Diversification and limited information in the Kelly game

Kelly criterion for variable pay-off

We determine Kelly criterion for a game with variable pay-off. The Kelly fraction satisfies a fundamental integral equation and is smaller than the classical Kelly fraction for the same game with the constant average pay-off.

量子双倍或全无博弈：自旋的凯利准则

A quantum double-or-nothing game: The Kelly Criterion for Spins

本文提出一种基于自旋1/2粒子的双倍或全无量子博弈，通过数值方法确定最优量子策略，证明其不同于经典凯利准则，推动量子金融发展。

基于效用的投资组合配置方法中的最优分散化与杠杆

Optimal Diversification and Leverage in a Utility-Based Portfolio Allocation Approach

本文在效用理论框架下结合指数与对数效用、复合概率分布及含效用方差的广义均值-方差目标，求解投资组合的最优分散化与杠杆，并解释 half-Kelly 准则。

Calculated Boldness: Optimizing Financial Decisions with Illiquid Assets

We consider games of chance played by someone with external capital that cannot be applied to the game and determine how this affects risk-adjusted optimal betting. Specifically, we focus on Kelly optimization as a metric, optimizing the expected logarithm of total capital including both capital in play and the external capital. For games with multiple rounds, we determine the optimal strategy through dynamic programming and construct a close approximation through the WKB method. The strategy can be described in terms of short-term utility functions, with risk aversion depending on the ratio o…

Game-Theoretic Optimal Portfolios in Continuous Time

We consider a two-person trading game in continuous time whereby each player chooses a constant rebalancing rule $b$ that he must adhere to over $[0,t]$. If $V_t(b)$ denotes the final wealth of the rebalancing rule $b$, then Player 1 (the `numerator player') picks $b$ so as to maximize $\mathbb{E}[V_t(b)/V_t(c)]$, while Player 2 (the `denominator player') picks $c$ so as to minimize it. In the unique Nash equilibrium, both players use the continuous-time Kelly rule $b^*=c^*=Σ^{-1}(μ-r\textbf{1})$, where $Σ$ is the covariance of instantaneous returns per unit time, $μ$ is the drift vector of th…

At What Frequency Should the Kelly Bettor Bet?

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 identically distributed returns X(k). The bettor selects the fraction of wealth K wagered at k = 0 and waits n steps before updating the bet size. Between updates, the proceeds from the previous bets remain at risk in the spirit of "buy and hold." Within this context, the main questions we consider are as follows: How does the optimal performance, we call it gn*…