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In 2015, Guglielmi and Badia discussed optimal strategies in a particular type of service system with two strategic servers. In their setup, each server can be either active or inactive and an active server can be requested to transmit a sequence of packets. The servers have varying probabilities of successfully transmitting when they are active, and both servers receive a unit reward if the sequence of packets is transmitted successfully. Guglielmi and Badia provided an analysis of optimal strategies in four scenarios: where each server does not know the other's successful transmission probability; one of the two servers is always inactive; each server knows the other's successful transmission probability and they are willing to cooperate. Unfortunately, the analysis by Guglielmi and Badia contained some errors. In this paper we correct these errors. We discuss three cases where both servers (I) communicate and cooperate; (II) neither communicate nor cooperate; (III) communicate but do not cooperate. In particular, we obtain the unique Nash equilibrium strategy in Case II through a Bayesian game formulation, and demonstrate that there is a region in the parameter space where there are multiple Nash equilibria in Case III. We also quantify the value of communication or cooperation by comparing the social welfare in the three cases, and propose possible regulations to make the Nash equilibrium strategy the socially optimal strategy for both Cases II and III. [ABSTRACT FROM AUTHOR]

Recent years have seen a large increase in the popularity of Texas hold ’em poker. It is now the most commonly played variant of the game, both in casinos and through online platforms. In this paper, we present a simulation study for games of Texas hold ’em with between two and 23 players. From these simulations, we estimate the probabilities of each player having been dealt the winning hand. These probabilities are calculated conditional on both partial information (that is, the player only having knowledge of his/her cards) and also on fuller information (that is, the true probabilities of each player winning given knowledge of the cards dealt to each player). Where possible, our estimates are compared to exact analytic results and are shown to have converged to three significant figures. With these results, we assess the poker strategies described in two recent pieces of popular culture. In comparing the ideas expressed in Taylor Swift’s song, New Romantics , and the betting patterns employed by James Bond in the 2006 film, Casino Royale , we conclude that Ms Swift demonstrates a greater understanding of the true probabilities of winning a game of Texas hold ’em poker. [ABSTRACT FROM AUTHOR]

In this paper, we consider an insurance company whose surplus (reserve) is modeled by a jump diffusion risk process. The insurance company can invest part of its surplus in n risky assets and purchase proportional reinsurance for claims. Our main goal is to find an optimal investment and proportional reinsurance policy which minimizes the ruin probability. We apply stochastic control theory to solve this problem. We obtain the closed form expression for the minimal ruin probability, optimal investment and proportional reinsurance policy. We find that the minimal ruin probability satisfies the Lundberg equality. We also investigate the effects of the diffusion volatility parameter, the market price of risk and the correlation coefficient on the minimal ruin probability, optimal investment and proportional reinsurance policy through numerical calculations. [ABSTRACT FROM AUTHOR]

In this paper, we deal with a class of reflected backward stochastic differential equations (RBSDEs) corresponding to the subdifferential operator of a lower semi-continuous convex function, driven by Teugels martingales associated with a Lévy process. We show the existence and uniqueness of the solution for RBSDEs by means of the penalization method. As an application, we give a probabilistic interpretation for the solutions of a class of partial differential-integral inclusions. [ABSTRACT FROM AUTHOR]

This paper deals with two-species convolution diffusion-competition models of Lotka-Volterra type with delays which describe more accurate information than the Laplacian diffusion-competition models. We first investigate the existence of travelling wave solutions of a class of nonlocal convolution diffusion systems with weak quasimonotonicity or weak exponential quasimonotonicity by a cross-iteration technique and Schauder's fixed point theorem. When the results are applied to the convolution diffusion-competition models with delays, we establish the existence of travelling wave solutions as well as asymptotic behaviour. [ABSTRACT FROM AUTHOR]

The aim of this paper is to find a concrete bound for the error involved when approximating the nth Hermite function (in the oscillating range) by an asymptotic formula due to D. Dominici. This bound is then used to study the accuracy of certain approximations to Hermite expansions and to Fourier transforms. A way of estimating an unknown probability density is proposed. [ABSTRACT FROM AUTHOR]

We investigate rare or small probability events in the context of large deviations of the stochastic Camassa–Holm equation. By the weak convergence approach and regularization, we get large deviations of the regularized equation. Then, by stochastic equations exponentially equivalent to the corresponding laws, we get large deviations of the stochastic Camassa–Holm equation. [ABSTRACT FROM AUTHOR]

The maximal return and optimal leverage of a constant proportion debt obligation with finite termination and two boundaries are analysed by numerically solving Hamilton–Jacobi–Bellman equations. We discuss the probabilities of the asset value reaching the upper or lower bound under the optimal control and the optimal control problem with a time-varying boundary. Furthermore, we also analyse the relationship between the optimal return, the optimal policy and different parameters. [ABSTRACT FROM PUBLISHER]

We study the optimal proportional reinsurance and investment problem in a general jump-diffusion financial market. Assuming that the insurer’s surplus process follows a jump-diffusion process, the insurer can purchase proportional reinsurance from the reinsurer and invest in a risk-free asset and a risky asset, whose price is modelled by a general jump-diffusion process. The insurance company wishes to maximize the expected exponential utility of the terminal wealth. By using techniques of stochastic control theory, closed-form expressions for the value function and optimal strategy are obtained. A Monte Carlo simulation is conducted to illustrate that the closed-form expressions we derived are indeed the optimal strategies, and some numerical examples are presented to analyse the impact of model parameters on the optimal strategies. [ABSTRACT FROM PUBLISHER]

We interpret a boundary-value problem arising in a cell growth model as a singular Sturm–Liouville problem that involves a functional differential equation of the pantograph type. We show that the probability density function of the cell growth model corresponds to the first eigenvalue and that there is a family of rapidly decaying eigenfunctions. [ABSTRACT FROM AUTHOR]

In this note, we study deterministic and stochastic models for the spread of cholera. The deterministic model for the total number of cholera cases fits the observed total number of cholera cases in some recent outbreaks. The stochastic model for the total number of cholera cases leads to a binomial type distribution with a mean that agrees with the deterministic model. [ABSTRACT FROM AUTHOR]

We consider families of general two-point quadrature formulae, using the extension of Montgomery's identity via Taylor's formula. The formulae obtained are used to present a number of inequalities for functions whose derivatives are from L p spaces and Bullentype inequalities. [ABSTRACT FROM AUTHOR]

Reflected Brownian motion is used in areas such as physiology, electrochemistry and nuclear magnetic resonance. We study the first-passage-time problem of this process which is relevant in applications; specifically, we find a Volterra integral equation for the distribution of the first time that a reflected Brownian motion reaches a nondecreasing barrier. Additionally, we note how a numerical procedure can be used to solve the integral equation. [ABSTRACT FROM AUTHOR]