相关论文: Exact Finite-Horizon Quantile Kelly for Repeated M…

The focal point of this paper is the so-called Kelly Criterion, a prescription for optimal resource allocation among a set of gambles which are repeated over time. The criterion calls for maximization of the expected value of the…

We study the finite mutually exclusive outcome version of risk-constrained Kelly optimization with explicit state prices. The market has outcome probabilities $p_i>0$, state prices $q_i>0$, terminal wealths $W_i=c+x_i/q_i$, and a…

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…

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…

We develop a finite-horizon model in which liquid-asset returns exhibit Levy-stable scaling on a data-driven window [tau_UV, tau_IR] and aggregate into a finite-variance regime outside. The window and the tail index alpha are identified…

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…

For a sequence of binary bets, the Kelly criterion provides a closed-form solution that maximizes the expected growth rate of wealth. In contrast, when multiple bets are placed simultaneously (e.g., in portfolio allocation or prediction…

This paper proves continuity of value functions in discounted periodic-review single-commodity total-cost inventory control problems with \revision{continuous inventory levels,} fixed ordering costs, possibly bounded inventory storage…

We provide sufficient conditions for the continuity of the free-boundary in a general class of finite-horizon optimal stopping problems arising for instance in finance and economics. The underlying process is a strong solution of one…

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…

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…

We develop the dynamic programming approach for a family of infinite horizon boundary control problems with linear state equation and convex cost. We prove that the value function of the problem is the unique regular solution of the…

Deep reinforcement learning (RL) works impressively in some environments and fails catastrophically in others. Ideally, RL theory should be able to provide an understanding of why this is, i.e. bounds predictive of practical performance.…

We study the fundamental and timely problem of learning long sequences in autoregressive modeling and next-token prediction under model misspecification, measured by the joint Kullback--Leibler (KL) divergence. Our goal is to characterize…

We show that the Wheeler-DeWitt equation with a consistent boundary condition is only compatible with an arrow of time that formally reverses in a recollapsing universe. Consistency of these opposite arrows is facilitated by quantum effects…

We consider a finite horizon repeated game with $N$ selfish players who observe their types privately and take actions, which are publicly observed. Their actions and types jointly determine their instantaneous rewards. In each period,…

We develop a continuous-time general equilibrium framework for economies with a heterogeneous population -- modeled as a continuum -- that repeatedly optimizes over short horizons under relative-income (Duesenberry-type) criteria. The…

We study an optimal execution problem in the infinite horizon setup. Our financial market is given by the Black-Scholes model with a linear price impact. The main novelty of the current note is that we study the constrained case where the…

Kelly criterion, that maximizes the expectation value of the logarithm of wealth for bookmaker bets, gives an advantage over different class of strategies. We use projective symmetries for a explanation of this fact. Kelly's approach allows…

This paper characterizes the best possible rate of growth of wealth in a Kelly betting game when repeatedly betting against a general i.i.d. null hypothesis $\mathscr{P}$, but the data are drawn i.i.d from an arbitrary alternative $Q$. We…