相关论文: Stopping strategies and gambler's ruin problem
In the extended gambler's ruin problem we can move one step forward or backward (classical gambler's ruin problem), we can stay where we are for a time unit (delayed action) or there can be absorption in the current state (game is…
We present here a new extended model of the gambler's ruin problem by incorporating delays in receiving of rewards and paying of penalties. When there is a difference between two delays, an exact analysis of the ruin probability is…
This note explores the mathematical theory to solve modern gamblers ruin problems. We establish a ruin framework and solve for the probability of bankruptcy. We also show how this relates to the expected time to bankruptcy and review the…
In this paper we provide formulas for the expectation of a conditional game duration in a finite state-space one-dimensional gambler's ruin problem with arbitrary winning $p(n)$ and losing $q(n)$ probabilities (i.e., they depend on the…
The gambler's ruin problem for correlated random walks (CRW), both with and without delays, is addressed using the Optional Stopping Theorem for martingales. We derive closed-form expressions for the ruin probabilities and the expected game…
We give explicit formulas for ruin probabilities in a multidimensional Generalized Gambler's ruin problem. The generalization is best interpreted as a game of one player against $d$ other players, allowing arbitrary winning and losing…
Assume that letters (from a finite alphabet) in a text form a Markov chain. We track two distinct words, $U$ and $D$. A gambler gains 1 point for each occurrence of $U$ (including overlapping occurrences) and loses 1 point for each…
Gambler's ruin estimates can be viewed as harmonic measure estimates for finite Markov chains which are absorbed (or killed) at boundary points. We relate such estimates to properties of the underlying chain and its Doob transform.…
For a family of multidimensional gambler models we provide formulas for the winning probabilities (in terms of parameters of the system) and for the distribution of game duration (in terms of eigenvalues of underlying one-dimensional…
We obtain expected number of arrivals, absorption probabilities and expected time before absorption for a discrete random walk on the integers with an infinite set of equidistant multiple function barriers
Using experimental mathematics and symbolic computation, we derive many moments for the duration of a three player (fair) gambler's ruin.
In this paper, we propose a new multi-armed bandit problem called the Gambler's Ruin Bandit Problem (GRBP). In the GRBP, the learner proceeds in a sequence of rounds, where each round is a Markov Decision Process (MDP) with two actions…
This paper treats of a kind of a gambler's ruin problem, which seeks the probability that a random walker first hits the origin at a certain time. In addition to a usual random walk which hops either rightwards or leftwards, the present…
The power of symbolic computation, as opposed to mere numerical computation, is illustrated with efficient algorithms for studying the generalized gambler's ruin problem in one and two dimensions. We also consider a new generalization of…
We derive an explicit formula for the probability of ruin of a gambler playing against an infinitely-rich adversary, when the games have payoff given by a general integer-valued probability distribution.
We obtain expected number of arrivals, absorption probabilities and expected time until absorption for an asymmetric discrete random walk on a graph in the presence of multiple function barriers. On each edge of the graph and in each vertex…
Consider gambler's ruin with three players, 1, 2, and 3, having initial capitals $A$, $B$, and $C$ units. At each round a pair of players is chosen (uniformly at random) and a fair coin flip is made resulting in the transfer of one unit…
We study quitting games and define the concept of absorption paths, which is an alternative definition to strategy profiles that accomodates both discrete time aspects and continuous time aspects, and is parameterized by the total…
We study multidimensional Cram\'er-Lundberg risk processes where agents, located on a large sparse network, receive losses form their neighbors. To reduce the dimensionality of the problem, we introduce classification of agents according to…
We consider the simple random walk on the $N$-dimensional integer lattice from the perspective of evaluating asymptotically the duration of play in the multidimensional gambler\apost s ruin problem. We show that, under suitable rescalings,…