TY - JOUR
T1 - Simulating Portfolio Decisions under Uncertainty When the Risky Asset and Short Rate Are Modulated by an Inhomogeneous and Asset-Dependent Markov Chain
AU - Vallejo-Jiménez, Benjamín
AU - Venegas-Martínez, Francisco
AU - De la Torre-Torres, Oscar V.
AU - Álvarez-García, José
N1 - Publisher Copyright:
© 2022 by the authors.
PY - 2022/8
Y1 - 2022/8
N2 - This paper aims to simulate portfolio decisions under uncertainty when the diffusion parameters of the risky asset and short rate paid for a bond are both modulated by a time-inhomogeneous Markov chain, with transition probabilities dependent on states, time, and asset prices. To do this, we first found closed-form solutions of the corresponding utility-maximization problem, which solves a rational consumer that makes portfolio and consumption decisions by using the corresponding infinitesimal generator associated with the Markov chain. Subsequently, as an illustration of the theoretical results obtained, several scenarios were simulated for the Mexican case. The expected economic policy was inferred from announced monetary policy decisions regarding the reference rate and possible changes in trend due to the lack of fiscal stimuli. Under this framework, states were defined from the current and expected economic policies, and transition probabilities were expressed in terms of the ratio between the prices of the risky asset and the bond. It should be noted, as far as the authors know, that no analytical solutions are known in the literature for the case of Markov-modulated time-inhomogeneous chains with transition probabilities that, themselves, are stochastic processes.
AB - This paper aims to simulate portfolio decisions under uncertainty when the diffusion parameters of the risky asset and short rate paid for a bond are both modulated by a time-inhomogeneous Markov chain, with transition probabilities dependent on states, time, and asset prices. To do this, we first found closed-form solutions of the corresponding utility-maximization problem, which solves a rational consumer that makes portfolio and consumption decisions by using the corresponding infinitesimal generator associated with the Markov chain. Subsequently, as an illustration of the theoretical results obtained, several scenarios were simulated for the Mexican case. The expected economic policy was inferred from announced monetary policy decisions regarding the reference rate and possible changes in trend due to the lack of fiscal stimuli. Under this framework, states were defined from the current and expected economic policies, and transition probabilities were expressed in terms of the ratio between the prices of the risky asset and the bond. It should be noted, as far as the authors know, that no analytical solutions are known in the literature for the case of Markov-modulated time-inhomogeneous chains with transition probabilities that, themselves, are stochastic processes.
KW - Markov regime switching
KW - diffusion process
KW - portfolio simulation
KW - short rate
UR - http://www.scopus.com/inward/record.url?scp=85137392232&partnerID=8YFLogxK
U2 - 10.3390/math10162926
DO - 10.3390/math10162926
M3 - Artículo
AN - SCOPUS:85137392232
SN - 2227-7390
VL - 10
JO - Mathematics
JF - Mathematics
IS - 16
M1 - 2926
ER -