TAILIEUCHUNG - Numerical Solution of Stochastic Differential Equations with Jumps in Finance

This research monograph concerns the design and analysis of discrete-time approximations for stochastic differential equations (SDEs) driven by Wiener processes and Poisson processes or Poisson jump measures. In financial and actuarial modeling and other areas of application, such jump diffusions are often used to describe the dynamics of various state variables. In finance these may represent, for instance, asset prices, credit ratings, stock indices, interest rates, exchange rates or commodity prices. The jump component can capture event-driven uncertainties, such as corporate defaults, operational failures or insured events. The book focuses on efficient and numerically stable strong and weak discrete-time approximations of solutions of SDEs. Strong approx-imations provide efficient tools. | rd Platen Bruti-Liberati Numerical Solution of Stochastic Differential Equations with Jumps in Finance Springer Stochastic Mechanics Random Media Signal Processing and Image Synthesis Mathematical Economics and Finance Stochastic Optimization Stochastic Control Stochastic Models in Life Sciences Stochastic Modelling and Applied Probability Formerly Applications of Mathematics 64 Edited by Advisory Board B. Rozovskii G. Grimmett M. Hairer I. Karatzas F. P. Kelly A. Kyprianou Y. Le Jan B. 0ksendal G. Papanicolaou E. Pardoux E. Perkins For other titles in this series go to http series .

• Quản trị kinh doanh
• Stochastic Processes
• Supermartingales
• Quadratic Variation
• Itˆo Integral
• Itˆo Formula
• Queueing system
• nite number
• shop assistants
• a forming of queues
• Queueing systems
• without queues
• Some general types
• stochastic processes Download free ebooks at bookboon
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• Probability Examples c 9 – Stochastic Processes 2 © 2009 Leif Mejlbro & Ventus Publishing ApS ISBN 978 87 7681 525 7 Download free ebooks at bookboon
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• Stochastic Processes 2 Contents Contents Introduction 1 1
• 1 1
• 2 1
• 3 1
• 4 1
• 5 1
• 6 1
• 7 2 3 4 5 Theoretical background The Poisson process Birth and death processes Queueing theory in general Queueing system of innitely many shop assistants Queueing system of a nite number of shop assistants
• and with forming of queues Queueing systems with a nite number of shop assistants and without queues Some general types of stochastic processes The Poisson process Birth and death processes Queueing theory Other types of stochastic processes Index 5 6 6 8 11 11 12 15 17 19 37 52 117 126 The next step for top performing gradua
• Probability random variables and stochastic processes
• Probability random variables
• Probability variables
• Discrete time stochastic processes
• Markov chains
• Continuous time stochastic processes
• Itô’s lemma
• Stochastic integral
• Preliminaries
• Lecture Introduction to Stochastic Processes
• Introduction to Stochastic Processes
• Disjoint time intervals
• The stochastic process
• Homogeneous Poisson proces
• Markov chain
• Discrete parameter stochastic process
• Time homogeneous Markov chain
• Lecture Probability Theory
• Probability Theory
• Lý thuyết xác suất
• Stationary Stochastic Processes
• Systems with Stochastic Inputs
• Homogeneous poisson processes
• Holds trivially
• Probability density function
• Order statistics property
• Conditional distribution
• Theorem superposition
• Probability generating function
• Poisson process
• stochastic calculus
• mathematics of finance
• Process Limits
• Random variables
• Invariant measur
• Unique stationary distribution
• Symmetric transition probability matrix
• SLLN for Markov chains
• The long run proportion
• Dissection principle
• Limiting distribution
• Aperiodic Markov chain
• Stationary distribution
• Homogeneous Poisson process
• Discrete Markov chains
• Positive real numbers
• Heuristic justification
• Rigorous justification
• Positive random variables
• Exponential distribution
• Poissonian increments
• Inhomogeneous Poisson process
• Discrete parameter Markov chain
• Countable state space
• Mathematical description
• Transition probabilities
• Simple random walk
• On off process
• Random walks on groups
• Gambler's ruin problem
• Chapman Kolmogorov equation
• Decomposition of state space
• Deterministically monotone Markov chain
• Communication classes
• The dissection principle
• Non empty closed subsets
• Recurrent Markov chain
• E valued random variables
• Power series
• Abel's limit theorem
• Proof of the theorem