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Maximum entropy distribution of stock price fluctuations
Maximum entropy distribution stock price fluctuations
2011/7/4
The principle of absence of arbitrage opportunities allows obtaining the distribution of
stock price fluctuations by maximizing its information entropy. This leads to a physical
description of the u...
Optimal Portfolio Diversification Using Maximum Entropy Principle
Diversification Entropy measure Portfolio selection Shrinkage rule Simulation methods
2011/4/2
Markowitz’s mean-variance (MV) efficient portfolio selection is one of the most widely used approaches in solving portfolio diversification problem. However, contrary to the notion of diversification,...
Zipf's law states that the number of firms with size greater than S is inversely proportional to S. Most explanations start with Gibrat's rule of proportional growth but require additional constraints...
Selling a stock at the ultimate maximum
Geometric Brownian motion optimal prediction optimal stopping ultimate maximum parabolic free-boundary problem smooth fit
2010/11/2
Assuming that the stock price Z = (Zt)0≤t≤T follows a geometric Brownian motion with drift μ 2 R and volatility > 0, and letting Mt = max0≤s≤t Zs for t 2 [0,T].
Maximum penalized quasi-likelihood estimation of the diffusion function
Maximum penalized quasi-likelihood estimation diffusion function
2010/10/21
We develop a maximum penalized quasi-likelihood estimator for estimating in a nonparametric way the diffusion function of a diffusion process, as an alternative to more traditional kernel-based estima...
Maximum Entropy Distributions Inferred from Option Portfolios on an Asset
Entropy Information Theory I-Divergence Asset Distribution Option Pricing Volatility Smile
2010/10/29
We obtain the Maximum Entropy distribution for an asset from call and digital option prices. A
rigorous mathematical proof of its existence and exponential form is given, which can also be applied to...
A general "bang-bang" principle for predicting the maximum of a random walk
Bernoulli random walk Brownian motion optimal prediction ultimate maximum stopping time convex function
2010/11/2
Let (Bt)0tT be either a Bernoulli random walk or a Brownian motion with drift, and let Mt := max{Bs : 0 s t}, 0 t T. This paper solves the general optimal prediction problem sup 0 T E[f(MT...