{ From user Lonnie, Model Earthquake_expense at 15-Aug-2011 12:37:34 PM }
SoftwareVersion 4.4.0


{ System Variables with non-default values: }
Description Time: Dynamic simulation periods are specified in Time's definition. This is usually a list of numbers or labels, typically in some unit of time (days, weeks, months, etc.).  Use the “Dynamic()” function in your variables to perform dynamic simulation.
SampleSize := 1000
TypeChecking := 1
Checking := 1
SaveOptions := 2
SaveValues := 0
AllWarnings := 0
{!40300|Sys_DomainSelfIndex := 1}

{!40300|ProactivelyEvaluate Index: 1}



Model Earthquake_expense
Title: Earthquake expense risk
Description: An example of risk analysis with time-dependence and costs of events shifted over time.   ~
~
Assume (for example):~
* Earthquakes are Poisson events with a mean rate of once every 10 years.~
* Damage caused by such a quake is lognormally distributed with a mean of $10M and a standard deviation of $6M.~
* Cost of damage gets incurred over the period of a year from the date of the quake as equipment is replaced, and buildings are repaired over time:~
   - 20% in the 1st quarter following quake~
   - 50% in 2nd quarter~
   - 20% in 3rd quarter~
   - 10% in 4th quarter~
~
Answer questions like:~
* What is the likelihood of more than one quake in a specific 10 year period.~
* For any number of seleted time windows (say quarter 3 of year 21):~
  - Distribution of expected costs (mean, std.dev, etc)~
  - Probability that in that time window my costs exceed $X?~

Author: Lonnie Chrisman, Ph.D.~
Lumina Decision Systems
Date: Thu, May 12, 2005 9:08 AM
SaveAuthor: Lonnie
SaveDate: Mon, Aug 15, 2011 12:37 PM
DefaultSize: 48,24
DiagState: 1,4,9,599,453,19
WindState: 2,398,34,476,450
FontStyle: Arial, 15
FileInfo: 0,Model Earthquake_expense,2,2,0,0,W:\Analytica\ExecDebug\Example Models\Risk Analysis\Earthquake expenses.ana
{!40400|Att_clearTypeFonts: -1}

Function Shiftarray(x, n; i: IndexType)
Title: ShiftArray(x, n, i)
Description: Returns an array containing the values of array x, with each element shifted n steps forward along index i (or back if n is negative). Leaves zero in first (or last) n elements, since there is no preceding (following) value to shift into them.
Definition: VAR r := Slice(x, i, Cumulate(1, i) - n);~
IF r = NULL THEN 0 ELSE r
NodeLocation: 88,488,1
NodeSize: 76,20
WindState: 2,102,90,476,278

Variable Earthquake_rate
Title: Earthquake rate
Units: Years / quake
Description: Mean number of years between earthquakes
Definition: 10
NodeLocation: 72,48,1
NodeSize: 56,24
WindState: 2,50,540,476,224

Chance Number_of_quakes
Title: Number of quakes
Units: quakes / quarter
Description: The number of quakes that occur in each time period (quarter).~
~
(The Year0 makes sure the distribution is resampled as independent for each time period.)
Definition: Poisson(1/(Earthquake_rate*4) + Year0)
NodeLocation: 192,48,1
NodeSize: 48,31
WindState: 2,399,355,476,224
ValueState: 2,75,382,753,384,0,SAMP
GraphSetup: Graphtool:0~
Distresol:10~
Diststeps:0~
Cdfresol:5~
Cdfsteps:1~
Symbolsize:6~
Baroverlap:0~
Linestyle:6~
Frame:1~
Grid:1~
Ticks:1~
Mesh:1~
Scales:1~
Rotation:45~
Tilt:0~
Depth:70~
Frameauto:1~
Showkey:1~
Xminimum:1~
Xmaximum:122~
Yminimum:0~
Ymaximum:1~
Zminimum:1~
Zmaximum:1~
Xintervals:0~
Yintervals:0~
Includexzero:0~
Includeyzero:0~
Includezzero:0~
Statsselect:[1,1,1,1,1,0,0,0]~
Probindex:[0.05,0.25,0.5,0.75,0.95]~

FontStyle: Arial, 8
ReformVal: [Year,Run]
NumberFormat: 1,D,4,5,0,0
Att__TotalsIndex: Index Year, SysVar Run

Variable Mean_damage
Title: Mean damage
Units: $
Description: Mean damage incurred when a quake occurs.
Definition: 10M
NodeLocation: 72,128,1
NodeSize: 48,24

Variable Std_dev_damage
Title: Std dev damage
Units: $
Description: Standard deviation on the damage incurred when an earthquake occurs.
Definition: 6M
NodeLocation: 72,184,1
NodeSize: 48,24

