5. agg Language Reference
Language Overview
Other
To view the grammar using a railroad diagram paste the specification below into the Edit Grammar tab of https://www.bottlecaps.de/rr/ui and then View Diagram. (Site diagram uses #DDDDDD as the base color.)
Sample Programs
Simple example
The following short program replicates Thought Experiemnt 1 from Neil Bodoff’s paper Capital Allocation by Percentile Layer
port BODOFF1 note{Bodoff Thought Experiment No. 1}
agg wind 1 claim sev dhistogram xps [0, 99] [0.80, 0.20] fixed
agg quake 1 claim sev dhistogram xps [0, 100] [0.95, 0.05] fixed
Other examples
port Complex~Portfolio~Mixed
agg LineA 50 claims sev lognorm 12 cv [2, 3, 4] wt [.3 .5 .2] mixed gamma 0.4
agg LineB 24 claims 10 x 5 sev lognorm 12 cv [{', '.join([str(i) for i in np.linspace(2,5, 20)])}] wt=20 mixed gamma 0.35
agg LineC 124 claims 120 x 5 sev lognorm 16 cv 3.4 mixed gamma 0.45
port Complex~Portfolio
agg Line3 50 claims [5 10 15] x 0 sev lognorm 12 cv [1, 2, 3] mixed gamma 0.25
agg Line9 24 claims [5 10 15] x 5 sev lognorm 12 cv [1, 2, 3] wt=3 mixed gamma 0.25
port Portfolio~2
agg CA 500 prem at .5 lr 15 x 12 sev gamma 12 cv [2 3 4] wt [.3 .5 .2] mixed gamma 0.4
agg FL 1.7 claims 100 x 5 sev 10000 * pareto 1.3 - 10000 poisson
agg IL 1e-8 * agg.CMP
agg OH agg.CMP * 1e-8
agg NY 500 prem at .5 lr 15 x 12 sev [20 30 40 10] * gamma [9 10 11 12] cv [1 2 3 4] wt =4 mixed gamma 0.4
sev proda 30000 * lognorm 2
sev prodc: 50000 * lognorm(3)
sev weird 50000 * beta(1, 4) + 10000
sev premsop1 25000 * lognorm 2.3; sev premsop2 35000 * lognorm 2.4;
sev premsop3 45000 * lognorm 2.8
agg Agg1 20 claims 10 x 2 sev lognorm 12 cv 0.2 mixed gamma 0.8
agg Agg2 20 claims 10 x 2 sev 15 * lognorm 2.5 poisson;
sev premsop1 25000 * lognorm 2.3;
agg Agg3 20 claims 10 x 2 on 25 * lognorm 2 fixed;
port MyFirstPortfolio
agg A1: 50 claims sev gamma 12 cv .30 (mixed gamma 0.014)
agg A2: 50 claims 30 xs 10 sev gamma 12 cv .30 (mixed gamma 0.014)
agg A3: 50 claims sev gamma 12 cv 1.30 (mixed gamma 0.014)
agg A4: 50 claims 30 xs 20 sev gamma 12 cv 1.30 (mixed gamma 0.14)
agg B 15 claims 15 xs 15 sev lognorm 12 cv 1.5 + 2 mixed gamma 4.8
agg Cat 1.7 claims 25 xs 5 sev 25 * pareto 1.3 0 - 25 poisson
agg ppa: 1e-8 * agg.PPAL
port distortionTest
agg mix 50 claims [50, 100, 150, 200] xs 0 sev lognorm 12 cv [1,2,3,4] poisson
agg low 500 premium at 0.5 5 xs 5 sev gamma 12 cv .30 mixed gamma 0.2
agg med 500 premium at 0.5 lr 15 xs 10 sev gamma 12 cv .30 mixed gamma 0.4
agg xsa 50 claims 30 xs 10 sev gamma 12 cv .30 mixed gamma 1.2
agg hcmp 1e-8 * agg.CMP
agg ihmp agg.PPAL * 1e-8
Below are a series of programs illustrating the different ways exposure, frequency and severity can be broadcast together, several different types of severity and all the different types of severity.
