In this paper we try to design the necessary calculation needed for backtesting trading systems when only candle chart data are available. We lay particular emphasis on situations which are not or not uniquely decidable and give possible strategies to handle such situations.

Banks make profits from the difference between short-term and long-term loan interest rates. To issue loans, banks raise funds from capital markets. Since the long-term loan rate is relatively stable, but short-term interest is usually variable, there is an interest rate risk. Therefore, banks...

The Growth-Optimal Portfolio (GOP) theory determines the path of bet sizes that maximize long-term wealth. This multi-horizon goal makes it more appealing among practitioners than myopic approaches, like Markowitz's mean-variance or risk parity. The GOP literature typically considers...

In a one price economy, the Fundamental Theorem of Asset Pricing (FTAP) establishes that no-arbitrage is equivalent to the existence of an equivalent martingale measure. Such an equivalent measure can be derived as the normal unit vector of the hyperplane that separates the attainable gain...

We develop an optimal trend following trading rule in a bull-bear switching market, where the drift of the stock price switches between two parameters corresponding to an uptrend (bull market) and a downtrend (bear market) according to an unobservable Markov chain. We consider a finite horizon...

We discuss here a dynamic implementation of the leverage space portfolio theory in the form of DJ-LSP position sizing index implemented the Dow Jones indexes. Our emphasis in this case study is on the practical issues related to the implementation

Inflection points in the the function for determining estimated geometric gain with respect to capital committed emerge when planning an investment for a finite time horizon. These are points where marginal increases in reward with respect to risk peaks. We analyze the properties of inflection...

This paper is concerned with the optimality of a trend following trading rule. The idea is to catch a bull market at its early stage, ride the trend, and liquidate the position at the first evidence of the subsequent bear market. We characterize the bull and bear phases of the markets...

We develop the theory of Kelly and Thorp in analyzing the optimal bet sizes for blackjack by incorporating the practical considerations of players wherein only a finite number of plays shall occur as well as pursuing maximizing risk-adjusted returns. We show that the ratio of return to bet size...