scholarly journals Penney's Game Odds From No-Arbitrage

2019 ◽  
Author(s):  
Joshua Benjamin Miller
Keyword(s):  
Fair Coin ◽  
No Arbitrage ◽  
Zero Sum ◽  
Betting Odds ◽  
Insight Into ◽  
Expected Duration

Penney's game is a two player zero-sum game in which each player chooses a three-flip pattern of heads and tails and the winner is the player whose pattern occurs first in repeated tosses of a fair coin. Because the players choose sequentially, the second mover has the advantage. In fact, for any three-flip pattern, there is another three-flip pattern that is strictly more likely to occur first. This paper provides a novel no-arbitrage argument that generates the winning odds corresponding to any pair of distinct patterns. The resulting odds formula is equivalent to that generated by Conway's ``leading number'' algorithm. The accompanying betting odds intuition adds insight into why Conway's algorithm works. The proof is simple and easy to generalize to games involving more than two outcomes, unequal probabilities, and competing patterns of various length. Additional results on the expected duration of Penney's game are presented. Code implementing and cross-validating the algorithms is included.

THE BRITTEN-JONES AND NEUBERGER SMILE-CONSISTENT WITH STOCHASTIC VOLATILITY OPTION PRICING MODEL: A FURTHER ANALYSIS

2002 ◽  
Vol 05 (01) ◽  
pp. 1-31 ◽  
Author(s):  
ALESSANDRO ROSSI
Keyword(s):  
Option Pricing ◽  
Stochastic Volatility ◽  
Pricing Model ◽  
Pricing Models ◽  
No Arbitrage ◽  
Option Pricing Model ◽  
Exotic Option ◽  
Exotic Option Pricing ◽  
Insight Into

In part of the recent financial literature, exotic option pricing models have been built by establishing a link with European-style options. All these models share the characteristic of being consistent with the observed market smile. They differ respect to the specification of the volatility process. This paper provides a deeper insight into the Britten-Jones and Neuberger (1999) smile-consistent no arbitrage with stochastic volatility option pricing model. Their approach is similar, in spirit, to that one of Derman and Kani (1997), but the implementation is simpler and faster. We explain the main features of the model by performing a set of exercises. In addition we propose some extensions of the model, which make it more flexible.

Maximizing the variance of the time to ruin in a multiplayer game with selection

2016 ◽  
Vol 48 (2) ◽  
pp. 610-630
Author(s):  
Ilie Grigorescu ◽  
Yi-Ching Yao
Keyword(s):  
Explicit Formula ◽  
Open Problem ◽  
Optimal Strategy ◽  
Value Function ◽  
Short Proof ◽  
Fair Coin ◽  
Expected Time ◽  
Maximum Value ◽  
Maximum Variance ◽  
Expected Duration

Abstract We consider a game with K ≥ 2 players, each having an integer-valued fortune. On each round, a pair (i,j) among the players with nonzero fortunes is chosen to play and the winner is decided by flipping a fair coin (independently of the process up to that time). The winner then receives a unit from the loser. All other players' fortunes remain the same. (Once a player's fortune reaches 0, this player is out of the game.) The game continues until only one player wins all. The choices of pairs represent the control present in the problem. While it is known that the expected time to ruin (i.e. expected duration of the game) is independent of the choices of pairs (i,j) (the strategies), our objective is to find a strategy which maximizes the variance of the time to ruin. We show that the maximum variance is uniquely attained by the (optimal) strategy, which always selects a pair of players who have currently the largest fortunes. An explicit formula for the maximum value function is derived. By constructing a simple martingale, we also provide a short proof of a result of Ross (2009) that the expected time to ruin is independent of the strategies. A brief discussion of the (open) problem of minimizing the variance of the time to ruin is given.

