Essays about: "Euler approximation"
Showing result 1 - 5 of 13 essays containing the words Euler approximation.
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1. Solving Ordinary Differential Equations and Systems using Neural Network Methods
University essay from Karlstads universitet/Institutionen för matematik och datavetenskap (from 2013)Abstract : The applications of differential equations are many. However, many differential equations modelling real-world scenarios are very complex and it can be of great difficulty to find an exact solution if one even exists. Thus, it is of importance to be able to approximate solutions of differential equations. READ MORE
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2. Pricing Put Options with Multilevel Monte Carlo Simulation
University essay from Mälardalens högskola/Akademin för utbildning, kultur och kommunikationAbstract : Monte Carlo path simulations are common in mathematical and computational finance as a way of estimating the expected values of a quantity such as a European put option, which is functional to the solution of a stochastic differential equation (SDE). The computational complexity of the standard Monte Carlo (MC) method grows quite large quickly, so in this thesis we focus on the Multilevel Monte Carlo (MLMC) method by Giles, which uses multigrid ideas to reduce the computational complexity. READ MORE
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3. Finite Difference Methods for the Black-Scholes Equation
University essay from Mälardalens högskola/Akademin för utbildning, kultur och kommunikationAbstract : Financial engineering problems are of great importance in the academic community and BlackScholes equation is a revolutionary concept in the modern financial theory. Financial instruments such as stocks and derivatives can be evaluated using this model. Option evaluation, is extremely important to trade in the stocks. READ MORE
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4. Analytic Approximation of Transition Probabilities
University essay from Lunds universitet/Matematisk statistikAbstract : A transition probability is essentially a likelihood of ’something random’ transitioning from one state of being to another. Though, more formally, for all intents and purposes, the ’something random’ is a sequence of random events, which is a stochastic process. There are many stochastic processes that are valuable to understand. READ MORE
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5. Monte Carlo Path Simulation and the Multilevel Monte Carlo Method
University essay from Umeå universitet/Institutionen för fysikAbstract : A standard problem in the field of computational finance is that of pricing derivative securities. This is often accomplished by estimating an expected value of a functional of a stochastic process, defined by a stochastic differential equation (SDE). READ MORE
