Portfolio decision with a quadratic utility and inflation risk (original) (raw)
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Intertemporal asset allocation strategies under inflationary risk
2006
A(τ): the Duffie-Kan coefficient (level term) (p. 49) A n (τ): the Duffie-Kan coefficient for the nominal bond model (p. 62) A r (τ): the Duffie-Kan coefficient for the real bond mode (p. 63) B(τ): the Duffie-Kan coefficient (linear term) (p. 49) B nr (τ), B rr (τ): the Duffie-Kan coefficient for the nominal bond model (p. 62) B rr (τ) :the Duffie-Kan coefficient for the real bond mode (p. 63) C t : nominal consumption at t (p. 25) c t : real consumption at t (p.35) F (X t): the drift coefficient for X t (p. 32) F t : the augmented natural filtration at t (p. 31) G(X t): the diffusion coefficient for X t (p. 32) g r (g π): the volatility parameter for r t (π t) (p. 62) I t : the price index at t (p31) J 0 (V 0 , R 0): the value function in the initial example (p. 25) J 1 (V 1 , R 1): the value function in the initial example (p. 25) J(t, T, v t , X t): the value function for the intertemporal asset allocation problem (p. 27) I would like to thank my first supervisor Professor Willi Semmler, who suggested the topic of this thesis, the intertemporal asset allocation problem, and advised the consideration of macroeconomic impacts on this problem, which has formed the guiding line of this thesis. Professor Semmler's comprehensive and balanced treatment of theoretical and empirical macroeconomics has had a remarkable influence on the structure of this thesis. I also want to express my deep gratitude to my second supervisor Professor Carl Chiarella in the School of Finance and Economics, at the University of Technology, Sydney (UTS). Many crucial points in this thesis, such as, the solution approach under inflation risk in Chapter 3, the no-arbitrage principle under inflation risk in Chapter 4, the second term structure models for modelling inflation-indexed bonds in Chapter 4 and the consideration of short-sale constraints for the intertemporal asset allocation problems in Chapter 6 were developed based upon ideas obtained in discussions with him. Some parts in the thesis have already appeared as working papers and have been submitted to journals for publication. I would also like to thank the critiques and comments from anonymous referees of Computational Economics on papers arising out of Section 4.3 and Chapter 6, which helped a lot to improve this thesis. Further thanks must be given to my colleagues at Bielefeld University and those at UTS, especially Dr. Wolfgang Lemke for many important comments on Section 4.3.3, Dr. Hing Hung for the discussion on technical details of the Kalman filter technique in Section 4.4.2, Evan Shellshear for the English wording, also
SSRN Electronic Journal, 2019
We consider a discrete-time optimal consumption and investment problem of an investor who is interested in maximizing his utility from consumption and terminal wealth subject to a random inflation in the consumption basket price over time. We consider two cases: (i) when the investor observes the basket price and (ii) when he receives only noisy signals on the basket price. We derive the optimal policies and show that a modified Mutual Fund Theorem consisting of three funds holds in both cases, as it does in the continuous-time setting. The compositions of the funds in the two cases are the same but in general the investor's allocations of his wealth into these funds differ.
Journal of Mathematical Finance, 2013
This paper examines optimal variational Merton portfolios (OVMP) with inflation protection strategy for a defined contribution (DC) Pension scheme. The mean and variance of the expected value of wealth for a pension plan member (PPM) are also considered in this paper. The financial market is composed of a cash account, inflation-linked bond and stock. The effective salary of the plan member is assumed to be stochastic. It was assumed that the growth rate of PPM's salary depends on some macroeconomic factors over time. The present value of PPM's future contribution was obtained. The sensitivity analysis of the present value of the contribution was established. The OVMP processes with inter-temporal hedging terms and inflation protection that offset any shocks to the stochastic salary of a PPM were established. The expected values of PPM's terminal wealth, variance and efficient frontier of the three classes of assets are obtained. The efficient frontier was found to be nonlinear and parabolic in shape. In this paper, we allow the stock price to be correlated to inflation risk index, and the effective salary of the PPM is correlated to inflation and stock risks. This will enable PPMs to determine extents of the stock market returns and risks, which can influence their contributions to the scheme.