Case Studies of School-Level Governance Dynamics in the Western Cape

2018 ◽  
Author(s):  
Ursula Hoadley ◽  
Brian Levy ◽  
Lawule Shumane ◽  
Shelly Wilburn
Keyword(s):  
Case Studies ◽  
Management Practices ◽  
Policy Design ◽  
Local Governance ◽  
School Level ◽  
Western Cape ◽  
Eastern Cape ◽  
Multi Stakeholder ◽  
Zero Sum ◽  
Insight Into

This chapter details four case studies of school-level management practices in the appointment process of school principals. The school-level processes are used as a lens through which to refract local governance dynamics, and thereby gain insight into the broader multi-stakeholder contexts within which the principal is embedded. The contrasts between the Western Cape and Eastern Cape provinces provide an ideal opportunity to explore a central theme of this book, namely how ‘good fit’ works—how preferred approaches to policy design and implementation might vary according to the contexts in which they are being undertaken. The chapter suggests that rather than viewing the interaction between hierarchical and horizontal governance as zero-sum, the task for practitioners is to find ways to make more effective the ‘both/and’ balance, with an emphasis on impersonal forms of decision-making.

Calibration problems in hydrogen luminosities

1966 ◽  
Vol 24 ◽  
pp. 322-330
Author(s):  
A. Beer
Keyword(s):  
Galactic Structure ◽  
B Stars ◽  
Insight Into

The investigations which I should like to summarize in this paper concern recent photo-electric luminosity determinations of O and B stars. Their final aim has been the derivation of new stellar distances, and some insight into certain patterns of galactic structure.

Why do people believe in a zero-sum economy?

2018 ◽  
Vol 41 ◽  
Author(s):  
Samuel G. B. Johnson
Keyword(s):  
Perspective Taking ◽  
Evolutionary Model ◽  
Everyday Experience ◽  
Coalitional Psychology ◽  
The Face ◽  
Zero Sum

AbstractZero-sum thinking and aversion to trade pervade our society, yet fly in the face of everyday experience and the consensus of economists. Boyer & Petersen's (B&P's) evolutionary model invokes coalitional psychology to explain these puzzling intuitions. I raise several empirical challenges to this explanation, proposing two alternative mechanisms – intuitive mercantilism (assigning value to money rather than goods) and errors in perspective-taking.

Stochasting modeling of planetary ring systems

1984 ◽  
Vol 75 ◽  
pp. 461-469 ◽  
Author(s):  
Robert W. Hart
Keyword(s):  
Maximum Entropy ◽  
Ring System ◽  
The Sun ◽  
Ultimate State ◽  
Interparticle Interactions ◽  
Ring Systems ◽  
First Order ◽  
Planetary Ring ◽  
Insight Into

ABSTRACTThis paper models maximum entropy configurations of idealized gravitational ring systems. Such configurations are of interest because systems generally evolve toward an ultimate state of maximum randomness. For simplicity, attention is confined to ultimate states for which interparticle interactions are no longer of first order importance. The planets, in their orbits about the sun, are one example of such a ring system. The extent to which the present approximation yields insight into ring systems such as Saturn's is explored briefly.

Skeletal elements of crinoid echinoderms: High-resolution structural and microanalytical results

1983 ◽  
Vol 41 ◽  
pp. 194-195
Author(s):  
D. F. Blake ◽  
L. F. Allard ◽  
D. R. Peacor
Keyword(s):  
High Resolution ◽  
Marine Invertebrates ◽  
Sea Urchins ◽  
Structural Features ◽  
Sea Stars ◽  
High Resolution Tem ◽  
Relationship Of ◽  
The Relationship ◽  
Insight Into

Echinodermata is a phylum of marine invertebrates which has been extant since Cambrian time (c.a. 500 m.y. before the present). Modern examples of echinoderms include sea urchins, sea stars, and sea lilies (crinoids). The endoskeletons of echinoderms are composed of plates or ossicles (Fig. 1) which are with few exceptions, porous, single crystals of high-magnesian calcite. Despite their single crystal nature, fracture surfaces do not exhibit the near-perfect {10.4} cleavage characteristic of inorganic calcite. This paradoxical mix of biogenic and inorganic features has prompted much recent work on echinoderm skeletal crystallography. Furthermore, fossil echinoderm hard parts comprise a volumetrically significant portion of some marine limestones sequences. The ultrastructural and microchemical characterization of modern skeletal material should lend insight into: 1). The nature of the biogenic processes involved, for example, the relationship of Mg heterogeneity to morphological and structural features in modern echinoderm material, and 2). The nature of the diagenetic changes undergone by their ancient, fossilized counterparts. In this study, high resolution TEM (HRTEM), high voltage TEM (HVTEM), and STEM microanalysis are used to characterize tha ultrastructural and microchemical composition of skeletal elements of the modern crinoid Neocrinus blakei.

