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A Note on the History of the Gambler's Ruin Problem

Seongjoo Song, Jongwoo Song
2013 Communications for Statistical Applications and Methods  
This paper deals with the history of one of the well-known and historically important problems in probability, "Gambler's ruin".  ...  We would like to introduce the problem in detail to readers and share the ideas on how new problems are developed, relating to old problems.  ...  His proof also counts on an incomplete induction like Huygens' proof. A complete proof of the general problem based on the difference equation was first given by Struyck (1716).  ... 
doi:10.5351/csam.2013.20.2.157 fatcat:n4tqvff7efch5hennuuuqn64eu

Kullback-Leibler Information in View of an Extended Version of κ-Records

Mosayeba Ahmadi, G.R. Mohtashami Borzadaran
2013 Communications for Statistical Applications and Methods  
This paper deals with the history of one of the well-known and historically important problems in probability, "Gambler's ruin".  ...  We would like to introduce the problem in detail to readers and share the ideas on how new problems are developed, relating to old problems.  ...  of the general problem based on the difference equation was first given byStruyck(1716).  ... 
doi:10.5351/csam.2013.20.1.001 fatcat:cvvsk47turgqbegmfmusxflp3y

Computation of ruin probabilities for general discrete-time Markov models [article]

Ilya Tkachev, Alessandro Abate
2013 arXiv   pre-print
We study the ruin problem over a risk process described by a discrete-time Markov model.  ...  Rather than focusing on a particular model for risk processes, we give a general characterization of the ruin probability by providing corresponding recursions and fixpoint equations.  ...  Atkinson for his help on the extremely precise and fast FIE toolbox [AS08] .  ... 
arXiv:1308.5152v1 fatcat:yd4qmds4mngwzavxf2zgcigtwm

Page 111 of Naval Research Logistics Vol. 6, Issue 2 [page]

1959 Naval Research Logistics  
rate p (<1) which is effective on the withdrawal account only; a ruin payment F that is paid to the player upon ruin or on leaving the game by withdrawing all assets; a ruin level B and a ruin condition  ...  In general, complex dynamic problems are soon encountered. This paper deals only with simple examples involving one and two person dynamic nonzero sum games. 2.  ... 

Proactive preservation of world heritage by crowdsourcing and 3D reconstruction technology

Hidehiko Shishido, Yutaka Ito, Youhei Kawamura, Toshiya Matsui, Atsuyuki Morishima, Itaru Kitahara
2017 2017 IEEE International Conference on Big Data (Big Data)  
Since over one million tourists annually visit the Angkor ruins, the effect on the buildings from the vibrations caused by these tourists is a huge problem for maintaining them.  ...  Using crowdsourcing and 3D reconstruction technology, we are organizing a proactive preservation project for the Angkor Thom Bayon Temple, which is a world cultural heritage site.  ...  As shown on the right of Fig. 1 , we applied various chemicals to stones made of the same material as the ruins and generated a 3D model to observe the breeding process of the bryophytes.  ... 
doi:10.1109/bigdata.2017.8258479 dblp:conf/bigdataconf/ShishidoIKMMK17 fatcat:45s7gnrcofdovg7z55ed4cbfiu

A three-player gambler's ruin problem: some extensions

Abid Hussain, Muhammad Hanif, Moazzam Naseer
2021 Scientific Inquiry and Review  
For the expected ruin time of the classic three-player symmetric game, Sandell derived a general formula by introducing an appropriate martingale and stopping time.  ...  The current work is also about three-player gambler's ruin problem with some extensions as well.  ...  The literature on asymmetric game for more than two players is more limited and no general expression available for the ruin time till to date.  ... 
doi:10.32350/sir.53.01 fatcat:nvmxr7sxojgrpn7mwcuo4ku4sa

A Bootstrap Test for the Probability of Ruin in the Compound Poisson Risk Process

Benjamin Baumgartner, Riccardo Gatto
2010 ASTIN Bulletin: The Journal of the International Actuarial Association  
In this article we propose a bootstrap test for the probability of ruin in the compound Poisson risk process.  ...  We adopt the P-value approach, which leads to a more complete assessment of the underlying risk than the probability of ruin alone.  ...  The uniformity of both P A, n and P B, n will be checked in the simulation study of Section 3. As already mentioned, computing the probability of ruin is generally not a simple problem.  ... 
doi:10.2143/ast.40.1.2049227 fatcat:6texwtwxmfem3bwusxkocfyci4

Asymptotic and numerical analysis of the optimal investment strategy for an insurer

