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 Pascucci, Andrea.
 Milan ; New York : Springer, ©2011.
 Description
 Book — 1 online resource (xvii, 719 pages).
 Summary

 ""Title Page ""; ""Copyright Page ""; ""Preface""; ""Table of Contents ""; ""General notations""; ""Shortenings""; ""Function spaces""; ""Spaces of processes""; ""1 Derivatives and arbitrage pricing""; ""1.1 Options""; ""1.1.1 Main purposes""; ""1.1.2 Main problems""; ""1.1.3 Rules of compounding""; ""1.1.4 Arbitrage opportunities and PutCall parity formula""; ""1.2 Riskneutral price and arbitrage pricing""; ""1.2.1 Riskneutral price""; ""1.2.2 Riskneutral probability""; ""1.2.3 Arbitrage price""; ""1.2.4 A generalization of the PutCall parity""; ""1.2.5 Incomplete markets""
 ""2 Discrete market models""""2.1 Discrete markets and arbitrage strategies""; ""2.1.1 Selffinancing and predictable strategies""; ""2.1.2 Normalized market""; ""2.1.3 Arbitrage opportunities and admissible strategies""; ""2.1.4 Equivalent martingale measure""; ""2.1.5 Change of numeraire""; ""2.2 European derivatives""; ""2.2.1 Pricing in an arbitragefree market""; ""2.2.2 Completeness""; ""2.2.3 Fundamental theorems of asset pricing""; ""2.2.4 Markov property""; ""2.3 Binomial model""; ""2.3.1 Martingale measure and arbitrage price""; ""2.3.2 Hedging strategies""
 ""2.3.3 Binomial algorithm""""2.3.4 Calibration""; ""2.3.5 Binomial model and BlackScholes formula""; ""2.3.6 BlackScholes differential equation""; ""2.4 Trinomial model""; ""2.4.1 Pricing and hedging in an incomplete market""; ""2.5 American derivatives""; ""2.5.1 Arbitrage price""; ""2.5.2 Optimal exercise strategies""; ""2.5.3 Pricing and hedging algorithms""; ""2.5.4 Relations with European options""; ""2.5.5 Freeboundary problem for American options""; ""2.5.6 American and European options in the binomial model""; ""3 Continuoustime stochastic processes""
 ""3.1 Stochastic processes and real Brownian motion""""3.1.1 Markov property""; ""3.1.2 Brownian motion and the heat equation""; ""3.2 Uniqueness""; ""3.2.1 Law of a continuous process""; ""3.2.2 Equivalence of processes""; ""3.2.3 Modifications and indistinguishable processes""; ""3.2.4 Adapted and progressively measurable processes""; ""3.3 Martingales""; ""3.3.1 Doobâ€?s inequality""; ""3.3.2 Martingale spaces: M2 and M2""; ""3.3.3 The usual hypotheses""; ""3.3.4 Stopping times and martingales""; ""3.4 RiemannStieltjes integral""; ""3.4.1 Boundedvariation functions""
 ""3.4.2 RiemannStieltjes integral and Ito formula""""3.4.3 Regularity of the paths of a Brownian motion""; ""4 Brownian integration""; ""4.1 Stochastic integral of deterministic functions""; ""4.2 Stochastic integral of simple processes""; ""4.3 Integral of L2processes""; ""4.3.1 Ito and RiemannStieltjes integral""; ""4.3.2 Ito integral and stopping times""; ""4.3.3 Quadratic variation process""; ""4.3.4 Martingales with bounded variation""; ""4.3.5 Covariation process""; ""4.4 Integral of L2locprocesses""; ""4.4.1 Local martingales""; ""4.4.2 Localization and quadratic variation""
 Meyer, Gunter H.
 New Jersey : World Scientific, [2015]
 Description
 Book — 1 online resource.
 Summary

 1. Comments on the pricing equations in finance. 1.1. Solutions and their properties. 1.2. Boundary conditions for the pricing equations
 2. The method of lines (MOL) for the diffusion equation. 2.1. The method of lines with continuous time (the vertical MOL). 2.2. The method of lines with continuous x (the horizontal MOL). 2.3. The method of lines with continuous x for multidimensional problems. 2.4. Free boundaries and the MOL in two dimensions
 3. The Riccati transformation method for linear two point boundary value problems. 3.1. The Riccati transformation on a fixed interval. 3.2. The Riccati transformation for a free boundary problem. 3.3. The numerical solution of the sweep equations
 4. European options
 5. American puts and calls
 6. Bonds and options for onefactor interest rate models
 7. Twodimensional diffusion problems in finance. 7.1. Front tracking in Cartesian coordinates. 7.2. American calls and puts in polar coordinates. 7.3. A threedimensional problem.
3. The timediscrete method of lines for options and bonds [electronic resource] : a PDE approach [2015]
 Meyer, Gunter H.
 Singapore ; Hackensack, N.J. : World Scientific Pub. Co., c2015.
 Description
 Book — xv, 269 p. : ill. (some col.).
 Summary

 Properties of Solutions of the PDEs of Finance Acceptable Boundary Conditions Numerical Solution with a Locally OneDimensional Free Boundary Solver European and American Puts and Calls Bonds and Bond Options for OneFactor Interest Rate Models Stochastic Volatility Models American Options on Two Assets Front Tracking in Cartesian and Polar Coordinates.
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 Crépey, Stéphane.
 Berlin ; New York : Springer, ©2013.
 Description
 Book — 1 online resource. Digital: text file; PDF.
 Summary

 An Introductory Course in Stochastic Processes
 Some Classes of DiscreteTime Stochastic Processes
 Some Classes of ContinuousTime Stochastic Processes
 Elements of Stochastic Analysis
 Pricing Equations
 Martingale Modeling
 Benchmark Models
 Numerical Solutions
 Monte Carlo Methods
 Tree Methods
 Finite Differences
 Calibration Methods
 Applications
 Simulation/Regression Pricing Schemes in Diffusive Setups
 Simulation/Regression Pricing Schemes in Pure Jump Setups
 JumpDiffusion Setup with Regime Switching (**)
 Backward Stochastic Differential Equations
 Analytic Approach
 Extensions
 Appendix
 Technical Proofs (**)
 Exercises
 Corrected Problem Sets.
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