Kelly Betting Can Be Too Conservative

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 arguments that the theory often leads to bets which are "too aggressive" with respect to various risk metrics. To remedy this problem, many papers include prescriptions for scaling down the bet size. Such schemes are referred to as Fractional Kelly Betting. In this paper, we take the opposite tack. That is, we show that in many cases, the theoretical Kelly-based results may lead to bets which are "too conservative" rather than too aggressive. To make this argument, we consider a random vector X with its assumed probability distribution and draw m samples to obtain an empirically-derived counterpart Xhat. Subsequently, we derive and compare the resulting Kelly bets for both X and Xhat with consideration of sample size m as part of the analysis. This leads to identification of many cases which have the following salient feature: The resulting bet size using the true theoretical distribution for X is much smaller than that for Xhat. If instead the bet is based on empirical data, "golden" opportunities are identified which are essentially rejected when the purely theoretical model is used. To formalize these ideas, we provide a result which we call the Restricted Betting Theorem. An extreme case of the theorem is obtained when X has unbounded support. In this situation, using X, the Kelly theory can lead to no betting at all.Comment: Accepted in 2016 IEEE 55th Conference on Decision and Control (CDC

On Feedback Control in Kelly Betting: An Approximation Approach

In this paper, we consider a simple discrete-time optimal betting problem using the celebrated Kelly criterion, which calls for maximization of the expected logarithmic growth of wealth. While the classical Kelly betting problem can be solved via standard concave programming technique, an alternative but attractive approach is to invoke a Taylor-based approximation, which recasts the problem into quadratic programming and obtain the closed-form approximate solution. The focal point of this paper is to fill some voids in the existing results by providing some interesting properties when such an approximate solution is used. Specifically, the best achievable betting performance, positivity of expected cumulative gain or loss and its associated variance, expected growth property, variance of logarithmic growth, and results related to the so-called survivability (no bankruptcy) are provided.Comment: To appear in the proceedings of the 2020 IEEE Conference on Control Technology and Applications (CCTA

Out-of-plane seismic response of stone masonry walls: experimental and analytical study of real piers

This paper presents the application of an existing simplified displacement-based procedure to the characterization of the nonlinear force-displacement relationship for the out-of-plane behaviour of unreinforced traditional masonry walls. According to this procedure, tri-linear models based on three different energy based criteria were constructed and confronted with three experimental tests on existing stone masonry constructions. Moreover, a brief introduction is presented regarding the main characteristics of the in situ cyclic testing recently carried out using distributed loads, as well as results obtained during the experimental campaigns performed. The comparison between the experimental and the analytical results are presented and discussed

Time--consistent investment under model uncertainty: the robust forward criteria

We combine forward investment performance processes and ambiguity averse portfolio selection. We introduce the notion of robust forward criteria which addresses the issues of ambiguity in model specification and in preferences and investment horizon specification. It describes the evolution of time-consistent ambiguity averse preferences. We first focus on establishing dual characterizations of the robust forward criteria. This offers various advantages as the dual problem amounts to a search for an infimum whereas the primal problem features a saddle-point. Our approach is based on ideas developed in Schied (2007) and Zitkovic (2009). We then study in detail non-volatile criteria. In particular, we solve explicitly the example of an investor who starts with a logarithmic utility and applies a quadratic penalty function. The investor builds a dynamical estimate of the market price of risk $\hat \lambda$ and updates her stochastic utility in accordance with the so-perceived elapsed market opportunities. We show that this leads to a time-consistent optimal investment policy given by a fractional Kelly strategy associated with $\hat \lambda$. The leverage is proportional to the investor's confidence in her estimate $\hat \lambda$

Applying Argumentation Analysis to Assess the Quality of University Oceanography Students' Scientific Writing

This article describes the methods and results of an assessment of students' scientific writing. The study was conducted in an introductory oceanography course in a large public university that used an interactive CD-ROM entitled, "Our Dynamic Planet." The CD provided students with geological data, which they used to build written arguments regarding plate tectonics. Twenty-four student papers from this course were analyzed for quality of written arguments by using both a grading rubric and an argumentation analysis model. Three implications were drawn from these initial studies. First, there is a clear need to help students understand how to use data representations as evidence for more theoretical arguments. Second, student writers need experiences receiving critiques of their own writing and analyzing others' scientific arguments. Third, the actual grading is dependent upon the socialization of the graders themselves (in this case, graduate students). Educational levels: Graduate or professional