Chance Damage_incurred
Title: Damage incurred
Units: $
Description: This is the damage incurred in a given time interval.
Definition: Number_of_quakes * Lognormal(mean:Mean_damage + Year0, stddev:Std_dev_damage)
NodeLocation: 192,128,1
NodeSize: 48,32
ValueState: 2,516,35,570,256,0,STAT
GraphSetup: Graphtool:0~
Distresol:10~
Diststeps:0~
Cdfresol:5~
Cdfsteps:1~
Symbolsize:6~
Baroverlap:0~
Linestyle:6~
Frame:1~
Grid:1~
Ticks:1~
Mesh:1~
Scales:1~
Rotation:45~
Tilt:0~
Depth:70~
Frameauto:1~
Showkey:1~
Xminimum:2005~
Xmaximum:2030~
Yminimum:-1u~
Ymaximum:1u~
Zminimum:0.05~
Zmaximum:0.95~
Xintervals:0~
Yintervals:0~
Includexzero:0~
Includeyzero:0~
Includezzero:0~
Statsselect:[1,1,1,1,1,0,0,0]~
Probindex:[0.01,0.05,0.25,0.5,0.75,0.95,0.99]~

ReformVal: [Year, Statistics1 ]
NumberFormat: 1,D,4,2,0,1

Variable Payout_schedule
Title: Payout Schedule
Units: % / quarter
Description: For each quarter following the earthquake, this encodes the proportion of damages paid in that quarter.
Definition: Table(Payout_offset)(~
0.2,0.5,0.2,0.1)
IndexVals: [0,1,2,3,4,5,6,7,8,9,10,11]
NodeLocation: 320,208,1
NodeSize: 48,24
DefnState: 2,34,66,416,303,0,MIDM
ValueState: 2,67,15,416,303,0,MIDM
NumberFormat: 1,%,4,0,0,0
Att__TotalsIndex: Variable Self

Variable Costs_by_time
Title: Costs by time
Units: $ / quarter
Description: Payout incurred each time interval.  The payout is delayed relative to when the earthquake occurs according to the payout_schedule.
Definition: Sum(Shiftarray( Damage_incurred, Payout_offset, Year )*Payout_schedule, Payout_offset)
NodeLocation: 320,128,1
NodeSize: 48,24
WindState: 2,102,90,533,443
ValueState: 2,8,15,1050,663,1,MEAN
GraphSetup: Graphtool:0~
Distresol:10~
Diststeps:0~
Cdfresol:5~
Cdfsteps:1~
Symbolsize:6~
Baroverlap:0~
Linestyle:6~
Frame:1~
Grid:1~
Ticks:1~
Mesh:1~
Scales:1~
Rotation:45~
Tilt:0~
Depth:70~
Frameauto:1~
Showkey:1~
Xminimum:2005~
Xmaximum:2030~
Yminimum:25K~
Ymaximum:275K~
Zminimum:1~
Zmaximum:1~
Xintervals:0~
Yintervals:0~
Includexzero:0~
Includeyzero:0~
Includezzero:0~
Statsselect:[1,1,1,1,1,0,0,0]~
Probindex:[0.05,0.25,0.5,0.75,0.95]~

ReformVal: [Year,Undefined,2]
NumberFormat: 1,D,4,2,0,1

Index Payout_offset
{!40000|Att_PrevIndexValue: [0,1,2,3]}
Title: Payout offset
Units: quarters
Definition: [0,1,2,3]
NodeLocation: 184,208,1
NodeSize: 48,24

FormNode Time_window_start1
Title: Time window start
Definition: 0
NodeLocation: 352,312,1
NodeSize: 192,16
NodeInfo: 1,0,0,1,0,0,0,72,0,1
Original: Time_window_start

FormNode Time_window_duratio1
Title: Time window duration
Definition: 0
NodeLocation: 352,344,1
NodeSize: 192,16
NodeInfo: 1,0,0,1,0,0,0,72,0,1
Original: Time_window_duration

Objective Number_of_quakes_in_
Title: Number of quakes in window
Units: quakes
Description: The number of quakes that occur in the selected time window.
Definition: sum(Number_of_quakes[Year=Time_window],Time_window)
NodeLocation: 456,48,1
NodeSize: 48,31
WindState: 2,586,268,476,224
ValueState: 2,71,517,537,329,1,PDFP
Aliases: FormNode Number_of_quakes_in1
GraphSetup: Graphtool:0~
Distresol:10~
Diststeps:0~
Cdfresol:5~
Cdfsteps:1~
Symbolsize:6~
Baroverlap:0~
Linestyle:9~
Frame:1~
Grid:1~
Ticks:1~
Mesh:1~
Scales:1~
Rotation:45~
Tilt:0~
Depth:70~
Frameauto:1~
Showkey:1~
Xminimum:1~
Xmaximum:4~
Yminimum:0~
Ymaximum:1~
Zminimum:1~
Zmaximum:1~
Xintervals:0~
Yintervals:0~
Includexzero:0~
Includeyzero:0~
Includezzero:0~
Statsselect:[1,1,1,1,1,0,0,0]~
Probindex:[0.05,0.25,0.5,0.75,0.95]~

