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Word number one Computational Methods in Insurance and Finance Homework Experts

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Stochastic Differential Equations

These are non-homogenous differential equations that are based on external stochastic processes. Stochastic processes are idealized as noise in nature. This idealization helps simplify the mathematical definition. However, the traditional calculus can no longer be applied in stochastic processes. Instead, the Ito calculus is recommended. Also, rather than the normal calculus chain rule, you should consider the Ito formula.

Random Numbers Generation

The use of statistical techniques that depend on simulation requires the use of random numbers. Most of the time, you can use software to generate a series of random numbers. For example, in R programming, there is the runif() function that can help you generate random numbers that are distributed uniformly over a fixed interval. However, before using this function you must understand how the random number generators work. Also, R's built-in functions can only work with distributions that are well-known and characterized.

Partial Differential Equations (PDE)

These types of mathematical differential equations are made up of multiple unknown variables. Partial differential equations' dependent variables have partial derivatives. These partial derivatives are usually denoted using subscripts. They are also sometimes represented by the nabla symbol in wave equations. If you want to determine if a specific finite element approach is suitable for the problem being solved by the PDE, then you have to check the functionalities of the PDE.