Related papers: The geometry of relative arbitrage
We study a mean-field version of rank-based models of equity markets such as the Atlas model introduced by Fernholz in the framework of Stochastic Portfolio Theory. We obtain an asymptotic description of the market when the number of…
We introduce a bond portfolio management theory based on foundations similar to those of stock portfolio management. A general continuous-time zero-coupon market is considered. The problem of optimal portfolios of zero-coupon bonds is…
We prove a general duality result for multi-stage portfolio optimization problems in markets with proportional transaction costs. The financial market is described by Kabanov's model of foreign exchange markets over a finite probability…
The market weight of a stock is its capitalization (cap) divided by the total market cap. Rank these weights from top to bottom. The capital distribution curve is a plot of weights versus ranks. For the US stock market, it is linear on a…
We consider a financial market in which two securities are traded: a stock and an index. Their prices are assumed to satisfy the Black-Scholes model. Besides assuming that the index is a tradable security, we also assume that it is…
In this study, we have investigated empirically the effects of market properties on the degree of diversification of investment weights among stocks in a portfolio. The weights of stocks within a portfolio were determined on the basis of…
In a discrete-time setting, we study arbitrage concepts in the presence of convex trading constraints. We show that solvability of portfolio optimization problems is equivalent to absence of arbitrage of the first kind, a condition weaker…
We study optimal portfolio choice models in markets with partial information about the stock's drift. We solve the single agent problem for general utilities using a new approach that yields regularity of the value function and closed form…
In a discrete-time market, we study model-independent superhedging, while the semi-static superhedging portfolio consists of {\it three} parts: static positions in liquidly traded vanilla calls, static positions in other tradable, yet…
We propose in this paper to consider the stock market as a physical system assimilate to a fluid evolving in a macroscopic space subject to a Force that influences its movement over time where this last is arising from the collision between…
In a stock market, the numeraire portfolio, if it exists, is the portfolio with the highest expected logarithmic growth rate at all times. A numeraire market is a stock market for which the market portfolio is the numeraire portfolio. We…
The main contribution of the paper is to employ the financial market network as a useful tool to improve the portfolio selection process, where nodes indicate securities and edges capture the dependence structure of the system. Three…
We study the explicit calculation of the set of superhedging portfolios of contingent claims in a discrete-time market model for d assets with proportional transaction costs. The set of superhedging portfolios can be obtained by a recursive…
We empirically test predictability on asset price by using stock selection rules based on maximum drawdown and its consecutive recovery. In various equity markets, monthly momentum- and weekly contrarian-style portfolios constructed from…
Optimal portfolio selection problems are determined by the (unknown) parameters of the data generating process. If an investor wants to realise the position suggested by the optimal portfolios, he/she needs to estimate the unknown…
In this paper we develop a concrete and fully implementable approach to the optimization of functionally generated portfolios in stochastic portfolio theory. The main idea is to optimize over a family of rank-based portfolios parameterized…
We develop a general theory of risk measures that determines the optimal amount of capital to raise and invest in a portfolio of reference traded securities in order to meet a pre-specified regulatory requirement. The distinguishing feature…
It has been widely observed that capitalization-weighted indexes can be beaten by surprisingly simple, systematic investment strategies. Indeed, in the U.S. stock market, equal-weighted portfolios, random-weighted portfolios, and other…
In an equity market model with "Knightian" uncertainty regarding the relative risk and covariance structure of its assets, we characterize in several ways the highest return relative to the market that can be achieved using nonanticipative…
Motivated by fairness concerns, we study the `portfolio problem': given an optimization problem with set $D$ of feasible solutions, a class $\mathbf{C}$ of fairness objective functions on $D$, and an approximation factor $\alpha \ge 1$, a…