P. Emms, S. Haberman
2007 Insurance, Mathematics & Economics  
survival probability in ruin theory.  ...  Calculation of the optimal asset allocation leads to a difficult numerical problem because of the boundary layer structure of the solution and the tail properties of the claim size distribution.  ...  (2002) who consider the effect a fixed investment in a risky asset has on the ruin probability.  ... 
doi:10.1016/j.insmatheco.2006.03.003 fatcat:inaoya2f3jhklmtnabc32jyble

Evolutionary Ruin And Stochastic Recreate: A Case Study On The Exam Timetabling Problem

Jingpeng Li, Rong Qu, Yindong Shen
2012 ECMS 2012 Proceedings edited by: K. G. Troitzsch, M. Moehring, U. Lotzmann  
Encouraging experimental results on exam timetabling problems are reported.  ...  It improves the original Ruin and Recreate principle's performance by incorporating an Evolutionary Ruin step which implements evolution within a single solution.  ...  Li has worked on five U.K. government-funded EPSRC projects and three Chinese government-funded NSFC research projects covering the topics of human scheduling, next generation decision support, novel research  ... 
doi:10.7148/2012-0347-0353 dblp:conf/ecms/LiQS12 fatcat:bkopsx6dafbghadr52inp55s7e

Three-Player Gambler's Ruin Problem: Some Extensions

Abid Hussain, Muhammad Hanif, Moazzam Naseer
2021 Scientific Inquiry and Review  
For calculating the expected ruin time of the classic three-player symmetric game, Sandell derived a general formula by introducing an appropriate martingale and stopping time.  ...  The current work is also about three-player gambler's ruin problem with some extensions.  ...  The literature on asymmetric game for more than two players is more limited and no general expression is available for the ruin time to date.  ... 
doi:10.32350/sir/53.01 fatcat:3cpwlwsjtzfdne66volx2uphre

Ruin and Recreate Principle Based Approach for the Quadratic Assignment Problem [chapter]

Alfonsas Misevicius
2003 Lecture Notes in Computer Science  
In this paper, we propose an algorithm based on so-called ruin and recreate (R&R) principle.  ...  The main components of this method are a ruin (mutation) procedure and a recreate (improvement) procedure.  ...  In the second phase, one tries to rebuild the solution just "ruined" as best as one can.  ... 
doi:10.1007/3-540-45105-6_71 fatcat:hlcb6sfnvnbxnhwdorf3pgghyq

The classic two‐player gambler's ruin problem with successive events: a generalized variance

Abid Hussain, Salman A. Cheema
2021 Computational and Mathematical Methods  
In this article, we present the general expressions for the variance of the ruin time of the classic two-player gambler's ruin problem with successive and nonoverlapping trials.  ...  ., decision is based on successive and nonoverlapping trials) is in favor of the player, who plays with a better skill set and reduces the chances of decision based only on luck.  ...  the player with a better skill set and thus reduced the likelihood of win or loss based only on luck. 7 provided the expressions of ruin probability (P x ), ruin time (E(T)) and conditional ruin times  ... 
doi:10.1002/cmm4.1156 fatcat:d5wug5fqc5cf3bux24z7dviegu

Generalized Gambler's Ruin Problem: Explicit Formulas via Siegmund Duality

Paweł Lorek
2016 Methodology and Computing in Applied Probability  
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 probabilities (including ties) depending on the current fortune with particular  ...  Partial support by the project RARE-318984, a Marie Curie IRSES Fellowship within the 7th European Community Framework Programme, is kindly acknowledged.  ... 
doi:10.1007/s11009-016-9507-6 fatcat:56owzb2d2vdfljh25umwaufypm

Page 4263 of Mathematical Reviews Vol. , Issue 2004e [page]

2004 Mathematical Reviews  
One of the crucial issues is to estimate the generator of the underlying Markov chain.  ...  The derivative of the final value of such a problem is discontinuous and on the two sides of the free boundary the second derivatives are different.  ... 

Ruin Problems of Multidimensional Risk Models under Constant Interest Rates and Dependent Risks with Heavy Tails

Xinmei Shen, Meng Yuan, Dawei Lu
2020 Mathematical Problems in Engineering  
By assuming a large initial capital and regularly varying distributions for the losses, we derive asymptotic estimates for the ruin probability under some dependence structure and study the optimal allocation  ...  Consider a discrete-time multidimensional risk model with constant interest rates where capital transfers between lines are partially allowed over each period.  ...  During the few works, Collamore [6, 7] addressed the multidimensional ruin problems with the general ruin set and studied the sampling techniques in a light-tailed case. Picard et al.  ... 
doi:10.1155/2020/9489612 fatcat:pi5wkym42nbjdon23sm623phbe
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