Some Limit Theorems for the Portfolio Growth Rate
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Abstract
Let 0≤a1≤a2≤... be a sequence of fixed non-negative integers, the limit properties investment portfolio growth rate from an+1 to an+n are studied. By constructing a sequence of random variables with one parameter and bounded expectations, and using the Borel-Cantelli lemma, the limit theorems for the growth rate of any investment portfolio and the general market conditions are obtained, and a way to Markov inequality and the Borel- Cantelli lemma and other tools to the strong limit theorem is given.
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