Gambler’s Ruin with Catastrophes and Windfalls

Gambler’s Ruin Model and Ga

In order to estimate the correct size of population, estimations of population sizing have been used in the genetic algorithms (GAs). The estimation considers a test function being optimized, a representation of individuals and a character of used operators. By means of the estimation model the right population size with taking into account the final overall quality of individuals is identified...

Gambler’s Ruin Problem with Relative Wealth Perception

We consider a modified version of Gambler’s Ruin Problem in which the gambler decides to quit based on the relative change of his or her wealth. For this purpose we consider two possible changes of wealth, namely the upward rally and the downward fall. We define upward rally as the difference of the current wealth and its historical minimum, while the downward fall is the difference of the hist...

Re-seeding invalidates tests of random number generators

Kim et al (Appl Math & Comput 199 (2008) 195) recently presented a test of random number generators based on the gambler’s ruin problem and concluded that several generators, including the widely used Mersenne Twister, have hidden defects. We show here that the test by Kim et al suffers from a subtle, but consequential error: Re-seeding the pseudorandom number generator with a fixed seed for ea...

Change-point detection of two-sided alternatives in the Brownian motion model and its connection to the gambler’s ruin problem with relative wealth perception

Approaches to Gambler’s Ruin with Catastrophe

on the state space {0, 1, 2, . . . , N + 1}. This Markov chain represents the “Gambler’s Ruin” problem with catastrophe, as shown in Figure 1. Each entry aij gives the probability of moving from state i to state j in a single step, given that the current state is i. The probability of moving in one step from state 1 to state 0, for instance, is b + c while the probability of moving in one step ...