors: Hirano, Shinya, Hibiki, Norio
• Format: Journal Article
• Language: English
• Published: Tokyo The Operations Research Society of Japan 2015; Nihon Opereshonzu Risachi Gakkai, Operations Research Society of Japan
• Subjects: Asset allocation; Computer simulation; finance; Investment policy; Investment strategy; Mathematical problems; multi-period asset allocation; Optimization; Risk assessment; Sensitivity analysis; simulation; Step functions; Stochastic models; stochastic optimization; Studies
• ISSN: 0453-4514; 2188-8299; 1878-6871
• DOI: 10.15807/jorsj.58.307

We need to solve a multi-period optimization problem to decide dynamic investment policies under various practical constraints. Hibiki (2001, 2003, 2006) develop a hybrid model where conditional decisions can be made in a simulation approach, and investment proportions are expressed by a step function of the amount of wealth. In this paper, we introduce an idea of a state-dependent function into the hybrid model as well as Takaya and Hibiki (2012). At first, we define the state-dependent function form for a multiple asset allocation problem with CVaR (Conditional Value at Risk) using the hybrid model, and we clarify that the function form is V-shaped and kinked at the VaR point. We propose a piecewise linear model with the V-shaped function to solve the multi-period and state-dependent asset allocation problem. We solve a three-period problem for five assets, and compare the piecewise linear model with the hybrid model. We conduct the sensitivity analysis for different risk averse coefficients and autocorrelations to examine the characteristics of the model.