# use to create sev and aggs so can illustrate use of sev. and agg. below
sev sev1 lognorm 10 cv .3
agg Agg0 1 claim sev lognorm 10 cv .09 fixed
agg Agg1 1 claim sev {10*np.exp(-.3**2/2)} @ lognorm .3 fixed note{{sigma=.3 mean=10}}
agg Agg2 1 claim sev {10*np.exp(-.3**2/2)} @ lognorm .3 # 5 fixed note{{shifted right by 5}}''' \
'''
agg Agg3 1 claim sev 10 @ lognorm 0.5 cv .3 fixed note{mean 0.5 scaled by 10 and cv 0.3}
agg Agg4 1 claim sev 10 @ lognorm 1 cv .5 + 5 fixed note{shifted right by 5}
agg Agg5 1 claim sev 10 @ gamma .3 fixed note{gamma distribution....can use any two parameter scipy.stats distribution plus expon, uniform and normal}
agg Agg6 1 claim sev 10 @ gamma 1 cv .3 # 5 fixed note{mean 10 x 1, cv 0.3 shifted right by 5}
agg Agg7 1 claim sev 2 @ pareto 1.6 # -2 fixed note{pareto alpha=1.6 lambda=2}
agg Agg8 1 claim sev 2 @ uniform 5 # 2.5 fixed note{uniform 2.5 to 12.5}
agg Agg9 1 claim 10 x 2 sev lognorm 20 cv 1.5 fixed note{10 x 2 layer, 1 claim}
agg Agg10 10 loss 10 xs 2 sev lognorm 20 cv 1.5 fixed note{10 x 2 layer, total loss 10, derives requency}
agg Agg11 14 prem at .7 10 x 1 sev lognorm 20 cv 1.5 fixed note{14 prem at .7 lr derive frequency}
agg Agg11 14 prem at .7 lr 10 x 1 sev lognorm 20 cv 1.5 fixed note{14 prem at .7 lr derive frequency, lr is optional}
agg Agg12: 14 prem at .7 lr (10 x 1) sev (lognorm 20 cv 1.5) fixed note{trailing semi and other punct ignored};
agg Agg13: 1 claim sev 50 @ beta 3 2 # 10 fixed note{scaled and shifted beta, two parameter distribution}
agg Agg14: 1 claim sev 100 @ expon # 10 fixed note{exponential single parameter, needs scale, optional shift}
agg Agg15: 1 claim sev 10 @ norm # 50 fixed note{normal is single parameter too, needs scale, optional shift}
# any scipy.stat distribution taking one parameter can be used; only cts vars supported on R+ make sense
agg Agg16: 1 claim sev 1 * invgamma 4.07 fixed note{inverse gamma distribution}
# mixtures
agg MixedLine1: 1 claim 25 xs 0 sev lognorm 10 cv [0.2, 0.4, 0.6, 0.8, 1.0] wts=5 fixed note{equally weighted mixture of 5 lognormals different cvs}
agg MixedLine2: 1 claim 25 xs 0 sev lognorm [10, 15, 20, 25, 50] cv [0.2, 0.4, 0.6, 0.8, 1.0] wts=5 fixed note{equal weighted mixture of 5 lognormals different cvs and means}
agg MixedLine3: 1 claim 25 xs 0 sev lognorm 10 cv [0.2, 0.4, 0.6, 0.8, 1.0] wt [.2, .3, .3, .15, .05] fixed note{weights scaled to equal 1 if input}
# limit profile
agg LimitProfile1: 1 claim [1, 5, 10, 20] xs 0 sev lognorm 10 cv 1.2 wt [.50, .20, .20, .1] fixed note{maybe input EL by band for wt}
agg LimitProfile2: 5 claim 20 xs 0 sev lognorm 10 cv 1.2 wt [.50, .20, .20, .1] fixed note{input EL by band for wt}
agg LimitProfile3: [10 10 10 10] claims [inf 10 inf 10] xs [0 0 5 5] sev lognorm 10 cv 1.25 fixed note{input counts directly}
# limits and distribution blend
agg Blend1 50 claims [5 10 15] x 0 sev lognorm 12 cv [1, 1.5, 3] fixed note{options all broadcast against one another, 50 claims of each}
