insurance: Insurance product
In nathanesau/stocins: Stochastic Interest Rate Models for Life Insurance
Description
Usage
Details
References
Examples
Description
A class used to describe the insurance product we are modeling.
Three types of insurance policies can be modeled:
1. Insurance policies issued to a single life, i.e. the isingle subclasses.
For these policies, the params argument should be a list with n for the
term of the contract, d for the death benefit and e for the
survival benefit. If e is not specified it is assumed to be 0. For a
policy issued to a single life, the class argument should be "isingle"
and the subclass argument should be either "term" for a term insurance
or "endow" for an endowment insurance. See the examples below.
2. Identical policies issued to many lives, i.e. the iport subclasses. For
these policies, the params argument should be a list with single
being an isingle object and c being a number specifying how
many identical policies are in the portfolio. For a portfolio of policies, the
class argument should be "iport" and the subclass argument should either be "term"
for a term insurance or "endow" for an endowment insurance. See the examples below.
3. A group of insurance portfolios, i.e. the igroup subclass. For a group
of policies, the params argument should be a list of iport objects
and the class argument should be "igroup". The subclass argument is not needed.
See the examples below.
Usage
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Details
For each class, several functions are available.
The z.moment function can be used to calculate the
raw moments of the present value of benefit random variable.
For the isingle classes all the moments are implemented,
for the iport classes the first three moments are implemented
and for the igroup class the first two moments are implemented.
The formulas from Parker (1992) were used to implement these moments.
The z.ev function can be used to calculate the first moment, the
z.sd function can be used to calculate the standard deviation and
the z.sk function can be used to calculate the skewness of the
present value of benefit random variable.
The z.insrisk function can be used to calculate the insurance risk
arising from uncertain mortality and z.invrisk can be used to calculate
the investment risk arising from uncertain investment returns. The formulas
from Parker (1997) were used to implement these functions.
The z.pdf function can be used to calculate the density function
of the present value of benefit random variable for the isingle classes.
This function has not been implemented for the iport and igroup
classes. For details on how this could be done, refer to Parker (1992) and
Parker (1997).
Refer to the examples below for how to use these functions.
References
Parker, Gary. An application of stochastic interest rate models in
life assurance. Diss. Heriot-Watt University, 1992.
Parker, G. (1997). Stochastic analysis of the interaction between
investment and insurance risks. North American actuarial journal, 1(2), 55–71.
Examples
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oumodel = iratemodel(list(delta0 = 0.1, delta = 0.06,
alpha = 0.1, sigma = 0.01), "ou")
mort = mortassumptions(list(x = 40, table = "MaleMort91"))
mort2 = mortassumptions(list(x = 50, table = "FemaleMort91"))
## isingle classes
termins = insurance(list(n = 10, d = 1), "isingle", "term")
endowins = insurance(list(n = 10, e = 1, d = 1), "isingle", "endow")
z.ev(termins, mort, oumodel) # first moment
z.moment(2, termins, mort, oumodel) # second moment
z.moment(3, termins, mort, oumodel) # third moment
z.sd(endowins, mort, oumodel) # standard deviation
z.sk(endowins, mort, oumodel) # skewness
plot(function(z) z.pdf(z, termins, mort, oumodel), 0.01, 1.0,
ylim = c(0, 0.15), lty = 1, xlab = "z", ylab = "f(z)")
legend('topleft', leg = c(paste0("P(Z=0) = ", round(kpx(1, mort), 5))),
lty = 1)
## iport classes
termport = insurance(list(single = termins, c = 1000), "iport", "term")
endowport = insurance(list(single = endowins, c = 1000), "iport", "endow")
z.moment(1, termport, mort, oumodel) / termport$c # average cost
z.sd(termport, mort, oumodel) / termport$c # average standard deviation
## igroup class
groupins = insurance(list(termport, endowport),
"igroup") # 1000 term contracts, 1000 endow contracts
groupmort = list(mort, mort2) # term contracts are age 40, endow contracts are age 50
z.moment(1, groupins, groupmort, oumodel) / groupins$c # average cost per policy
z.insrisk(groupins, groupmort, oumodel) / termport$c^2 # insrisk per policy
z.invrisk(groupins, groupmort, oumodel) / termport$c^2 # invrisk per policy
z.sd(groupins, groupmort, oumodel) / termport$c # sd per policy
nathanesau/stocins documentation built on May 23, 2019, 12:19 p.m.
