Optimal DC pension investment with square-root factor processes under stochastic income and inflation risks
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Optimal DC pension investment with square-root factor processes under stochastic income and inflation risks. / Zhang, Yumo.
I: Optimization, Bind 72, Nr. 12, 2023, s. 2951 - 2988.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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TY - JOUR
T1 - Optimal DC pension investment with square-root factor processes under stochastic income and inflation risks
AU - Zhang, Yumo
N1 - Publisher Copyright: © 2022 Informa UK Limited, trading as Taylor & Francis Group.
PY - 2023
Y1 - 2023
N2 - This paper studies optimally defined contribution (DC) pension investment problems under the expected utility maximization framework with stochastic income and inflation risks. The member has access to a financial market consisting of a risk-free asset (money account), an inflation-indexed bond, and a stock. The market price of volatility risk is assumed to depend on an affine-form, Markovian, square-root factor process, while the return rate and the volatility of the stock are possibly given by general non-Markovian, unbounded stochastic processes. This financial framework recovers the Black–Scholes model, constant elasticity of variance (CEV) model, Heston model, 3/2 model, 4/2 model, and some non-Markovian models as exceptional cases. To tackle the potentially non-Markovian structures, we adopt a backward stochastic differential equation (BSDE) approach. By solving the associated BSDEs explicitly, closed-form expressions for the optimal investment strategies and optimal value functions are obtained for the power, logarithmic, and exponential utility functions. Moreover, explicit solutions to some special cases of our portfolio model are provided. Finally, numerical examples are provided to illustrate the effects of model parameters on the optimal investment strategies under the 4/2 model.
AB - This paper studies optimally defined contribution (DC) pension investment problems under the expected utility maximization framework with stochastic income and inflation risks. The member has access to a financial market consisting of a risk-free asset (money account), an inflation-indexed bond, and a stock. The market price of volatility risk is assumed to depend on an affine-form, Markovian, square-root factor process, while the return rate and the volatility of the stock are possibly given by general non-Markovian, unbounded stochastic processes. This financial framework recovers the Black–Scholes model, constant elasticity of variance (CEV) model, Heston model, 3/2 model, 4/2 model, and some non-Markovian models as exceptional cases. To tackle the potentially non-Markovian structures, we adopt a backward stochastic differential equation (BSDE) approach. By solving the associated BSDEs explicitly, closed-form expressions for the optimal investment strategies and optimal value functions are obtained for the power, logarithmic, and exponential utility functions. Moreover, explicit solutions to some special cases of our portfolio model are provided. Finally, numerical examples are provided to illustrate the effects of model parameters on the optimal investment strategies under the 4/2 model.
KW - backward stochastic differential equation
KW - Expected utility maximization
KW - inflation risk
KW - square-root factor process
KW - stochastic income
UR - http://www.scopus.com/inward/record.url?scp=85130704000&partnerID=8YFLogxK
U2 - 10.1080/02331934.2022.2081083
DO - 10.1080/02331934.2022.2081083
M3 - Journal article
AN - SCOPUS:85130704000
VL - 72
SP - 2951
EP - 2988
JO - Optimization
JF - Optimization
SN - 0233-1934
IS - 12
ER -
ID: 309111282