We study the detailed convergence of the binomial tree scheme. It is known that the scheme is first order. We find the exact constants, and show it is possible to modify Richardson extrapolation to get a method of order three-halves. We see that the delta, used in hedging, converges at the same rate. We analyze this by first embedding the tree scheme in the Black-Scholes diffusion model by mean...

An edge-colored graph G is conflict-free connected if, between each pair of distinct vertices, there exists a path containing a color used on exactly one of its edges. The conflict-free connection number of a connected graph G, denoted by cfc(G), is defined as the smallest number of colors that are required in order to make G conflict-free connected. A coloring of vertices of a hypergraph H = (...

BACKGROUND Wild plants are used as food for human populations where people still depend on natural resources to survive. This study aimed at identifying wild plants and edible uses known in four rural communities of the Pantanal-Brazil, estimating the use value and understanding how distance to the urban areas, gender, age and number of different environments available in the vicinity can influ...

As the transition to renewable energy sources progresses, their integration makes electricity production increasingly fluctuating, also causing amplified volatility in electricity prices on energy markets. To contribute to power grid stability, utilities need to balance volatile supply through shifting demand. This measure of demand side management creates flexibility, being enabled as the inte...

In this expository paper we illustrate the generality of game theoretic probability protocols of Shafer and Vovk (2001) in finite-horizon discrete games. By restricting ourselves to finite-horizon discrete games, we can explicitly describe how discrete distributions with finite support and the discrete pricing formulas, such as the Cox-Ross-Rubinstein formula, are naturally derived from game-th...

Contents 1. Introduction 1 2. The central limit theorem 1 3. The normal approximation of the binomial distribution 2 4. The normal approximation of the mixed binomial distribution 4 5. The law of large numbers approximation of a mixed binomial distribution 6 6. Finding the mixed binomial distribution by using Monte Carlo simulations 6 6.

Problem statement: The modeling of claims count is one of the most important topics in actuarial theory and practice. Many attempts were implemented in expanding the classes of mixed and compound distributions, especially in the distribution of exponential family, resulting in a better fit on count data. In some cases, it is proven that mixed distributions, in particular mixed Poisson and mixed...

This paper describes the frequency and number of Sphyrion laevigatum in the skin of Genypterus blacodes, an important economic resource in Chile. The analysis of a spatial distribution model indicated that the parasites tended to cluster. Variations in the number of parasites per host could be described by a negative binomial distribution. The maximum number of parasites observed per host was two.

We present new families of lower bounds for the price of the American put option on a dividend paying stock when the stock follows a log normal process and the option can be exercised continuously to a finite horizon . By put call parity, these bounds can be easily converted to bounds on the price of the Ameican call option on a dividend paying stock. By numerically optimizing these bounds, we ...