Portfolio Choice and the Bayesian Kelly Criterion

We derive optimal gambling and investment policies for cases in which the underlying stochastic process has parameter values that are unobserved random variables. For the objective of maximizing logarithmic utility when the underlying stochastic process is a simple random walk in a random environmen...

Ausführliche Beschreibung

Bibliographische Detailangaben
Veröffentlicht in:	Advances in Applied Probability. - Applied Probability Trust. - 28(1996), 4, Seite 1145-1176
1. Verfasser:	Browne, Sid (VerfasserIn)
Weitere Verfasser:	Whitt, Ward
Format:	Online-Aufsatz
Sprache:	English
Veröffentlicht:	1996
Zugriff auf das übergeordnete Werk:	Advances in Applied Probability
Schlagworte:	Betting systems Proportional gambling Kelly criterion Portfolio theory Logarithmic utility Random walks in a random environment Kiefer process Time-changed Brownian motion Conjugate priors Bayesian control mehr... Mathematics Physical sciences Behavioral sciences Applied sciences Economics Philosophy


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245	1	0	\|a Portfolio Choice and the Bayesian Kelly Criterion
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520			\|a We derive optimal gambling and investment policies for cases in which the underlying stochastic process has parameter values that are unobserved random variables. For the objective of maximizing logarithmic utility when the underlying stochastic process is a simple random walk in a random environment, we show that a state-dependent control is optimal, which is a generalization of the celebrated Kelly strategy: the optimal strategy is to bet a fraction of current wealth equal to a linear function of the posterior mean increment. To approximate more general stochastic processes, we consider a continuous-time analog involving Brownian motion. To analyze the continuous-time problem, we study the diffusion limit of random walks in a random environment. We prove that they converge weakly to a Kiefer process, or tied-down Brownian sheet. We then find conditions under which the discrete-time process converges to a diffusion, and analyze the resulting process. We analyze in detail the case of the natural conjugate prior, where the success probability has a beta distribution, and show that the resulting limit diffusion can be viewed as a rescaled Brownian motion. These results allow explicit computation of the optimal control policies for the continuous-time gambling and investment problems without resorting to continuous-time stochastic-control procedures. Moreover they also allow an explicit quantitative evaluation of the financial value of randomness, the financial gain of perfect information and the financial cost of learning in the Bayesian problem.
540			\|a Copyright 1996 Applied Probability Trust
650		4	\|a Betting systems
650		4	\|a Proportional gambling
650		4	\|a Kelly criterion
650		4	\|a Portfolio theory
650		4	\|a Logarithmic utility
650		4	\|a Random walks in a random environment
650		4	\|a Kiefer process
650		4	\|a Time-changed Brownian motion
650		4	\|a Conjugate priors
650		4	\|a Bayesian control
650		4	\|a Mathematics \|x Applied mathematics \|x Statistics \|x Random walk
650		4	\|a Physical sciences \|x Physics \|x Mechanics \|x Fluid mechanics \|x Brownian motion
650		4	\|a Behavioral sciences \|x Leisure studies \|x Recreation \|x Games \|x Gambling
650		4	\|a Applied sciences \|x Engineering \|x Control engineering \|x Control systems \|x Automatic control \|x Optimal control
650		4	\|a Behavioral sciences \|x Leisure studies \|x Recreation \|x Games \|x Gambling \|x Betting
650		4	\|a Mathematics \|x Pure mathematics \|x Probability theory \|x Random variables
650		4	\|a Behavioral sciences \|x Psychology \|x Cognitive psychology \|x Cognitive processes \|x Decision making \|x Optimal policy
650		4	\|a Economics \|x Economic disciplines \|x Information economics
650		4	\|a Mathematics \|x Mathematical values \|x Mathematical variables \|x Mathematical independent variables
650		4	\|a Philosophy \|x Epistemology \|x Knowledge \|x Perfect information \|x General Applied Probability
655		4	\|a research-article
700	1		\|a Whitt, Ward \|e verfasserin \|4 aut
773	0	8	\|i Enthalten in \|t Advances in Applied Probability \|d Applied Probability Trust \|g 28(1996), 4, Seite 1145-1176 \|w (DE-627)269247009 \|w (DE-600)1474602-5 \|x 00018678 \|7 nnns
773	1	8	\|g volume:28 \|g year:1996 \|g number:4 \|g pages:1145-1176
856	4	0	\|u https://www.jstor.org/stable/1428168 \|3 Volltext
856	4	0	\|u https://doi.org/10.2307/1428168 \|3 Volltext
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952			\|d 28 \|j 1996 \|e 4 \|h 1145-1176