PDF4PRO ⚡AMP

Modern search engine that looking for books and documents around the web

Example: stock market

1 Gambler’s Ruin Problem - Columbia University

1 gambler s ruin ProblemConsider a gambler who starts with an initial fortune of $1 and then on each successive gambleeither wins $1 or loses $1 independent of the past with probabilitiespandq= 1 the total fortune after thenthgamble. The gambler s objective is to reach a totalfortune of $N, without first gettingruined(running out of money). If the gambler succeeds,then the gambler is said towinthe game. In any case, the gambler stops playing after winningor getting ruined, whichever happens first. There is nothing special about starting with $1,more generally the gambler starts with $iwhere 0< i < the game proceeds,{Rn:n 0}forms a simple random walkRn= 1+ + n, R0=i,where{ n}forms an sequence of distributed asP( = 1) =p, P( = 1) =q=1 p, and r

1 Gambler’s Ruin Problem Consider a gambler who starts with an initial fortune of $1 and then on each successive gamble either wins $1 or loses $1 independent of the past with probabilities p and q

Tags:

  University, Columbia university, Columbia, Gamblers, Ruin, Gambler s ruin

Information

Domain:

Source:

Link to this page:

Please notify us if you found a problem with this document:

Spam in document Broken preview Other abuse

Transcription of 1 Gambler’s Ruin Problem - Columbia University