Handbook On Optimal Growth 1

Handbook on Optimal Growth 1

The problem of e?cient or optimal allocation of resources is a fundamental concern of economic analysis. The theory of optimal economic growth can be viewedasanaspectofthiscentraltheme,whichemphasizesingeneraltheissues arising in the allocation of resources over an in?nite time horizon, and in p- ticular the consumption-investment decision process in models in which there is no natural ”terminal date”. This broad scope of ”optimal growth theory” is one which has evolved over time, as economists have discovered new interp- tations of its central results, as well as new applications of its basic methods. The purpose of this handbook is to provide surveys of some signi?cant results of the theory of optimal growth,as well as the techniques of dynamic optimi- tion theory on which they are based. Armed with the results and methods of this theory, a researcher should be in an advantageous position to apply these versatile methods of analysis to new issues in the area of dynamic economics, as well as to contribute to the further development of the mathematical te- niques of optimization over time. The survey included in this volume all have as a common starting point the seminal contribution of Frank Ramsey (1928).

Handbook of Optimal Growth

The Kelly Capital Growth Investment Criterion

This volume provides the definitive treatment of fortune's formula or the Kelly capital growth criterion as it is often called. The strategy is to maximize long run wealth of the investor by maximizing the period by period expected utility of wealth with a logarithmic utility function. Mathematical theorems show that only the log utility function maximizes asymptotic long run wealth and minimizes the expected time to arbitrary large goals. In general, the strategy is risky in the short term but as the number of bets increase, the Kelly bettor's wealth tends to be much larger than those with essentially different strategies. So most of the time, the Kelly bettor will have much more wealth than these other bettors but the Kelly strategy can lead to considerable losses a small percent of the time. There are ways to reduce this risk at the cost of lower expected final wealth using fractional Kelly strategies that blend the Kelly suggested wager with cash. The various classic reprinted papers and the new ones written specifically for this volume cover various aspects of the theory and practice of dynamic investing. Good and bad properties are discussed, as are fixed-mix and volatility induced growth strategies. The relationships with utility theory and the use of these ideas by great investors are featured.