Related papers: Extended gambler's ruin problem

We introduce an evolutionary game with feedback between perception and reality, which we call the reality game. It is a game of chance in which the probabilities for different objective outcomes (e.g., heads or tails in a coin toss) depend…

In this paper a class of Ornstein--Uhlenbeck processes driven by compound Poisson processes is considered. The jumps arrive with exponential waiting times and are allowed to be two-sided. The jumps are assumed to form an iid sequence with…

In this paper we investigate Gaussian risk models which include financial elements such as inflation and interest rates. For some general models for inflation and interest rates, we obtain an asymptotic expansion of the finite-time ruin…

We study the evolutionary robustness of strategies in infinitely repeated prisoners' dilemma games in which players make mistakes with a small probability and are patient. The evolutionary process we consider is given by the replicator…

We consider a sequential inspection game where an inspector uses a limited number of inspections over a larger number of time periods to detect a violation (an illegal act) of an inspectee. Compared with earlier models, we allow varying…

Exploration and trapping properties of random walkers that may evanesce at any time as they walk have seen very little treatment in the literature, and yet a finite lifetime is a frequent occurrence, and its effects on a number of random…

The problem of how many trajectories of a random walker in a potential are needed to reconstruct the values of this potential is studied. We show that this problem can be solved by calculating the probability of survival of an abstract…

In games with a large number of players where players may have overlapping objectives, the analysis of stable outcomes typically depends on player types. A special case is when a large part of the player population consists of imitation…

In this paper, we unify two popular approaches for the definition of actuarial ruin with implementation delays, also known as Parisian ruin. Our new definition of ruin includes both deterministic delays and exponentially distributed delays:…

We study a risk sensitive control version of the lifetime ruin probability problem. We consider a sequence of investments problems in Black-Scholes market that includes a risky asset and a riskless asset. We present a differential game that…

In this paper we give few expressions and asymptotics of ruin probabilities for a Markov modulated risk process for various regimes of a time horizon, initial reserves and a claim size distribution. We also consider few versions of the ruin…

We consider two players, starting with $m$ and $n$ units, respectively. In each round, the winner is decided with probability proportional to each player's fortune, and the opponent loses one unit. We prove an explicit formula for the…

We consider zero sum stochastic games. For every discount factor $\lambda$, a time normalization allows to represent the game as being played on the interval [0, 1]. We introduce the trajectories of cumulated expected payoff and of…

Consider a two-player game repeated N times. Player 1 can choose between two styles (for interpretability, offensive and defensive), whereas Player 2 uses a single fixed style. Let X N\,:= \#wins -\#losses for Player 1 after N games, and…

Consider a random walk in $\mathbb{R}^d$ that starts at the origin and whose increment distribution assigns zero probability to any affine hyperplane. We solve Sylvester's problem for these random walks by showing that the probability that…

We calculate the survival probability of a stationary target in one dimension surrounded by diffusive or subdiffusive traps of time-dependent density. The survival probability of a target in the presence of traps of constant density is…

We give elementary examples within a framework for studying decisions under uncertainty where probabilities are only roughly known. The framework, in gambling terms, is that the size of a bet is proportional to the gambler's perceived…

We study a class of adversarial bandit optimization problems in which the loss functions may be non-convex and non-smooth. In each round, the learner observes a loss that consists of an underlying linear component together with an…

This paper presents a sharp approximation of the density of long runs of a random walk conditioned on its end value or by an average of a functions of its summands as their number tends to infinity. The conditioning event is of moderate or…

An extension of the traditional two-armed bandit problem is considered, in which the decision maker has access to some side information before deciding which arm to pull. At each time t, before making a selection, the decision maker is able…