cap: Covariance Allocation Principle

In OCA: Optimal Capital Allocations

Covariance Allocation Principle

Description

\loadmathjax

This function implements the covariance allocation principle for optimal capital allocation.

Usage

cap(Loss, Capital)

Arguments

Loss	A matrix containing the individual losses in each column
Capital	A scalar representing the capital to be allocated to each loss.

Details

The Covariance Allocation Principle correspond to the following expression:

\mjtdeqn

K_i = \fracKVar[S] Cov(X_i, S), \quad i=1, ..., n,K_i = \dfracKVar[S] Cov(X_i, S), \quad i=1, ..., n,

where \mjteqnK_iK_iK_i is the capital to be allocated to the ith loss, \mjteqnKK is the total capital to be allocated, \mjteqnX_iX_i is the individual unit loss and S is the total (aggretate) loss, this comes from \mjteqn\sum_iX_i\sum_iX_i. \mjteqnCov(X_i, S)Cov(X_i, S) is the covariance between the individual loss \mjteqnX_iX_i and the aggregate loss S; and \mjteqnVar(S)Var(S) is the variance of the aggregate loss.

Value

A vector containing each asset and the corresponding capital allocation. If Capital=1, then the returned value will be the proportions of capital required by each loss to be faced.

Author(s)

Jilber Urbina

References

Dhaene J., Tsanakas A., Valdez E. and Vanduffel S. (2011). Optimal Capital Allocation Principles. The Journal of Risk and Insurance. Vol. 00, No. 0, 1-28.

Urbina, J. (2013) Quantifying Optimal Capital Allocation Principles based on Risk Measures. Master Thesis, Universitat Politècnica de Catalunya.

Urbina, J. and Guillén, M. (2014). An application of capital allocation principles to operational risk and the cost of fraud. Expert Systems with Applications. 41(16):7023-7031.

Examples

data(dat1, dat2)
Loss <- cbind(Loss1=dat1[1:400, ], Loss2=unname(dat2))
# Proportions of capital to be allocated to each bussines unit
cap(Loss, Capital=1)

# Capital allocation,
# capital is determined as the empirical VaR of the losses at 99\%
K <- quantile(rowSums(Loss),  probs = 0.99)
cap(Loss, Capital=K)

OCA documentation built on Feb. 16, 2023, 8:27 p.m.