Related papers: Almost sure null bankruptcy of testing-by-betting …
We study the limiting behavior of the mixed strategies that result from optimal no-regret learning strategies in a repeated game setting where the stage game is any 2 by 2 competitive game. We consider optimal no-regret algorithms that are…
We investigate the asymptotic of ruin probabilities when the company combines the life- and non-life insurance businesses and invests its reserve into a risky asset with stochastic volatility and drift driven by a two-state Markov process.…
We identify a subtle security issue that impacts mechanism design in scenarios in which agents can absolutely commit to strategies. Absolute commitments allow the strategy of an agent to depend on the commitments made by the other agents.…
This paper concerns an insurance firm's surplus process observed at renewal inspection times, with a focus on assessing the probability of the surplus level dropping below zero. For various types of inter-inspection time distributions, an…
We propose a methodology to construct tests for the null hypothesis that the pricing errors of a panel of asset returns are jointly equal to zero in a linear factor asset pricing model -- that is, the null of "zero alpha". We consider, as a…
Suppose that the outcomes of a roulette table are not entirely random, in the sense that there exists a successful betting strategy. Is there a successful `separable' strategy, in the sense that it does not use the winnings from betting on…
We study the problems of sequential nonparametric two-sample and independence testing. Sequential tests process data online and allow using observed data to decide whether to stop and reject the null hypothesis or to collect more data,…
We consider repeated zero-sum games with incomplete information on the side of Player 2 with the total payoff given by the non-normalized sum of stage gains. In the classical examples the value $V_N$ of such an $N$-stage game is of the…
A major bottleneck in characterizing the failure modes of generative AI systems is the cost and time of annotation and evaluation. Consequently, adaptive testing paradigms have gained popularity, where one opportunistically decides which…
This paper studies oligopolistic irreversible investment with closed-loop strategies. These permit fully dynamic interactions that result in much richer strategic behavior than previous studies with open-loop strategies allow. The tradeoff…
We consider a continuous-time game-theoretic model of an investment market with short-lived assets and endogenous asset prices. The first goal of the paper is to formulate a stochastic equation which determines wealth processes of investors…
In this article we show that the payment flow of a linear tax on trading gains from a security with a semimartingale price process can be constructed for all c\`agl\`ad and adapted trading strategies. It is characterized as the unique…
In this paper, we prove the global risk optimality of the hedging strategy of contingent claim, which is explicitly (or called semi-explicitly) constructed for an incomplete financial market with external risk factors of non-Gaussian…
Can a probabilistic gambler get arbitrarily rich when all deterministic gamblers fail? We study this problem in the context of algorithmic randomness, introducing a new notion -- almost everywhere computable randomness. A binary sequence…
In game-theoretic learning, several agents are simultaneously following their individual interests, so the environment is non-stationary from each player's perspective. In this context, the performance of a learning algorithm is often…
We design and analyze minimax-optimal algorithms for online linear optimization games where the player's choice is unconstrained. The player strives to minimize regret, the difference between his loss and the loss of a post-hoc benchmark…
A run of all failures, a run of all successes, or complete separation in a logistic regression each tempts the analyst to declare a probability of exactly zero or one. The central message of this paper is that all three phenomena share a…
It is widely speculated that auditors' public forecasts of bankruptcy are, at least in part, self-fulfilling prophecies in the sense that they might actually cause bankruptcies that would not have otherwise occurred. This conjecture is hard…
Sequential monitoring of randomized trials traditionally relies on parametric assumptions or asymptotic approximations. We discuss a family of nonparametric sequential tests - collectively called e-RT - for binary, event-only, and…
We study non-rectangular robust Markov decision processes under the average-reward criterion, where the ambiguity set couples transition probabilities across states and the adversary commits to a stationary kernel for the entire horizon. We…