B. Ross Barmish
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View article: On the Benefit of Nonlinear Control for Robust Logarithmic Growth: Coin Flipping Games as a Demonstration Case
On the Benefit of Nonlinear Control for Robust Logarithmic Growth: Coin Flipping Games as a Demonstration Case Open
The takeoff point for this paper is the voluminous body of literature addressing recursive betting games with expected logarithmic growth of wealth being the performance criterion. Whereas almost all existing papers involve use of linear f…
View article: A Data-Driven Control-Theoretic Paradigm for Pandemic Mitigation with Application to Covid-19
A Data-Driven Control-Theoretic Paradigm for Pandemic Mitigation with Application to Covid-19 Open
In this paper, we introduce a new control-theoretic paradigm for mitigating the spread of a virus. To this end, our discrete-time controller, aims to reduce the number of new daily deaths, and consequently, the cumulative number of deaths.…
View article: The Impact of Execution Delay on Kelly-Based Stock Trading: High-Frequency Versus Buy and Hold
The Impact of Execution Delay on Kelly-Based Stock Trading: High-Frequency Versus Buy and Hold Open
Stock trading based on Kelly's celebrated Expected Logarithmic Growth (ELG)\ncriterion, a well-known prescription for optimal resource allocation, has\nreceived considerable attention in the literature. Using ELG as the performance\nmetric…
View article: On Positive Solutions of a Delay Equation Arising When Trading in Financial Markets
On Positive Solutions of a Delay Equation Arising When Trading in Financial Markets Open
We consider a discrete-time, linear state equation with delay which arises as a model for a trader's account value when buying and selling a risky asset in a financial market. The state equation includes a nonnegative feedback gain $α$ and…
View article: A Conjecture Involving Positive Solutions of a Simple Scalar Linear Time-Varying State Equation with Delay
A Conjecture Involving Positive Solutions of a Simple Scalar Linear Time-Varying State Equation with Delay Open
A simple conjecture is presented concerning positive solutions of a scalar, time-varying, linear state equation with delay. Although the equation arises in the context of stock trading, no knowledge of finance is needed in the analysis to …
View article: On Risk Reduction in Kelly Betting Using the Conservative Expected Value
On Risk Reduction in Kelly Betting Using the Conservative Expected Value Open
The celebrated Kelly betting strategy guarantees, with probability one, higher long-run wealth than any other causal investment strategy. However, on the way to its long-term supremacy, this strategy has a notable downfall: it typically di…
View article: Rebalancing Frequency Considerations for Kelly-Optimal Stock Portfolios in a Control-Theoretic Framework
Rebalancing Frequency Considerations for Kelly-Optimal Stock Portfolios in a Control-Theoretic Framework Open
In this paper, motivated by the celebrated work of Kelly, we consider the problem of portfolio weight selection to maximize expected logarithmic growth. Going beyond existing literature, our focal point here is the rebalancing frequency wh…
View article: A Generalization of the Robust Positive Expectation Theorem for Stock Trading via Feedback Control
A Generalization of the Robust Positive Expectation Theorem for Stock Trading via Feedback Control Open
The starting point of this paper is the so-called Robust Positive Expectation (RPE) Theorem, a result which appears in literature in the context of Simultaneous Long-Short stock trading. This theorem states that using a combination of two …
View article: A Generalization of the Robust Positive Expectation Theorem for Stock\n Trading via Feedback Control
A Generalization of the Robust Positive Expectation Theorem for Stock\n Trading via Feedback Control Open
The starting point of this paper is the so-called Robust Positive Expectation\n(RPE) Theorem, a result which appears in literature in the context of\nSimultaneous Long-Short stock trading. This theorem states that using a\ncombination of t…
View article: At What Frequency Should the Kelly Bettor Bet?
At What Frequency Should the Kelly Bettor Bet? Open
We study the problem of optimizing the betting frequency in a dynamic game setting using Kelly's celebrated expected logarithmic growth criterion as the performance metric. The game is defined by a sequence of bets with independent and ide…
View article: On inefficiency of markowitz-style investment strategies when drawdown is important
On inefficiency of markowitz-style investment strategies when drawdown is important Open
The focal point of this paper is the issue of "drawdown" which arises in recursive betting scenarios and related applications in the stock market. Roughly speaking, drawdown is understood to mean drops in wealth over time from peaks to sub…
View article: On Kelly Betting: Some Limitations
On Kelly Betting: Some Limitations Open
The focal point of this paper is the so-called Kelly Criterion, a prescription for optimal resource allocation among a set of gambles which are repeated over time. The criterion calls for maximization of the expected value of the logarithm…
View article: On Inefficiency of Markowitz-Style Investment Strategies When Drawdown is Important
On Inefficiency of Markowitz-Style Investment Strategies When Drawdown is Important Open
The focal point of this paper is the issue of "drawdown" which arises in recursive betting scenarios and related applications in the stock market. Roughly speaking, drawdown is understood to mean drops in wealth over time from peaks to sub…
View article: On Drawdown-Modulated Feedback Control in Stock Trading
On Drawdown-Modulated Feedback Control in Stock Trading Open
Control of drawdown, that is, the control of the drops in wealth over time from peaks to subsequent lows, is of great concern from a risk management perspective. With this motivation in mind, the focal point of this paper is to address the…
View article: Kelly Betting Can Be Too Conservative
Kelly Betting Can Be Too Conservative Open
Kelly betting is a prescription for optimal resource allocation among a set of gambles which are typically repeated in an independent and identically distributed manner. In this setting, there is a large body of literature which includes a…
View article: On Robustness of Simultaneous Long-Short Stock Trading Control with Time-Varying Price Dynamics
On Robustness of Simultaneous Long-Short Stock Trading Control with Time-Varying Price Dynamics Open
This paper provides a time-varying extension of the so-called Robust Positive Expectation Theorem which arises in the context of Simultaneous Long-Short (SLS) stock trading. In the literature, the original version of the theorem applies to…
View article: A general framework for pairs trading with a control-theoretic point of view
A general framework for pairs trading with a control-theoretic point of view Open
Pairs trading is a market-neutral strategy that exploits historical correlation between stocks to achieve statistical arbitrage. Existing pairs-trading algorithms in the literature require rather restrictive assumptions on the underlying s…