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A Note on the History of the Gambler's Ruin Problem
2013
Communications for Statistical Applications and Methods
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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
2013
Communications for Statistical Applications and Methods
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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]
2013
arXiv
pre-print
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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
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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
2017
2017 IEEE International Conference on Big Data (Big Data)
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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
2021
Scientific Inquiry and Review
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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
2010
ASTIN Bulletin: The Journal of the International Actuarial Association
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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
2007
Insurance, Mathematics & Economics
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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
2012
ECMS 2012 Proceedings edited by: K. G. Troitzsch, M. Moehring, U. Lotzmann
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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
2021
Scientific Inquiry and Review
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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]
2003
Lecture Notes in Computer Science
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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
2021
Computational and Mathematical Methods
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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
2016
Methodology and Computing in Applied Probability
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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
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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
2020
Mathematical Problems in Engineering
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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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