agg Blend2 50 claims [5 10 15] x 0 sev lognorm 12 cv [1, 1.5, 3] wt=3 fixed note{options all broadcast against one another, 50 claims of each}
agg Blend5cv1 50 claims 5 x 0 sev lognorm 12 cv 1 fixed
agg Blend10cv1 50 claims 10 x 0 sev lognorm 12 cv 1 fixed
agg Blend15cv1 50 claims 15 x 0 sev lognorm 12 cv 1 fixed
agg Blend5cv15 50 claims 5 x 0 sev lognorm 12 cv 1.5 fixed
agg Blend10cv15 50 claims 10 x 0 sev lognorm 12 cv 1.5 fixed
agg Blend15cv15 50 claims 15 x 0 sev lognorm 12 cv 1.5 fixed
# semi colon can be used for newline and backslash works
agg Blend5cv3 50 claims 5 x 0 sev lognorm 12 cv 3 fixed; agg Blend10cv3 50 claims 10 x 0 sev lognorm 12 cv 3 fixed
agg Blend15cv3 50 claims 15 x 0 sev \
lognorm 12 cv 3 fixed
# not sure if it will broadcast limit profile against severity mixture...
agg LimitProfile4: [10 30 15 5] claims [inf 10 inf 10] xs [0 0 5 5] sev lognorm 10 cv [1.0, 1.25, 1.5] wts=3 fixed note{input counts directly}
# the logo
agg logo 1 claim {np.linspace(10, 250, 20)} xs 0 sev lognorm 100 cv 1 fixed'''
# empirical distributions
agg dHist1 1 claim sev dhistogram xps [1, 10, 40] [.5, .3, .2] fixed note{discrete histogram}
agg cHist1 1 claim sev chistogram xps [1, 10, 40] [.5, .3, .2] fixed note{continuous histogram, guessed right hand endpiont}
agg cHist2 1 claim sev chistogram xps [1 10 40 45] [.5 .3 .2] fixed note{continuous histogram, explicit right hand endpoint, don't need commas}
agg BodoffWind 1 claim sev dhistogram xps [0, 99] [0.80, 0.20] fixed note{examples from Bodoffs paper}
agg BodoffQuake 1 claim sev dhistogram xps [0, 100] [0.95, 0.05] fixed
# set up fixed sev for future use
sev One dhistogram xps [1] [1] note{a certain loss of 1}
# sev, agg and port: using built in objects [have to exist prior to running program]
agg ppa: 0.01 * agg.PPAL note{this is using lmult on aggs, needs a dictionary specification to adjust means}
agg cautoQS: 1e-5 * agg.CAL note{lmult is quota share or scale for rmul see below }
agg cautoClms: agg.CAL * 1e-5 note{rmult adjusts the claim count}
# scaling works with distributions already made by uw
agg mdist: 5000 * agg.dHist1
# frequency options
agg FreqFixed 10 claims sev sev.One fixed
agg FreqPoisson 10 claims sev sev.One poisson note{Poisson frequency}
agg FreqBernoulli .8 claims sev sev.One bernoulli note{Bernoulli en is frequency }
agg FreqBinomial 10 claims sev sev.One binomial 0.5
agg FreqPascal 10 claims sev sev.One pascal .8 3
# mixed freqs
agg FreqNegBin 10 claims sev sev.One (mixed gamma 0.65) note{gamma mixed Poisson = negative binomial}
agg FreqDelaporte 10 claims sev sev.One mixed delaporte .65 .25
agg FreqIG 10 claims sev sev.One mixed ig .65
agg FreqSichel 10 claims sev sev.One mixed delaporte .65 -0.25
agg FreqSichel.gamma 10 claims sev sev.One mixed sichel.gamma .65 .25
agg FreqSichel.ig 10 claims sev sev.One mixed sichel.ig .65 .25
agg FreqBeta 10 claims sev sev.One mixed beta .5 4 note{second param is max mix}
Pre-processing
Programs are processed one line at a time. Before passing to the lexer, the following pre-processing occurs.
