Handbook in Monte Carlo Simulation: Applications in by Paolo Brandimarte
By Paolo Brandimarte
An obtainable therapy of Monte Carlo equipment, options, and purposes within the box of finance and economics
Providing readers with an in-depth and entire advisor, the Handbook in Monte Carlo Simulation: functions in monetary Engineering, probability administration, and Economics provides a well timed account of the functions of Monte Carlo equipment in monetary engineering and economics. Written via a world prime specialist within the box, the guide illustrates the demanding situations confronting present-day monetary practitioners and offers a number of purposes of Monte Carlo ideas to respond to those concerns.
The publication is geared up into 5 components: creation and motivation; enter research, modeling, and estimation; random variate and pattern direction new release; output research and variance relief; and purposes starting from choice pricing and threat administration to optimization.
The Handbook in Monte Carlo Simulation good points:
• An introductory part for uncomplicated fabric on stochastic modeling and estimation aimed toward readers who might have a precis or overview of the essentials
• rigorously crafted examples as a way to spot strength pitfalls and downsides of every approach
• An available remedy of complex issues akin to low-discrepancy sequences, stochastic optimization, dynamic programming, danger measures, and Markov chain Monte Carlo methods
• various items of R code used to demonstrate basic rules in concrete phrases and inspire experimentation
The Handbook in Monte Carlo Simulation: functions in monetary Engineering, threat administration, and Economics is a whole reference for practitioners within the fields of finance, company, utilized records, econometrics, and engineering, in addition to a complement for MBA and graduate-level classes on Monte Carlo equipment and simulation.
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Additional info for Handbook in Monte Carlo Simulation: Applications in Financial Engineering, Risk Management, and Economics
12 Several global optimization algorithms have been proposed, and some of them do guarantee the global optimality of the reported solution. Unfortunately, these algorithms are typically restricted to a specific class of functions, and the optimality guarantee may require demanding computations. As an alternative, if we are not able to exploit specific structural properties of the problem, and a near-optimal solution is enough, possibly the optimal one but with no proof of its status, we may resort to general-purpose stochastic search algorithms.
Equivalently, maximizing a concave function is relatively easy. This is good news for an economist wishing to solve a decision problem featuring a concave utility function or a financial engineer minimizing a convex risk measure. However, there are cases in which such a nice condition is not met, and the need for global optimization methods arises. The following example illustrates a typical function featuring a large number of local optima. 6 The Rastrigin function The Rastrigin function is a sort of benchmark to test global optimization algorithms, as well as to illustrate how bad an objective function can be.
Nevertheless, there are approximate dynamic programming approaches that do not guarantee optimality, but typically provide us with very good decisions. The exact approach should be chosen case by case, but what they have in common is the role of Monte Carlo methods: • To generate scenarios • To learn an optimal policy • To evaluate the performance of a policy by simulation 1,5 Pitfalls in Monte Carlo simulation Monte Carlo methods are extremely flexible and powerful tools; furthermore, they are conceptually very simple, at least in their naive and crude form.