Related papers: Optimal Betting: Beyond the Long-Term Growth
Financial markets, with their vast range of different investment opportunities, can be seen as a system of many different simultaneous games with diverse and often unknown levels of risk and reward. We introduce generalizations to the…
In modern portfolio theory, the balancing of expected returns on investments against uncertainties in those returns is aided by the use of utility functions. The Kelly criterion offers another approach, rooted in information theory, that…
A portfolio of different stocks and a risk-less security whose composition is dynamically maintained stable by trading shares at any time step leads to a growth of the capital with a nonrandom rate. This is the key for the theory of…
In this paper, we study the Kelly criterion in the continuous time framework building on the work of E.O. Thorp and others. The existence of an optimal strategy is proven in a general setting and the corresponding optimal wealth process is…
Prompted by a recent experiment by Victor Haghani and Richard Dewey, this note generalises the Kelly strategy (optimal for simple investment games with log utility) to a large class of practical utility functions and including the effect of…
Risk and uncertainty will always be a matter of experience, luck, skills, and modelling. Leverage is another concept, which is critical for the investor decisions and results. Adaptive skills and quantitative probabilistic methods need to…
We consider the problem of maximizing the asymptotic growth rate of an investor under drift uncertainty in the setting of stochastic portfolio theory (SPT). As in the work of Kardaras and Robertson we take as inputs (i) a Markovian…
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…
We introduce new mathematical methods to study the optimal portfolio size of investment portfolios over time, considering investors with varying skill levels. First, we explore the benefit of portfolio diversification on an annual basis for…
In this paper, we consider a discrete-time portfolio with $m \geq 2$ assets optimization problem which includes the rebalancing~frequency as an additional parameter in the maximization. The so-called Kelly Criterion is used as the…
We consider the classic Kelly gambling problem with general distribution of outcomes, and an additional risk constraint that limits the probability of a drawdown of wealth to a given undesirable level. We develop a bound on the drawdown…
In an information-processing investment game, such as the growth of a population of organisms in a changing environment, Kelly betting maximizes the expected log rate of growth. In this paper, we show that Kelly bets are closely related to…
The paper provides a mathematical model and a tool for the focused investing strategy as advocated by Buffett, Munger, and others from this investment community. The approach presented here assumes that the investor's role is to think about…
We examine the problem of optimal portfolio allocation within the framework of utility theory. We apply exponential utility to derive the optimal diversification strategy and logarithmic utility to determine the optimal leverage. We enhance…
Betting markets are gaining in popularity. Mean beliefs generally differ from prices in prediction markets. Logarithmic utility is employed to study the risk and return adjustments to prices. Some consequences are described. A modified…
We investigate the problem of gambling with uncertainty in outcome probabilities. Stochastic optimization models are proposed for optimal investing on events with mutually exclusive outcomes when probabilities are estimated using…
We formulate an adaptive version of Kelly's horse model in which the gambler learns from past race results using Bayesian inference. A known asymptotic scaling for the difference between the growth rate of the gambler and the optimal growth…
We study the problem of optimal long term portfolio selection with a view to beat a benchmark. Two kinds of objectives are considered. One concerns the probability of outperforming the benchmark and seeks either to minimise the decay rate…
We study the consistency of sample mean-variance portfolios of arbitrarily high dimension that are based on Bayesian or shrinkage estimation of the input parameters as well as weighted sampling. In an asymptotic setting where the number of…
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…