1. MONTE CARLO
SIMULATION

2. MONTE CARLO SIMULATION
• A problem solving technique used to approximate the probability of
certain outcomes by running multiple trial runs, called simulations,
using random variables.
• The technique is used by professionals in widely disparate fields
such as
• Finance
• Project management
• Energy, manufacturing
• Engineering
• Research and development
• Insurance
• oil & gas and the environment.

3. HISTORY
• Monte Carlo simulation was named after the city in Monaco.
• The technique was first used by scientists working on the
atom bomb.

4. HOW MCS WORKS
• In Monte Carlo simulation, the entire system is simulated a
large number (e.g., 1000) of times. Each simulation is equally
likely, referred to as a realization of the system. For each
realization, all of the uncertain parameters are sampled (i.e., a
single random value is selected from the specified distribution
describing each parameter). The system is then simulated
through time such that the performance of the system can be
computed. This results is a large number of separate and
independent results, each representing a possible “future” for
the system. The results of the independent system realizations
are assembled into probability distributions of possible
outcomes. As a result, the outputs are probability
distributions.

5. EXAMPLE: ROLLING DICE
• As a simple example of a Monte Carlo simulation,
consider calculating the probability of a particular sum of the
throw of two dice (with each die having values one through
six). In this particular case, there are 36 combinations of dice
rolls:

6. • Based on this, We can manually compute the probability of a
particular outcome. For example, there are six different ways
that the dice could sum to seven. Hence, the probability of
rolling seven is equal to 6 divided by 36 = 0.167.
• Without computer, we could throw the dice a hundred
times and record how many times each outcome occurs. If
the dice totaled seven 18 times (out of 100 rolls), we would
conclude that the probability of rolling seven is approximately
0.18 (18%).

7. • But Better than rolling dice a hundred times, we can easily use
a computer to simulate rolling the dice 10,000 times (or
more). Because we know the probability of a particular
outcome for one die. The output of 10,000 realizations:

8. HOW THE RESULTS ARE
ACCURATE
• The accuracy of a Monte Carlo simulation is a function of the
number of realizations.

9. ADVANTAGES
• Probabilistic Results:
Results show not only what could happen, but how likely
each outcome is.
• Graphical Results:
In Monte Carlo simulation , it’s easy to create graphs of
different outcomes and their chances of occurrence.
• Sensitivity Analysis:
In Monte Carlo simulation, it’s easy to see which inputs
had the biggest effect on results.

10. APPLICATIONS
• Physical Sciences
• Engineering
• Computational Biology
• Applied Statistics
• Games
• Design and visuals
• Finance and business
• Telecommunications
• Mathematics