NumberFormat: 2,D,4,2,0,0,4,0,$,0,"ABBREV",0

Objective Costs_in_window
Title: Costs in window
Units: $
Description: Total cost incurred in time window.~
Costs are incurred quarter by quarter during the time following an earthquake.
Definition: Sum(Costs_by_time[Year=Time_window],Time_window)
NodeLocation: 456,128,1
NodeSize: 48,32
WindState: 2,598,376,476,224
ValueState: 2,351,125,499,474,1,CDFP
Aliases: FormNode Payout_in_window1
GraphSetup: Graphtool:0~
Distresol:10~
Diststeps:0~
Cdfresol:1~
Cdfsteps:1~
Symbolsize:6~
Baroverlap:0~
Linestyle:10~
Frame:3~
Grid:3~
Ticks:1~
Mesh:1~
Scales:1~
Rotation:45~
Tilt:0~
Depth:70~
Frameauto:3~
Showkey:1~
Xminimum:0~
Xmaximum:5M~
Yminimum:0~
Ymaximum:1~
Zminimum:1~
Zmaximum:1~
Xintervals:0~
Yintervals:0~
Includexzero:0~
Includeyzero:0~
Includezzero:0~
Statsselect:[1,1,1,1,1,0,0,0]~
Probindex:[0.05,0.25,0.5,0.75,0.95]~

FontStyle: Arial, 6
ReformVal: [M_step_1001, Std_dev_damage ]
NumberFormat: 1,D,4,2,0,1

FormNode Number_of_quakes_in1
Title: Number of quakes in window
Definition: 1
NodeLocation: 352,376,1
NodeSize: 192,16
NodeInfo: 1,0,0,1,0,0,0,72,0,1
Original: Number_of_quakes_in_

FormNode Payout_in_window1
Title: Payout in window
Definition: 1
NodeLocation: 352,408,1
NodeSize: 192,16
NodeInfo: 1,0,0,1,0,0,0,72,0,1
Original: Costs_in_window

Text Te1
Description: Statistics for a selected time window:
NodeLocation: 352,344,-1
NodeSize: 200,88
NodeInfo: 1,0,0,1,1,1,1,,0,
NodeFont: Arial Black, 15

Module Time_and_window
Title: Time and window
Author: Max Henrion
Date: Thu, May 12, 2005 1:47 PM
DefaultSize: 48,24
NodeLocation: 72,280,1
NodeSize: 48,24
NodeInfo: 1,1,0,1,1,1,0,,0,
DiagState: 1,129,358,539,213,3

Index Year
{!40000|Att_PrevIndexValue: [2005,2005.25,2005.5,2005.75,2006,2006.25,2006.5,2006.75,2007,2007.25,2007.5,2007.75,2008,2008.25,2008.5,2008.75,2009,2009.25,2009.5,2009.75,2010,2010.25,2010.5,2010.75,2011,2011.25,2011.5,2011.75,2012,2012.25,2012.5,2012.75,2013,2013.25,2013.5,2013.75,2014,2014.25,2014.5,2014.75,2015,2015.25,2015.5,2015.75,2016,2016.25,2016.5,2016.75,2017,2017.25,2017.5,2017.75,2018,2018.25,2018.5,2018.75,2019,2019.25,2019.5,2019.75,2020,2020.25,2020.5,2020.75,2021,2021.25,2021.5,2021.75,2022,2022.25,2022.5,2022.75,2023,2023.25,2023.5,2023.75,2024,2024.25,2024.5,2024.75,2025,2025.25,2025.5,2025.75,2026,2026.25,2026.5,2026.75,2027,2027.25,2027.5,2027.75,2028,2028.25,2028.5,2028.75,2029,2029.25,2029.5,2029.75,2030]}
Title: Year
Description: Year index, by quarter.
Definition: Sequence(Start_year, Start_year + Years_to_horizon, 1/4)
NodeLocation: 184,72,1
NodeSize: 48,24
NodeInfo: 1,1,1,1,1,1,0,,0,
ValueState: 2,720,52,416,303,0,MIDM
NumberFormat: 1,F,4,2,0,0

Variable Time_window_start
Title: Time window start
Units: Year
Description: The starting year of a time window that we are examining in more detail
Definition: 2008
NodeLocation: 296,40,1
NodeSize: 48,28
Aliases: FormNode Time_window_start1

Variable Time_window_duration
Title: Time window duration
Units: quarters
Description: Number of quarters in time window being examined.
Definition: 40
NodeLocation: 296,104,1
NodeSize: 48,28
Aliases: FormNode Time_window_duratio1

Index Time_window
{!40000|Att_PrevIndexValue: [2021,2021.25,2021.5,2021.75]}
Title: Time window
Definition: Time_window_start + Sequence(0,  (Time_window_duration - 1)/4, 1/4)
NodeLocation: 424,72,1
NodeSize: 48,24
WindState: 2,102,90,581,266
NumberFormat: 1,F,4,2,0,0

Variable Start_year
Title: Start year
Definition: 2005
NodeLocation: 64,104,1
NodeSize: 48,28

Variable Years_to_horizon
Title: Years to horizon
Definition: 25
NodeLocation: 64,40,1
NodeSize: 48,28

Variable Year0
Title: Year0
Description: Array of zeroes indexed by Year, useful for creating independent distributions over time.
Definition: 0*Year
NodeLocation: 184,160,1
NodeSize: 48,24

Close Time_and_window

Close Earthquake_expense