-
Notifications
You must be signed in to change notification settings - Fork 5
/
adjCoef.R
226 lines (213 loc) · 8.38 KB
/
adjCoef.R
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
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
### actuar: Actuarial Functions and Heavy Tailed Distributions
###
### Compute the adjustment coefficient in ruin theory, that is the
### smallest (strictly) positive root of the Lundberg equation
###
### h(r) = E[e^(r X - r c W)] = 1,
###
### where X is the claim size random variable, W the inter-occurence
### time and c the premium rate.
###
### AUTHORS: Christophe Dutang, Vincent Goulet <[email protected]>
adjCoef <- function(mgf.claim, mgf.wait = mgfexp, premium.rate, upper.bound,
h, reinsurance = c("none", "proportional", "excess-of-loss"),
from, to, n = 101)
{
reinsurance <- match.arg(reinsurance)
## Sanity check
if (missing(mgf.claim) && missing(h))
stop(sprintf("one of %s or %s is needed",
sQuote("mgf.claim"), sQuote("h")))
## === NO REINSURANCE CASE ===
##
## Moment generating functions are unidimensional, premium rate
## and adjustment coefficient are both single numeric values.
if (reinsurance == "none")
{
## For each of 'mgf.claim', 'mgf.wait' and 'h' (if needed): if
## the expression is only the name of a function (say f),
## build a call 'f(x)'. Otherwise, check that the expression
## is a function call containing an 'x'. Taken from 'curve'
## and 'discretize'.
##
## NOTE: argument 'h' will be used iff 'mgf.claim' is missing,
## thereby giving priority to 'mgf.claim'.
if (missing(mgf.claim))
{
sh <- substitute(h)
if (is.name(sh))
{
fcall <- paste(sh, "(x)")
h1 <- function(x)
eval(parse(text = fcall),
envir = list(x = x),
enclos = parent.frame(2))
}
else
{
if (!(is.call(sh) && match("x", all.vars(sh), nomatch = 0L)))
stop(sprintf("%s must be a function or an expression containing %s",
sQuote("h"), sQuote("x")))
h1 <- function(x)
eval(sh,
envir = list(x = x),
enclos = parent.frame(2))
}
}
else
{
smgfx <- substitute(mgf.claim)
if (is.name(smgfx))
{
fcall <- paste(smgfx, "(x)")
mgfx <- parse(text = fcall)
}
else
{
if (!(is.call(smgfx) && match("x", all.vars(smgfx), nomatch = 0L)))
stop(sprintf("%s must be a function or an expression containing %s",
sQuote("mgf.claim"), sQuote("x")))
mgfx <- smgfx
}
smgfw <- substitute(mgf.wait)
if (is.name(smgfw))
{
fcall <- paste(smgfw, "(x)")
mgfw <- parse(text = fcall)
}
else
{
if (!(is.call(smgfw) && match("x", all.vars(smgfw), nomatch = 0L)))
stop(sprintf("%s must be a function or an expression containing %s",
sQuote("mgf.wait"), sQuote("x")))
mgfw <- smgfw
}
h1 <- function(x)
eval(mgfx) * eval(mgfw, list(x = -x * premium.rate))
}
f1 <- function(r) (h1(r) - 1)^2
return(optimize(f1, c(0, upper.bound - .Machine$double.eps),
tol = sqrt(.Machine$double.eps))$minimum)
