Some limit theorems for the log-optimal portfolio

Optimal portfolio allocation with imposed price limit constraint

Daily price limits are adopted by many securities exchanges in countries such as the USA, Canada, Japan and various other countries in Europe and Asia, in order to increase the stability of the financial market. These limits confine the price of the financial asset during all trading stages of any trading day to a range, usually determined based on the previous day’s closing price. In this pape...

Some Limit Theorems

Some Converse Limit Theorems for Exchangeable Bootstraps

The bootstrap Glivenko-Cantelli and bootstrap Donsker theorems of Giné and Zinn (1990) contain both necessary and sufficient conditions for the asymptotic validity of Efron’s nonparametric bootstrap. In the more general case of exchangeably weighted bootstraps, Praestgaard and Wellner (1993) and Van der Vaart and Wellner (1996) give analogues of the sufficiency half of the Theorems of Giné and ...

Some Useful Functions for Functional Limit Theorems

Many useftil descriptions of stochastic models can be obtained from functional limit theorems (invariance principles or weak convergence theorems for probability meastires on function ŝpaces). These descriptions typically come from standard functional limit theorems via the o^ntinuous mapping theorem. This paper facilitates applications of the continuous mapping theorem by determining when seve...

Empirical log-optimal portfolio selections: a survey∗

In this paper the static portfolio and the dynamic log-optimal portfolio for memoryless and for stationary market processes are studied. We illustrate their performance (average annual yield) for NYSE data. 1 Notations Consider a market consisting of d assets. The evolution of the market in time is represented by a sequence of price vectors s1, s2, . . . ∈ R+, where sn = (s (1) n , . . . , s (d...