Remove C++ style // comments, through end of line
Remove \n in [ ] (vectors) that appear from using
f'{np.linspace(...) }'Semicolons are mapped to newline
Backslash (Python sytle line continuations) are mapped to space
\n\t is replaced with space, supporting the tabbed indented Portfolio layout
Split on newlines
Lexer term definitions
Ignored characters: tab, colon, comma, ( ) |. Thus, parenthesis and colons can be used to improve readability.
Aggregate names must not include underscore. Portfolio names may include underscore.
tokens = {ID, BUILTIN_AGG, BUILTIN_SEV,NOTE,
SEV, AGG, PORT,
NUMBER, INFINITY,
PLUS, MINUS, TIMES, DIVIDE, SCALE_MULTIPLY, LOCATION_ADD,
LOSS, PREMIUM, AT, LR, CLAIMS, SPECIFIED,
XS,
CV, WEIGHTS, EQUAL_WEIGHT, XPS,
MIXED, FREQ, EMPIRICAL, TWEEDIE,
NET, OF, CEDED, TO, OCCURRENCE, AGGREGATE, PART_OF, SHARE_OF,
AND, PERCENT,
EXPONENT, EXP,
DFREQ, DSEV, RANGE
}
ignore = ' \t,\\|'
literals = {'[', ']', '!', '(', ')'}
NOTE = r'note\{[^\}]*\}' # r'[^\}]+'
BUILTIN_AGG = r'agg\.[a-zA-Z][a-zA-Z0-9_:~]*'
BUILTIN_SEV = r'sev\.[a-zA-Z][a-zA-Z0-9_:~]*'
FREQ = r'binomial|poisson|bernoulli|pascal|geometric|fixed'
# number regex including unary minus; need before MINUS else that grabs the minus sign in -3 etc.
NUMBER = r'\-?(\d+\.?\d*|\d*\.\d+)([eE](\+|\-)?\d+)?'
ID = r'[a-zA-Z][\.:~_a-zA-Z0-9]*'
EXPONENT = r'\^|\*\*'
PLUS = r'\+'
MINUS = r'\-'
TIMES = r'\*'
DIVIDE = r'/'
PERCENT = '%'
SCALE_MULTIPLY = r'@'
LOCATION_ADD = '#'
EQUAL_WEIGHT = r'='
RANGE = ':'
ID['occurrence'] = OCCURRENCE
ID['unlimited'] = INFINITY
ID['aggregate'] = AGGREGATE
ID['dfreq'] = DFREQ
ID['dsev'] = DSEV
# ID['part'] = PART
# ID['share'] = SHARE
# when using an empirical freq the claim count is specified
# must use "specified claims" ... sets e_n = -1
ID['specified'] = SPECIFIED
ID['empirical'] = EMPIRICAL
ID['tweedie'] = TWEEDIE
ID['premium'] = PREMIUM
ID['mixed'] = MIXED
ID['unlim'] = INFINITY
ID['claims'] = CLAIMS
ID['ceded'] = CEDED
ID['claim'] = CLAIMS
ID['loss'] = LOSS
ID['prem'] = PREMIUM
ID['port'] = PORT
ID['net'] = NET
ID['sev'] = SEV
ID['agg'] = AGG
ID['nps'] = EMPIRICAL
ID['xps'] = XPS
ID['wts'] = WEIGHTS
ID['inf'] = INFINITY
ID['and'] = AND
ID['exp'] = EXP
ID['wt'] = WEIGHTS
ID['at'] = AT
ID['cv'] = CV
ID['lr'] = LR
ID['xs'] = XS
ID['of'] = OF
ID['to'] = TO
ID['po'] = PART_OF
ID['so'] = SHARE_OF
ID['x'] = XS
Language Specification
The `agg` Language Grammar:
- answer ::= sev_out
- agg_outport_outexpr
port_out ::= PORT name note agg_list
- agg_list ::= agg_list agg_out
- agg_out
- agg_out ::= AGG name exposures layers sev_clause occ_reins freq agg_reins note
- AGG name dfreq layers sev_clause occ_reins agg_reins noteAGG name TWEEDIE expr expr exprAGG name builtin_agg notebuiltin_agg agg_reins note
- sev_out ::= SEV name sev note
- SEV name dsev note
- freq ::= freq ZM expr
- freq ZTMIXED ID expr exprMIXED ID exprFREQ expr exprFREQ exprFREQ
- agg_reins ::= AGGREGATE NET OF reins_list
- AGGREGATE CEDED TO reins_list%prec LOW
- occ_reins ::= OCCURRENCE NET OF reins_list
- OCCURRENCE CEDED TO reins_list
- reins_list ::= reins_list AND reins_clause
- reins_clause
- reins_clause ::= expr XS expr
- expr SHARE_OF expr XS exprexpr PART_OF expr XS expr
- sev_clause ::= SEV sev %prec LOW
- dsevBUILTIN_SEV
- sev ::= sev “!”
