Abstract
The question of post-retirement optimal consumption and investment of retirement savings is addressed. This problem has received considerably less attention than that of how to invest for retirement. With the increase in life span and an increase in private pension funds, a retiree has considerable flexibility in both how to consume and how to continue to invest their retirement funds. Our interest is in developing a platform that allows a wide variety of behavioural aspects to be modeled and also enables explicit constraints to be imposed. To enable the flexibility we seek it is necessary to model the problem as a large-scale nonlinearly constrained optimization problem, which is solved using a sequential quadratic programming algorithm. Fortunately, modern optimization methods are now sufficiently powerful as to enable solving such problems. A key point is that, though the problems are large, they have a rich structure.
Problems in this class have been addressed assuming that an investor is rational in the sense that when making financial decisions the preference relation of the investor satisfies all the axioms of choice. Research in behavioural science indicates that not all financial decisions of an average person satisfy the axioms of choice. The algorithm we propose enables the problem to be solved for a user-specified utility function that does not satisfy all the axioms of choice.
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Gupta, A., Murray, W. How to Spend and Invest Retirement Savings. Annals of Operations Research 124, 205–224 (2003). https://doi.org/10.1023/B:ANOR.0000004770.40172.16
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DOI: https://doi.org/10.1023/B:ANOR.0000004770.40172.16