Structure and function of neural networks in the retina

1988 ◽  
Vol 46 ◽  
pp. 26-27
Author(s):  
Peter Sterling
Keyword(s):  
Ganglion Cells ◽  
Three Dimensional ◽  
Structure And Function ◽  
Synaptic Connections ◽  
Visual Axis ◽  
One Dimensional ◽  
Cat Retina ◽  
Ultrathin Sections ◽  
And Function ◽  
Insight Into

The synaptic connections in cat retina that link photoreceptors to ganglion cells have been analyzed quantitatively. Our approach has been to prepare serial, ultrathin sections and photograph en montage at low magnification (˜2000X) in the electron microscope. Six series, 100-300 sections long, have been prepared over the last decade. They derive from different cats but always from the same region of retina, about one degree from the center of the visual axis. The material has been analyzed by reconstructing adjacent neurons in each array and then identifying systematically the synaptic connections between arrays. Most reconstructions were done manually by tracing the outlines of processes in successive sections onto acetate sheets aligned on a cartoonist's jig. The tracings were then digitized, stacked by computer, and printed with the hidden lines removed. The results have provided rather than the usual one-dimensional account of pathways, a three-dimensional account of circuits. From this has emerged insight into the functional architecture.

Radiation Damage Studies with the HVEM

1972 ◽  
Vol 30 ◽  
pp. 680-681
Author(s):  
J. J. Laidler ◽  
B. Mastel
Keyword(s):  
Radiation Damage ◽  
Stainless Steels ◽  
Volume Expansion ◽  
Austenitic Stainless Steels ◽  
Test Facility ◽  
Fast Breeder Reactors ◽  
Breeder Reactors ◽  
Under Construction ◽  
Development Laboratory ◽  
Insight Into

One of the major materials problems encountered in the development of fast breeder reactors for commercial power generation is the phenomenon of swelling in core structural components and fuel cladding. This volume expansion, which is due to the retention of lattice vacancies by agglomeration into large polyhedral clusters (voids), may amount to ten percent or greater at goal fluences in some austenitic stainless steels. From a design standpoint, this is an undesirable situation, and it is necessary to obtain experimental confirmation that such excessive volume expansion will not occur in materials selected for core applications in the Fast Flux Test Facility, the prototypic LMFBR now under construction at the Hanford Engineering Development Laboratory (HEDL). The HEDL JEM-1000 1 MeV electron microscope is being used to provide an insight into trends of radiation damage accumulation in stainless steels, since it is possible to produce atom displacements at an accelerated rate with 1 MeV electrons, while the specimen is under continuous observation.

Failure Analysis With the Scanning Electron Microscope

1972 ◽  
Vol 30 ◽  
pp. 482-483
Author(s):  
John R. Devaney
Keyword(s):  
Electron Microscope ◽  
Scanning Electron Microscope ◽  
Integrated Circuits ◽  
Failure Analysis ◽  
High Reliability ◽  
Military Applications ◽  
Small Structure ◽  
Useful Life ◽  
Insight Into ◽  
Scanning Electron

Occasionally in history, an event may occur which has a profound influence on a technology. Such an event occurred when the scanning electron microscope became commercially available to industry in the mid 60's. Semiconductors were being increasingly used in high-reliability space and military applications both because of their small volume but, also, because of their inherent reliability. However, they did fail, both early in life and sometimes in middle or old age. Why they failed and how to prevent failure or prolong “useful life” was a worry which resulted in a blossoming of sophisticated failure analysis laboratories across the country. By 1966, the ability to build small structure integrated circuits was forging well ahead of techniques available to dissect and analyze these same failures. The arrival of the scanning electron microscope gave these analysts a new insight into failure mechanisms.

Sign in / Sign up

Export Citation Format

Share Document