Description Usage Arguments Details Value References See Also Examples

The function `AtlasModel`

is used to create a ` marketmodel`

object which represents an Atlas model with user-provided parameters.

1 | ```
AtlasModel(n, g, sigma)
``` |

`n` |
a positive integer representing the number of stocks in the market |

`g` |
a positive number. In this model, |

`sigma` |
a positive number representing the common volatility of the stocks. |

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.

A `marketmodel`

object.

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

1 2 3 4 5 | ```
# 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)
``` |

```
Loading required package: zoo
Attaching package: 'zoo'
The following objects are masked from 'package:base':
as.Date, as.Date.numeric
```

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