Transcript Example - Ukrainian Risk Laboratory

PARALLEL COMPUTATIONS IN NONLIFE
INSURANCE BUSINESS OPTIMIZATION
BOGDAN NORKIN
V. M. Glushkov
Institute of Cybernetics
Kiev, Ukraine
HPC – UA 2012
OUTLINE
• Introduction: parallel actuarial calculations
• Problem – simulation of insurance company
• Model – risk process
• Data – Insurance company statistics
• Method – GPU accelerated simulations
• Goal – optimization of insurance business.
• RiskManagenentSystem overview
• Usage examples
RESERVS
RISK PROCESS MODEL
RUIN
EXSAMPLE - RISK PROCESS WITH
DIVIDEND BARRIER
c  Rt  dt
PARALLEL ACTUARIAL COMPUTATIONS
THE METHOD OF SUCCESSIVE APPROXIMATIONS
Our Equation
 ( x, t )  Ax ,t (, )
Method of successive approximations

k 1
( x, t )  Ax ,t (, )
k
For example…
 ( xi , t j )  
k 1
tj
0

U ( xi , )
0

 k U ( xi , )  z, t j    dF ( z, )  1  F  , t j 

CALCULATING K+1 ITERATION
Let us have K-th iteration

x
CALCULATING K+1 ITERATION
This is time grid

x
CALCULATING K+1 ITERATION
To obtain
 k 1
we use values of
 k in grid nodes
 k  x1 
 k 1  x1 
x1
x2
xk
CALCULATING K+1 ITERATION
To obtain
 k 1
And so on…
we use values of
 k in grid nodes
CALCULATING K+1 ITERATION
To obtain
 k 1
we use values of
 k in grid nodes

And so on… just the same way
x
CALCULATING K+1 ITERATION
To obtain

 k 1
we use values of
 k in grid nodes
Due to independent nature of calculations we can use
more then one core (up to number of greed nodes)….
 k 1  x j 
 k 1  xi 
x
CALCULATING K+1 ITERATION
To obtain
 k 1
we use values of
 k in grid nodes

And as a result we can interpolate
 k 1
x
RESERVS
COMPANY RESERVES SIMULATION
RUIN
We need millions of such simulations!
For real time modelling we need parallelization
PARALLEL ACTUARIAL COMPUTATIONS
Parallel actuarial simulations
Random outcome = Company simulation (Inputs)
Inputs
– hundreds
Simulations
– millions
Example:
Ruin Probability = Fraction of ruined trajectories
OPTIMIZATION PROBLEM
Dividend maximization
Subject to Bound on
• Ruin Probability ( ≤ 10-3 )
• Residual capital
RMS 0.2 - RISK MANAGEMENT SYSTEM




Realistic simulation
models
Adjusted to law
regulations
Real world data
Optimization over any
parameter (multi
criteria task)



Based on parallel
simulations
GPU accelerated powered by CUDA
User friendly 
MAIN FEATURES
•On
the basis of company's claim statistics
One can:
•Estimate
•
•
•
•Build
ruin probability,
projected dividend size
residual reserve.
efficient frontier.
•Investigate any dependences.
MAIN BUGS
Just an α version…
SYSTEM OVERVIEW
Probability
of insolvency (Ruin)
as a function
of parameter
(dividend rate)
SYSTEM OVERVIEW
Resudual capital and
dividends
as functions
of parameter
(dividend rate)
SYSTEM OVERVIEW
Efficient frontier
(Profit vs Risk)
allows to select
a tradeoff point
CLAIM STATISTICS
Per quarter normalized claim statistics of a wellknown Ukrainian insurance company with foreign
capital.
EXTREME DEPENDENCES ILLUSTRATION–
RUIN PROBABILITY
DIVIDENDS & RESIDUAL RESERVE
EFFICIENT FRONTIER EXAMPLE
CONCLUSIONS
•
•
•
•
•
Insurance simulation model based on real world
data.
Risk/Profit optimization (Efficient frontier
constructing)
Any parameter can be an optimization variable.
Real time GPU accelerated Monte Carlo method.
(about 1 second for billions of trajectories)
And at last User friendly interface turns RMS 0.2 in
a very efficient and nice system 
REFERENCES
•
•
•
•
Kaufmann R., Gadmer A., Klett R. Introduction to dynamic financial
analysis // ASTIN Bulletin, Vol. 31, No. 1, 2001, pp. 213-249.
Norkin B. Parallel computations in insurance business optimization
//Proceedings of the 1-st International Conference on High
Performance Computing. October 12-14, 2011, Kyiv, Ukraine. – P. 3339.
Норкин Б.В. Распараллеливание методов оценки риска
банкротства страховой компании // Теорія оптимальних рішень.
– Київ : Інститут Кібернетики, 2010. – Стор. 33-39.
Норкин Б.В. О вероятности разорения управляемого процесса
авторегрессии // Комп’ютерна математика. Ін-т кібернетики ім.
В.М. Глушкова. Київ, 2011. – С. 142-150.
THANK YOU FOR ATTENTION!
BOGDAN NORKIN
[email protected]
V. M. Glushkov
Institute of Cybernetics
Kiev, Ukraine
HPC – UA 2012