- sev PLUS numbers %prec LOCATION_ADDsev MINUS numbers %prec LOCATION_ADDnumbers TIMES sev %prec SCALE_MULTIPLYids numbers CV numbers weightsids numbers numbers weightsids numbers weightsids xpsidsBUILTIN_SEV
xps ::= XPS doutcomes dprobs
dsev ::= DSEV doutcomes dprobs
dfreq ::= DFREQ doutcomes dprobs
- doutcomes ::= “[” numberl “]”
- “[” expr RANGE expr “]”“[” expr RANGE expr RANGE expr “]”
- dprobs ::= “[” numberl “]”
- weights ::= WEIGHTS EQUAL_WEIGHT expr
- WEIGHTS “[” numberl “]”
- layers ::= numbers XS numbers
- note ::= NOTE
- %prec LOW
- exposures ::= numbers CLAIMS
- numbers LOSSnumbers PREMIUM AT numbers LR
- ids ::= “[” idl “]”
- ID
- idl ::= idl ID
- ID
- builtin_agg ::= expr HOMOG_MULTIPLY builtin_agg
- expr TIMES builtin_aggbuiltin_agg PLUS exprbuiltin_agg MINUS exprBUILTIN_AGG
name ::= ID
- numbers ::= “[” numberl “]”
- expr
- numberl ::= numberl expr
- expr
expr ::= term
- term ::= term DIVIDE factor
- factor
- factor ::= PLUS factor
- MINUS factorpower“(” term “)”EXP “(” term “)”
- power ::= atom EXPONENT factor
- atom
- atom ::= NUMBER PERCENT
- INFINITYNUMBER
FREQ ::= ‘binomial|poisson|bernoulli|pascal|geometric|fixed’
BUILTINID ::= ‘sev|agg|port|meta.ID’
NOTE ::= ‘note{TEXT}’
EQUAL_WEIGHT ::= “=”
AGG ::= ‘agg’
AGGREGATE ::= ‘aggregate’
AND ::= ‘and’
AT ::= ‘at’
CEDED ::= ‘ceded’
CLAIMS ::= ‘claims|claim’
CONSTANT ::= ‘constant’
CV ::= ‘cv’
DFREQ ::= ‘dfreq’
DSEV ::= ‘dsev’
EXP ::= ‘exp’
EXPONENT ::= ‘^|**’
HOMOG_MULTIPLY ::= “@”
INFINITY ::= ‘inf|unlim|unlimited’
LOSS ::= ‘loss’
LR ::= ‘lr’
MIXED ::= ‘mixed’
NET ::= ‘net’
OCCURRENCE ::= ‘occurrence’
OF ::= ‘of’
PART_OF ::= ‘po’
PERCENT ::= ‘%’
PORT ::= ‘port’
PREMIUM ::= ‘premium|prem’
SEV ::= ‘sev’
SHARE_OF ::= ‘so’
TO ::= ‘to’
WEIGHTS ::= ‘wts|wt’
XPS ::= ‘xps’
xs ::= “xs|x”