Defensive online portfolio selection

The class of defensive online portfolio selection algorithms,designed for fi nite investment horizon, is introduced. The Game Constantly Rebalanced Portfolio and the Worst Case Game Constantly Rebalanced Portfolio, are presented and theoretically analyzed. The analysis exploits the rich set of mathematical tools available by means of the connection between Universal Portfolios and the Game- Theoretic framework. The empirical performance of the Worst Case Game Constantly Rebalanced Portfolio algorithm is analyzed through numerical experiments concerning the FTSE 100, Nikkei 225, Nasdaq 100 and S&P500 stock markets for the time interval, from January 2007 to December 2009, which includes the credit crunch crisis from September 2008 to March 2009. The results emphasize the relevance of the proposed online investment algorithm which signi fi cantly outperformed the market index and the minimum variance Sharpe-Markowitz’s portfolio.on-line portfolio selection; universal portfolio; defensive strategy

Behavior of Investors on a Multi-Asset Market

This paper analyzes the field of investors’ decision-making on a multi-asset market. It does it through a simulation games on a social network framework. It has been demonstrated that more stocks there are in the game and more changing alternatives investors have available to choose from, tougher it is for them to make decisions. Despite in most simulations the safest alternative was dominant, many investors opt for portfolio of the safest and the riskiest stock, by which they back the risk they take with some safe stocks. Non-omniscient investors behave chaotically. In all the cases, liquidity agents proved to be decisive elements of the games, though not always able to deliver the information of all the alternatives when too many alternatives are available.social networks, behavioral finance, portfolio analysis, multi-asset game, chaos

Defensive online portfolio selection

The class of defensive online portfolio selection algorithms,designed for fi nite investment horizon, is introduced. The Game Constantly Rebalanced Portfolio and the Worst Case Game Constantly Rebalanced Portfolio, are presented and theoretically analyzed. The analysis exploits the rich set of mathematical tools available by means of the connection between Universal Portfolios and the Game- Theoretic framework. The empirical performance of the Worst Case Game Constantly Rebalanced Portfolio algorithm is analyzed through numerical experiments concerning the FTSE 100, Nikkei 225, Nasdaq 100 and S&P500 stock markets for the time interval, from January 2007 to December 2009, which includes the credit crunch crisis from September 2008 to March 2009. The results emphasize the relevance of the proposed online investment algorithm which signi fi cantly outperformed the market index and the minimum variance Sharpe-Markowitz’s portfolio

Forward utilities and Mean-field games under relative performance concerns

We introduce the concept of mean field games for agents using Forward utilities of CARA type to study a family of portfolio management problems under relative performance concerns. Under asset specialization of the fund managers, we solve the forward-utility finite player game and the forward-utility mean-field game. We study best response and equilibrium strategies in the single common stock asset and the asset specialization with common noise. As an application, we draw on the core features of the forward utility paradigm and discuss a problem of time-consistent mean-field dynamic model selection in sequential time-horizons.Comment: 24 page

Multilinear Superhedging of Lookback Options

In a pathbreaking paper, Cover and Ordentlich (1998) solved a max-min portfolio game between a trader (who picks an entire trading algorithm, $\theta(\cdot)$) and "nature," who picks the matrix $X$ of gross-returns of all stocks in all periods. Their (zero-sum) game has the payoff kernel $W_\theta(X)/D(X)$, where $W_\theta(X)$ is the trader's final wealth and $D(X)$ is the final wealth that would have accrued to a $\$1$ deposit into the best constant-rebalanced portfolio (or fixed-fraction betting scheme) determined in hindsight. The resulting "universal portfolio" compounds its money at the same asymptotic rate as the best rebalancing rule in hindsight, thereby beating the market asymptotically under extremely general conditions. Smitten with this (1998) result, the present paper solves the most general tractable version of Cover and Ordentlich's (1998) max-min game. This obtains for performance benchmarks (read: derivatives) that are separately convex and homogeneous in each period's gross-return vector. For completely arbitrary (even non-measurable) performance benchmarks, we show how the axiom of choice can be used to "find" an exact maximin strategy for the trader.Comment: 41 pages, 3 figure

Learning To Play The Trading Game

Can we train a stock trading bot that can take decisions in high-entropy envi- ronments like stock markets to generate profits based on some optimal policy? Can we further extend this learning for any general trading problem? Quantitative Al- gorithms are responsible for more than 75% of the stock trading around the world. Creating a stock market prediction model is comparatively easy. But creating a prof- itable prediction model is still considered as a challenging task in the field of machine learning and deep learning due to the unpredictability of the financial markets. Us- ing biologically inspired computing techniques of reinforcement learning (RL) and artificial neural networks(ANN), this project attempts to train an agent who takes decisions based on the optimal decision policies learned. Different existing RL tech- niques and their slightly modified variants will be used to train the agent, and the trained model is then tested against different stock prices and also stock portfolio settings to see if the agent has learned the rules of the game and can it act optimally irrespective of the testing data provided. This work aims to provide general users with simple recommendations about the possible investment decisions of selected stocks in the portfolio. Results of the implemented approaches do seem to work somewhat well on specific periods of stock market time series, but they are observed to be fragile. Selected strategies do not guarantee similar results on all historical time-periods, nor they are guaranteed to provide exceptional performance on unpredictable future stock market time-series data