}
## === WITH REINSURANCE CASES ===
##
## Claim amount moment generating function is a function of 'x'
## and the retention level 'y', inter-occurence time moment
## generating function is a function of 'x', premium rate and
## adjustment coefficient are both functions of the retention
## level 'y'.
##
## Do same as in the no reinsurance case for each of 'mgf.claim',
## 'mgf.wait' and 'h' (if needed) and also 'premium'. The first
## must be functions of 'x' and 'y', whereas the last one is a
## function of 'y' only.
if (missing(mgf.claim))
{
sh <- substitute(h)
if (is.name(sh))
{
fcall <- paste(sh, "(x, y)")
h2 <- function(x, y)
eval(parse(text = fcall),
envir = list(x = x, y = y),
enclos = parent.frame(2))
}
else
{
if (!(is.call(sh) && all(match(c("x", "y"), all.vars(sh), nomatch = 0L))))
stop(sprintf("%s must be a function or an expression containing %s and %s",
sQuote("h"), sQuote("x"), sQuote("y")))
h2 <- function(x, y)
eval(sh,
envir = list(x = x, y = y),
enclos = parent.frame(2))
}
}
else
{
if (!is.function(premium.rate))
stop(sprintf("%s must be a function when using reinsurance",
sQuote("premium.rate")))
smgfx <- substitute(mgf.claim)
if (is.name(smgfx))
{
fcall <- paste(smgfx, "(x, y)")
mgfx <- parse(text = fcall)
}
else
{
if (!(is.call(smgfx) && all(match(c("x", "y"), all.vars(smgfx), nomatch = 0L))))
stop(sprintf("%s must be a function or an expression containing %s and %s",
sQuote("mgf.claim"), sQuote("x"), sQuote("y")))
mgfx <- smgfx
}
smgfw <- substitute(mgf.wait)
if (is.name(smgfw))
{
fcall <- paste(smgfw, "(x)")
mgfw <- parse(text = fcall)
}
else
{
if (!(is.call(smgfw) && match("x", all.vars(smgfw), nomatch = 0L)))
stop(sprintf("%s must be a function or an expression containing %s",
sQuote("mgf.wait"), sQuote("x")))
mgfw <- smgfw
}
spremium <- substitute(premium.rate)
if (is.name(spremium))
{
fcall <- paste(spremium, "(y)")
premium.rate <- parse(text = fcall)
}
else
{
if (!(is.call(spremium) && match("y", all.vars(spremium), nomatch = 0L)))
stop(sprintf("%s must be a function or an expression containing %s",
sQuote("premium.rate"), sQuote("y")))
premium.rate <- spremium
}
h2 <- function(x, y)
eval(mgfx) * eval(mgfw, list(x = -x * eval(premium.rate)))
}
f2 <- function(x, y) (h2(x, y) - 1)^2
retention <- seq(from, to, length.out = n)
## Compute the adjustment coefficient for each retention level.
## The output of 'sapply' is a matrix with minima in the first
## line.
##
## The sapply() below passes the retention levels (argument 'y' of
## function 'f') to optimize(). Since the first two arguments ('f'
## and 'interval') of the latter function are specified, the
## retention levels end up in '...' and hence are considered as
## second argument of 'f'. *This requires R >= 2.6.0 to work since
## argument '...' comes much earlier in the definition of
## optimize().
coef <- sapply(retention, optimize, f = f2,
interval = c(0, upper.bound-.Machine$double.eps),
tol = sqrt(.Machine$double.eps))[1L, ]
## Make a function from the (retention, coefficient) pairs
## computed above, joining the points by straight line segments.
FUN <- approxfun(retention, coef, rule = 2, method = "linear")
comment(FUN) <- paste(toupper(substring(reinsurance, 1L, 1L)),
substring(reinsurance, 2L),
" reinsurance",
sep = "", collapse = "")
class(FUN) <- c("adjCoef", class(FUN))
attr(FUN, "call") <- sys.call()
FUN
}
plot.adjCoef <- function(x, xlab = "x", ylab = "R(x)",
main = "Adjustment Coefficient",
sub = comment(x), type = "l", add = FALSE, ...)
{
xx <- eval(expression(x), envir = environment(x))
yy <- eval(expression(y), envir = environment(x))
if (add)
lines(xx, yy, ..., main = main, xlab = xlab, ylab = ylab,
type = type)
else
plot(xx, yy, ..., main = main, xlab = xlab, ylab = ylab,
type = type)
mtext(sub, line = 0.5)
}