投资组合增长率的若干极限定理

Some Limit Theorems for the Portfolio Growth Rate

设0≤a_1≤a_2≤...是一列固定的非负整数序列,研究其在时间段a_n+1至a_n+n内投资组合增长率的极限性质。通过构造带1个参数并且期望有限的随机变量,利用Borel-Cantelli引理,获得了任意投资组合增长率的性质和一般市场条件下的极限定理。并给出了将Markov不等式和Borel-Cantelli引理等工具应用于强极限定理的一种途径。

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 BorelCantelli lemma and other tools to the strong limit theorem is given.