TY - JOUR
T1 - The optimal mean variance problem with inflation
AU - Liu, Jingzhen
AU - Yiu, Ka Fai Cedric
AU - Bensoussan, Alain
PY - 2016/1
Y1 - 2016/1
N2 - The risk of ination is looming under the current low interest rate environment. Assuming that the investment includes a fixed interest asset and n risky assets under ination, we consider two scenarios: ination rate can be observed directly or through a noisy observation. Since the ination rate is random, all assets become risky. Under this circumstance, we formulate the portfolio selection problem and derive the efficient frontier by solving the associated HJB equation. We find that for a given expected portfolio return, investment at time t is linearly proportional to the price index level. Moreover, the risk for the real value of the portfolio is no longer minimal when all the wealth is put into the fixed interest asset. Finally, for the mutual fund theorem, two funds are needed now instead of the traditional single fund. If an ination linked bond can be included in the portfolio, the problem is reduced to the traditional mean variance problem with a risk-free and n + 1 risky assets with real returns.
AB - The risk of ination is looming under the current low interest rate environment. Assuming that the investment includes a fixed interest asset and n risky assets under ination, we consider two scenarios: ination rate can be observed directly or through a noisy observation. Since the ination rate is random, all assets become risky. Under this circumstance, we formulate the portfolio selection problem and derive the efficient frontier by solving the associated HJB equation. We find that for a given expected portfolio return, investment at time t is linearly proportional to the price index level. Moreover, the risk for the real value of the portfolio is no longer minimal when all the wealth is put into the fixed interest asset. Finally, for the mutual fund theorem, two funds are needed now instead of the traditional single fund. If an ination linked bond can be included in the portfolio, the problem is reduced to the traditional mean variance problem with a risk-free and n + 1 risky assets with real returns.
KW - HJB equation
KW - Ination
KW - Mean variance
KW - Partial information
UR - http://www.scopus.com/inward/record.url?scp=84948692427&partnerID=8YFLogxK
UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-84948692427&origin=recordpage
U2 - 10.3934/dcdsb.2016.21.185
DO - 10.3934/dcdsb.2016.21.185
M3 - 21_Publication in refereed journal
VL - 21
SP - 185
EP - 203
JO - Discrete and Continuous Dynamical Systems - Series B
JF - Discrete and Continuous Dynamical Systems - Series B
SN - 1531-3492
IS - 1
ER -