Related papers: On Kelly Betting: Some Limitations
It is a common misconception that in order to make consistent profits as a trader, one needs to posses some extra information leading to an asset value estimation more accurate than that reflected by the current market price. While the idea…
For an exponential utility maximizing investment strategy in a Black-Scholes Setting, fixed upper and lower constraints are introduced on the terminal wealth. This is equivalent to combining the optimal strategy with options. The resulting…
This paper studies the income fluctuation problem with capital income risk (i.e., dispersion in the rate of return to wealth). Wealth returns and labor earnings are allowed to be serially correlated and mutually dependent. Rewards can be…
We introduce and study a mathematical model of an art collector. In our model, the collector is a rational agent whose actions in the art market are driven by two competing long-term objectives, namely sustainable financial health and…
For a single event with finitely many mutually exclusive outcomes, the full Kelly problem is to maximize expected log wealth over nonnegative stakes together with an optional cash position. The optimal formula is classical, but the…
Capital allocation principles are used in various contexts in which a risk capital or a cost of an aggregate position has to be allocated among its constituent parts. We study capital allocation principles in a performance measurement…
Ergodicity describes an equivalence between the expectation value and the time average of observables. Applied to human behaviour, ergodic theories of decision-making reveal how individuals should tolerate risk in different environments. To…
The restricted max-min fair allocation problem seeks an allocation of resources to players that maximizes the minimum total value obtained by any player. It is NP-hard to approximate the problem to a ratio less than 2. Comparing the current…
This paper presents a novel approach for optimizing betting strategies in sports gambling by integrating Von Neumann-Morgenstern Expected Utility Theory, deep learning techniques, and advanced formulations of the Kelly Criterion. By…
Randomized mechanisms, which map a set of bids to a probability distribution over outcomes rather than a single outcome, are an important but ill-understood area of computational mechanism design. We investigate the role of randomized…
A drawdown constraint forces the current wealth to remain above a given function of its maximum to date. We consider the portfolio optimisation problem of maximising the long-term growth rate of the expected utility of wealth subject to a…
Resource allocation is the process of optimizing the rare resources. In the area of security, how to allocate limited resources to protect a massive number of targets is especially challenging. This paper addresses this resource allocation…
Asset allocation is an investment strategy that aims to balance risk and reward by constantly redistributing the portfolio's assets according to certain goals, risk tolerance, and investment horizon. Unfortunately, there is no simple…
From the Hamilton-Jacobi-Bellman equation for the value function we derive a non-linear partial differential equation for the optimal portfolio strategy (the dynamic control). The equation is general in the sense that it does not depend on…
For independent multi-outcome events under multiplicative parlay pricing, we give a short exact proof of the optimal Kelly strategy using the implicit-cash viewpoint. The proof is entirely eventwise. One first solves each event in…
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 consider concurrent stochastic games played on graphs with reachability and safety objectives. These games can be solved by value iteration as well as strategy iteration, each of them yielding a sequence of under-approximations of the…
In this paper we examine problems motivated by on-line financial problems and stochastic games. In particular, we consider a sequence of entirely arbitrary distinct values arriving in random order, and must devise strategies for selecting…
This paper investigates a continuous-time portfolio optimization problem with the following features: (i) a no-short selling constraint; (ii) a leverage constraint, that is, an upper limit for the sum of portfolio weights; and (iii) a…
Gambles are random variables that model possible changes in monetary wealth. Classic decision theory transforms money into utility through a utility function and defines the value of a gamble as the expectation value of utility changes.…