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Description Usage Details References Examples
Description
A class used to describe the insurance product we are modeling. Three types of insurance policies can be modeled:
1. Insurance policies issued to a single life, i.e. the isingle subclasses.
For these policies, the params argument should be a list with n for the
term of the contract, d for the death benefit and e for the
survival benefit. If e is not specified it is assumed to be 0. For a
policy issued to a single life, the class argument should be "isingle"
and the subclass argument should be either "term" for a term insurance
or "endow" for an endowment insurance. See the examples below.
2. Identical policies issued to many lives, i.e. the iport subclasses. For
these policies, the params argument should be a list with single
being an isingle object and c being a number specifying how
many identical policies are in the portfolio. For a portfolio of policies, the
class argument should be "iport" and the subclass argument should either be "term"
for a term insurance or "endow" for an endowment insurance. See the examples below.
3. A group of insurance portfolios, i.e. the igroup subclass. For a group
of policies, the params argument should be a list of iport objects
and the class argument should be "igroup". The subclass argument is not needed.
See the examples below.
Usage
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 |
Details
For each class, several functions are available.
The z.moment function can be used to calculate the
raw moments of the present value of benefit random variable.
For the isingle classes all the moments are implemented,
for the iport classes the first three moments are implemented
and for the igroup class the first two moments are implemented.
The formulas from Parker (1992) were used to implement these moments.
The z.ev function can be used to calculate the first moment, the
z.sd function can be used to calculate the standard deviation and
the z.sk function can be used to calculate the skewness of the
present value of benefit random variable.
The z.insrisk function can be used to calculate the insurance risk
arising from uncertain mortality and z.invrisk can be used to calculate
the investment risk arising from uncertain investment returns. The formulas
from Parker (1997) were used to implement these functions.
The z.pdf function can be used to calculate the density function
of the present value of benefit random variable for the isingle classes.
This function has not been implemented for the iport and igroup
classes. For details on how this could be done, refer to Parker (1992) and
Parker (1997).
Refer to the examples below for how to use these functions.
References
Parker, Gary. An application of stochastic interest rate models in life assurance. Diss. Heriot-Watt University, 1992.
Parker, G. (1997). Stochastic analysis of the interaction between investment and insurance risks. North American actuarial journal, 1(2), 55–71.
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 | oumodel = iratemodel(list(delta0 = 0.1, delta = 0.06,
alpha = 0.1, sigma = 0.01), "ou")
mort = mortassumptions(list(x = 40, table = "MaleMort91"))
mort2 = mortassumptions(list(x = 50, table = "FemaleMort91"))
## isingle classes
termins = insurance(list(n = 10, d = 1), "isingle", "term")
endowins = insurance(list(n = 10, e = 1, d = 1), "isingle", "endow")
z.ev(termins, mort, oumodel) # first moment
z.moment(2, termins, mort, oumodel) # second moment
z.moment(3, termins, mort, oumodel) # third moment
z.sd(endowins, mort, oumodel) # standard deviation
z.sk(endowins, mort, oumodel) # skewness
plot(function(z) z.pdf(z, termins, mort, oumodel), 0.01, 1.0,
ylim = c(0, 0.15), lty = 1, xlab = "z", ylab = "f(z)")
legend('topleft', leg = c(paste0("P(Z=0) = ", round(kpx(1, mort), 5))),
lty = 1)
## iport classes
termport = insurance(list(single = termins, c = 1000), "iport", "term")
endowport = insurance(list(single = endowins, c = 1000), "iport", "endow")
z.moment(1, termport, mort, oumodel) / termport$c # average cost
z.sd(termport, mort, oumodel) / termport$c # average standard deviation
## igroup class
groupins = insurance(list(termport, endowport),
"igroup") # 1000 term contracts, 1000 endow contracts
groupmort = list(mort, mort2) # term contracts are age 40, endow contracts are age 50
z.moment(1, groupins, groupmort, oumodel) / groupins$c # average cost per policy
z.insrisk(groupins, groupmort, oumodel) / termport$c^2 # insrisk per policy
z.invrisk(groupins, groupmort, oumodel) / termport$c^2 # invrisk per policy
z.sd(groupins, groupmort, oumodel) / termport$c # sd per policy
|
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