Profit signature from a profit vector

Converts a Chapter 17 profit vector \(\mathbf{Pr}=(Pr_0,\dots,Pr_n)\) into the corresponding profit signature \(\mathbf{\Pi}=(\Pi_0,\dots,\Pi_n)\) using Equation (17.3).

Usage

Pi_signature(Pr, p_tau)

Arguments

Pr

Profit vector of length \(n+1\).

p_tau

One-year in-force probabilities. This may have length \(n-1\) or \(n\). If length \(n\), the final entry is ignored for the profit-signature calculation.

Value

Numeric vector of length \(n+1\).

Examples

Pr <- c(-15.00, 8.42, 8.40, 8.61)
Pi_signature(Pr, p_tau = c(0.99858, 0.99847, 0.99834))
#>        Pi0        Pi1        Pi2        Pi3 
#> -15.000000   8.420000   8.388072   8.584619