Related papers: Gambler's ruin probability - a general formula
This survey treats the problem of ruin in a risk model when assets earn investment income. In addition to a general presentation of the problem, topics covered are a presentation of the relevant integro-differential equations, exact and…
We study a dynamic model of a non-life insurance portfolio. The foundation of the model is a compound Poisson process that represents the claims side of the insurer. To introduce clusters of claims appearing, e.g. with catastrophic events,…
We consider the game-theoretic scenario of testing the performance of Forecaster by Sceptic who gambles against the forecasts. Sceptic's current capital is interpreted as the amount of evidence he has found against Forecaster. Reporting the…
Suppose a gambler starts with a fortune in (0,1) and wishes to attain a fortune of 1 by making a sequence of bets. Assume thay whenever the gambler stakes the amount s, the gambler's fortune increases by s with probability w and decreases…
Given a skew-symmetric matrix, the corresponding two-player symmetric zero-sum game is defined as follows: one player, the row player, chooses a row and the other player, the column player, chooses a column. The payoff of the row player is…
We introduce and discuss a nonlinear kinetic equation of Boltzmann type which describes the evolution of wealth in a pure gambling process, where the entire sum of wealths of two agents is up for gambling, and randomly shared between the…
We introduce General Lotto games with Scouts: a General Lotto game with asymmetric information. There are two players, Red and Blue, who both allocate resources to a field. However, scouting capabilities afford Blue to gain information,…
A strategy for playing the game of roulette is presented in this paper. The strategy is based on the same probabilistic argument that leads to the well-known Birthday Paradox in Probability theory. Following the strategy, a player will have…
We study the asymptotic behavior of the ratio of total return (or total profit) to total amount bet in a casino game. While the limit is well understood when the sequence of wagers is independent and identically distributed, here we…
In this paper we study the joint ruin problem for two insurance companies that divide between them both claims and premia in some specified proportions (modeling two branches of the same insurance company or an insurance and re-insurance…
Combinatorial Game Theory is a branch of mathematics and theoretical computer science that studies sequential 2-player games with perfect information. Normal play is the convention where a player who cannot move loses. Here, we generalize…
Consider two insurance companies (or two branches of the same company) that divide between them both claims and premia in some specified proportions. We model the occurrence of claims according to a renewal process. One ruin problem…
In Major League Baseball, strategy and planning are major factors in determining the outcome of a game. Previous studies have aided this by building machine learning models for predicting the winning team of any given game. We extend this…
We consider the permutation analogue of Penney's game for words. Two players, in order, each choose a permutation of length $k\ge3$; then a sequence of independent random values from a continuous distribution is generated, until the…
We characterize winning strategies in various infinite games involving filters on the natural numbers in terms of combinatorics or structural properties of the given filter. These generalize several ultrafilter games of Galvin.
This note presents a kind of the strong law of large numbers for an insurance risk caused by a single catastrophic event rather than by an accumulation of independent and identically distributed risks. We derive this result by a large…
We demonstrate how to efficiently compute the probability of victory in Fire Emblem arena battles. The probability can be expressed in terms of a multivariate recurrence relation which lends itself to a straightforward dynamic programming…
We give a formula and an estimation for the number of irreducible polynomials in two (or more) variables over a finite field.
Can revealing one's competitive capabilities to an opponent offer strategic benefits? In this paper, we address this question in the context of General Lotto games, a class of two-player competitive resource allocation models. We consider…
In this work, we derive a complete characterization of all ruin-inducing probability measures that preserve the structure of a given compound renewal process in terms of suitable pairs of functions $(\gamma,\delta)$. This result allows us…