The talk DOES NOT purport to show how gambling on horse races and playing the stock market can lead to bankruptcy. Rather, it is concerned with common elements in the three activities--horse races ( gambling in general ), stock market , and operation of a commercial company. The common element is : What is the fraction f of the capital available at any time should one reinvest.? In the talk we derive the optimal and critical fractions. We show that if the fraction invested is greater than the critical one, ruin or bankruptcy is certain. On the other hand, if the fraction of capital invested is less than the critical value, there is a mathematical guarantee that the investor will not be ruined. The optimal fraction is called the Kelly fraction. It is the one which maximizes the expected exponential rate of increase of the capital. The talk uses very elementary mathematics--there is just one integral and two derivatives. So, most of the staff and students should not have too much difficulty in understanding the major part of the talk.
 

Convenor:Kais Hamza