RelValAnalysis (version 1.0)

AtlasModel: Atlas Model

Description

The function AtlasModel is used to create a marketmodel object which represents an Atlas model with user-provided parameters.

Usage

AtlasModel(n, g, sigma)

Value

A marketmodel object.

Details

The definition of the Atlas model follows Example 5.3.3 in Fernholz (2002). The stochastic differential equation of the market capitalizations X_i(t) for the i-th stock takes the form dlog X_i(t) = gamma_i(t)dt + sigma dW_i(t), i = 1, ..., n, where gamma_i(t) = ng if stock i is the smallest, and is 0 otherwise. It is the simplest market model which exhibits an asymptotic Pareto-shaped capital distribution curve.

References

Fernholz, E. R. (2002) Stochastic portfolio theory. Springer.

See Also

marketmodel, SimMarketModel

Examples

# Create an Atlas model of 100 stocks
model <- AtlasModel(n = 100, g = 0.001, sigma = 0.2)

# Simulate the Atlas model to get 5 years of monthly data
market <- SimMarketModel(model, n.years = 5, frequency = 12)