Many retirees are anxious about how much they can spend from their retirement assets each year and avoid later running out of funds. I know the feeling, as I have been there myself. Many years ago, I unexpectedly faced early retirement.

There were some investments, a pension, and future Social Security. But how much could I spend each year? Could I keep on living as I had been, or did I need to undertake some serious retrenchment?

Unlike most in such a predicament, I should have known the answer. Earlier, I had been a financial economist as a tenured professor at the University of California, Berkeley. In fact, at that time I published a paper in the American Economic Review with an academic solution to such a problem. The title was, “Lifetime Portfolio Selection in Continuous Time for a Multiplicative Class of Utility Functions.”

My experience, however, had not just been academic. I also had practical experience as a business economist. For 10 years I headed up the economics area at a New York bank.

None of this experience, however, seemed of much help. I had no clue as to whether I needed to undertake some serious retrenchment, or whether I could continue living as I had been. But if I didn’t know the answer, presumably I wasn’t the only one. Finding an answer was clearly a worthy topic for some serious research.

If I had known how long it would take I am sure I would have never started. And as usual almost all of the work ended up on the cutting room floor. Nevertheless, I believe that I have now come up with the answer I was looking for many years ago.

The solution is to obtain optimal limits on the amount that can be withdrawn each year. These limits depend on the remaining value of the assets at that time and the longest that additional withdrawals might be required. This solution applies not only to individuals making withdrawals over retirement, but also to the management of the assets in a trust. This is a trust for which the beneficiary might be an individual of any age or an organization.

An overview of the solution based on finding optimal limits for the drawdowns that can be made at any time is provided in a paper at this site. This paper is called, ”Optimal Wealth Drawdowns”. It is available by clicking on Decumulation.

I have also written a book that applies this system to various issues of drawing down assets over retirement. This book is called: The Retrenchment Rule: When It’s Too Late to Save More for Retirement. It is available on Amazon.

The Contents and Chapter 1 of the book are also available at this site. This introductory chapter applies the system using as an example annual returns that were actually realized in the past on investments in the U. S.. These results are compared to alternatives that might have been used to drawdown investments. This introductory chapter also contains a brief chapter-by-chapter summary of the book. The Contents and Chapter 1 of the book are available by clicking on Book and Chapter 1.

Many are not ready to retire, and are in the process of accumulating assets for that purpose. A paper at this site uses simulated investment returns to develop efficient strategies for accumulating assets for retirement or other purposes. This paper is called, “Efficient Wealth Accumulation”. It is available by clicking on Accumulation.

Further details of my background can be found in Biography. Earlier papers I have written on retirement and other topics are given in Papers. If you have any questions or comments about items at this site please email me at Contact.

## Motivation

Many retirees are anxious about how much they can spend from their retirement assets each year and avoid later running out of funds. I know the feeling, as I have been there myself. Many years ago, I unexpectedly faced early retirement.

There were some investments, a pension, and future Social Security. But how much could I spend each year? Could I keep on living as I had been, or did I need to undertake some serious retrenchment?

Unlike most in such a predicament, I should have known the answer. Earlier, I had been a financial economist as a tenured professor at the University of California, Berkeley. In fact, at that time I published a paper in the

American Economic Reviewwith an academic solution to such a problem. The title was, “Lifetime Portfolio Selection in Continuous Time for a Multiplicative Class of Utility Functions.”My experience, however, had not just been academic. I also had practical experience as a business economist. For 10 years I headed up the economics area at a New York bank.

None of this experience, however, seemed of much help. I had no clue as to whether I needed to undertake some serious retrenchment, or whether I could continue living as I had been. But if I didn’t know the answer, presumably I wasn’t the only one. Finding an answer was clearly a worthy topic for some serious research.

If I had known how long it would take I am sure I would have never started. And as usual almost all of the work ended up on the cutting room floor. Nevertheless, I believe that I have now come up with the answer I was looking for many years ago.

The solution is to obtain optimal limits on the amount that can be withdrawn each year. These limits depend on the remaining value of the assets at that time and the longest that additional withdrawals might be required. This solution applies not only to individuals making withdrawals over retirement, but also to the management of the assets in a trust. This is a trust for which the beneficiary might be an individual of any age or an organization.

An overview of the solution based on finding optimal limits for the drawdowns that can be made at any time is provided in a paper at this site. This paper is called, ”Optimal Wealth Drawdowns”. It is available by clicking on Decumulation.

I have also written a book that applies this system to various issues of drawing down assets over retirement. This book is called:

The Retrenchment Rule: When It’s Too Late to Save More for Retirement.It is available on Amazon.The Contents and Chapter 1 of the book are also available at this site. This introductory chapter applies the system using as an example annual returns that were actually realized in the past on investments in the U. S.. These results are compared to alternatives that might have been used to drawdown investments. This introductory chapter also contains a brief chapter-by-chapter summary of the book. The Contents and Chapter 1 of the book are available by clicking on Book and Chapter 1.

Many are not ready to retire, and are in the process of accumulating assets for that purpose. A paper at this site uses simulated investment returns to develop efficient strategies for accumulating assets for retirement or other purposes. This paper is called, “Efficient Wealth Accumulation”. It is available by clicking on Accumulation.

Further details of my background can be found in Biography. Earlier papers I have written on retirement and other topics are given in Papers. If you have any questions or comments about items at this site please email me at Contact.