The ruin time for 3-player gambler’s problem: an approximate formula

2021 ◽  
pp. 1-9
Author(s):  
Abid Hussain ◽  
Salman A. Cheema ◽  
Summaira Haroon ◽  
Tanveer Kifayat
Keyword(s):  
Approximate Formula ◽  
Ruin Time

REFRACTION ARRIVALS THROUGH THIN HIGH‐VELOCITY LAYERS

Geophysics ◽  
1965 ◽  
Vol 30 (2) ◽  
pp. 204-212 ◽  
Author(s):  
J. H. Rosenbaum
Keyword(s):  
Exponential Decay ◽  
High Velocity ◽  
Elastic Layer ◽  
Approximate Formula ◽  
Asymptotic Theory ◽  
Surrounding Medium ◽  
Low Frequency ◽  
Horizontal Distance ◽  
Symmetric Mode ◽  
Elastic Parameters

The first significant refraction arrival through a thin high‐velocity elastic layer in an elastic medium has been investigated theoretically by means of an asymptotic theory. This first low‐frequency arrival is closely connected with the longitudinal plate wave in the thin layer. When the medium surrounding the layer is a fluid, the signal does not decay exponentially with horizontal distance; when the surrounding medium is a solid, the signal does decay exponentially. A very simple approximate formula for this exponential decay is presented and compared with numerical results of the more rigorous theory. The decay as well as the shape of the signal is dependent upon the contrast in elastic parameters between the plate and the surrounding medium. Higher‐frequency early arrivals, associated with the second symmetric mode, have also been investigated. They exhibit greater exponential decay with horizontal distance than the low‐frequency first arrivals.

CLASSICAL DIFFUSION AND QUANTAL LOCALIZATION OF A KICKED PARTICLE IN A WELL

1988 ◽  
Vol 02 (01) ◽  
pp. 103-120 ◽  
Author(s):  
AVRAHAM COHEN ◽  
SHMUEL FISHMAN
Keyword(s):  
Diffusion Coefficient ◽  
Classical Limit ◽  
Approximate Formula ◽  
Quantum Systems ◽  
Potential Well ◽  
Diffusive Growth ◽  
Classical Chaos ◽  
The One ◽  
Short Time ◽  
Infinite Potential Well

The classical and quantal behavior of a particle in an infinite potential well, that is periodically kicked is studied. The kicking potential is K|q|α, where q is the coordinate, while K and α are constants. Classically, it is found that for α > 2 the energy of the particle increases diffusively, for α < 2 it is bounded and for α = 2 the result depends on K. An approximate formula for the diffusion coefficient is presented and compared with numerical results. For quantum systems that are chaotic in the classical limit, diffusive growth of energy takes place for a short time and then it is suppressed by quantal effects. For the systems that are studied in this work the origin of the quantal localization in energy is related to the one of classical chaos.

The reaction of [Rh(CO)2Cl]2 with hexafluorobut-2-yne

1978 ◽  
Vol 31 (3) ◽  
pp. 661 ◽  
Author(s):  
RS Dickson ◽  
SH Johnson
Keyword(s):  
Molecular Structure ◽  
Approximate Formula ◽  
Chemical Properties ◽  
Extensive Study ◽  
Rhodium Complex ◽  
And Chemical Properties

The reaction of [Rh(CO)2Cl]2 with CF3C≡CCF3 gives a fluorocarbon-rhodium complex of approximate formula [RhCl(CO)2 or 3(C4F6)]n,xH2O,yC6H6. The complex is an intermediate in the formation of tetrakis(trifluoromethyl)cyclopentadienone from CF3C≡CCF3 and CO in the presence of[Rh(CO)2Cl]2. The molecular structure of the complex remains obscure despite extensive study of its spectroscopic and chemical properties. The major products formed in the reactions of the complex with σ-cyclopentadienylthallium and with triphenylphosphine are (η- C5H5)2Rh2(CO)2(CF3C2CF3)and Rh(CO)Cl(PPh3)2 respectively.

scholarly journals Optimal Dividend and Capital Injection Problem with Transaction Cost and Salvage Value: The Case of Excess-of-Loss Reinsurance Based on the Symmetry of Risk Information

Symmetry ◽  
2018 ◽  
Vol 10 (7) ◽  
pp. 276 ◽  
Author(s):  
Qingyou Yan ◽  
Le Yang ◽  
Tomas Baležentis ◽  
Dalia Streimikiene ◽  
Chao Qin
Keyword(s):  
Transaction Cost ◽  
Risk Information ◽  
Insurance Company ◽  
Optimal Control Strategy ◽  
Ruin Time ◽  
Discounted Cost ◽  
Capital Injection ◽  
Surplus Process ◽  
Optimal Dividend ◽  
A Company

This paper considers the optimal dividend and capital injection problem for an insurance company, which controls the risk exposure by both the excess-of-loss reinsurance and capital injection based on the symmetry of risk information. Besides the proportional transaction cost, we also incorporate the fixed transaction cost incurred by capital injection and the salvage value of a company at the ruin time in order to make the surplus process more realistic. The main goal is to maximize the expected sum of the discounted salvage value and the discounted cumulative dividends except for the discounted cost of capital injection until the ruin time. By considering whether there is capital injection in the surplus process, we construct two instances of suboptimal models and then solve for the corresponding solution in each model. Lastly, we consider the optimal control strategy for the general model without any restriction on the capital injection or the surplus process.

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