HARA utility maximization in a Markov-switching bond–stock market. Issue 11 (2nd November 2017)

• Record Type: Journal Article
• Authors: Escobar, M.; Neykova, D.; Zagst, R.
• Is Part Of: Quantitative finance. Volume 17:Issue 11(2017)
• Page Start: 1715
• Page End: 1733
• Publication Date: 2017-11-02
• Subjects: Portfolio optimization -- Markov chains -- HARA utility -- Hamilton–Jacobi–Bellman equations; G11 -- C61; Finance -- Periodicals; Business mathematics -- Periodicals; Finance -- Mathematical models -- Periodicals; Investments -- Mathematics -- Periodicals; Economics -- Periodicals; Finances -- Modèles mathématiques -- Périodiques; 332.015118
• DOI: 10.1080/14697688.2017.1302600
• Languages: English
• ISSNs: 1469-7688

Abstract

Abstract: We present a flexible multidimensional bond–stock model incorporating regime switching, a stochastic short rate and further stochastic factors, such as stochastic asset covariance. In this framework we consider an investor whose risk preferences are characterized by the hyperbolic absolute risk-aversion utility function and solve the problem of optimizing the expected utility from her terminal wealth. For the optimal portfolio we obtain a constant-proportion portfolio insurance-type strategy with a Markov-switching stochastic multiplier and prove that it assures a lower bound on the terminal wealth. Explicit and easy-to-use verification theorems are proven. Furthermore, we apply the results to a specific model. We estimate the model parameters and test the performance of the derived optimal strategy using real data. The influence of the investor's risk preferences and the model parameters on the portfolio is studied in detail. A comparison to the results with the power utility function is also provided.