连续市场下的增长最优投资策略

The Growth Optimal Portfolio in Continuous Markets

考虑由m+1个资产构成的金融市场,假定每一个资产的价格是严格正的It过程,这里不要求其中一个必须是债券(无风险资产)。给出了增长最优投资策略(GOP)存在时,投资策略的比例所满足的必要条件,以及类似得到以不同的资产作为记账单位得到的折现增长最优投资策略存在时投资策略比例所满足的必要条件,并证明了这些比例之间满足一个固定的形式.同时在一定条件成立下,推出了增长最优投资策略的价格过程。若市场存在等价鞅测度,证明了以增长最优投资策略作为记账单位所对应的等价鞅测度就是客观概率测度P.

In this paper,we consider a financial market which consists of m＋1 assets.The price of each asset is assumed to be a strictly positive It process.Here it is not necessary that one of them should be a bond（i.e.riskless asset）.The necessary condition that the proportion has to satisfy when a growth optimal portfolio（GOP） exists is given.When different assets are taken as the numeraire assets,the necessary conditions that the proportions have to satisfy when the discounted GOPs exists are given analogously.And it is proved that those proportions satisfy a uniform expression.Meanwhile,when some conditions come into existence,the value processes of the GOP are figured out.Supposing that an equivalent martingale measure exists in the market,when the GOP is taken as the numeraire asset,the corresponding martingale measure is the objective probability measure P.