SimulationNotes17.04.21 - Business Modeling and Simulation...

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Statistics for Management and Economics + XLSTAT Bind-in
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Business Modeling and Simulation Contents 1 Basics of Simulation 2 1.1 Dart Game and the Estimation of π . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2 A Dinner Deal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.3 Excel Skills . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.3.1 Data Array and Matrix Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.3.2 Random Variables, PDF, and CDF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.3.3 Generate Random Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.3.4 Simulation, sampling, sample, sample path . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.3.5 Statistics and Histogram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.4 Textbooks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2 Decision Making under Uncertainty 8 2.1 A Sales Promotion Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.1.1 Hints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.2 Flextrola . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.2.1 Hints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.3 Newsvendor Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.4 Excel Skills . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.4.1 Loops and Data Table . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.4.2 Logical Operations and Indicators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 3 Financial Models 15 3.1 An Insurance Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 3.1.1 Hints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 3.2 Pricing Asian Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 3.3 Hedging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 3.4 Investment Strategies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 3.4.1 Hint . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 1
We have textbook solutions for you!
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Statistics for Management and Economics + XLSTAT Bind-in
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Chapter 22 / Exercise 22.8
Statistics for Management and Economics + XLSTAT Bind-in
Keller
Expert Verified
1 Basics of Simulation Simulation is a way of thinking. It tells stories in a logical way. Just as every story has actors, plots, and contexts, so does simulation. In a story, we want to know who are the actors, how they interact, under what context, and what are the outcomes of their interactions. In simulation, random variables are our actors, and we seek to understand how and why their interplay leads to certain outcomes. For each simulation, we must first specify the relevant random variables. Like actors, they each have names and behaviors (personalities, characters). For example, Bernoulli, Binomial, and Nor- mal are the names of typical random variables. Their behaviors are uniquely defined by their distribution functions—probability distribution function (PDF) f , or cumulative distribution func- tion (CDF) F . Depending on the problem, either one can be pleasant to work with. Their relation is F ( x ) = x −∞ f ( t ) dt for continuous case, and F ( x ) = t i x f ( t i ) for discrete case. Second, we care about the context of the simulation. This is done by specifying the business and other environmental parameters. For example, the time horizon, the production cost, and the market price. Along with the parameters of random variables, they constitute the INPUT of the simulation. Third, we need to figure out the logic—the plot—of the simulation. That is, how the random variables interact in each context. This is the fun part of the simulation: as the logic depends on the problem specifics, we must analyze each on its own merit. Once we have specified the INPUT and the logic, we are ready to run the simulation. The OUTPUT records the outcomes and statistics that interest us. For example, the mean profit and its 95% confidence internal. Typically it involves statistic analysis. Taking together, we have OUPUT = LOGIC( INPUT ) . Simulation builds on one simple idea: The expectation of a random variable X can be approximated by averaging the realizations { x 1 , x 2 , · · · , x N } of X , and the probability of an event (e.g., ( X > 0) ) can be approximated by averaging its indicators 1 * ( x i > 0) : E [ X ] N i =1 x i N , P ( X > 0) N i =1 1 * ( x i > 0) N .

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