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Record Nr. |
UNINA9910139005203321 |
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Autore |
Janssen Jacques |
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Titolo |
Applied diffusion processes from engineering to finance [[electronic resource] /] / Jacques Janssen, Oronzio Manca, Raimando Manca |
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Pubbl/distr/stampa |
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ISBN |
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1-118-57833-3 |
1-118-57834-1 |
1-299-47558-2 |
1-118-57668-3 |
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Descrizione fisica |
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1 online resource (411 p.) |
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Collana |
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Altri autori (Persone) |
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MancaOronzio |
MancaRaimondo |
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Disciplina |
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Soggetti |
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Business mathematics |
Differential equations, Partial |
Diffusion processes |
Engineering mathematics |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Description based upon print version of record. |
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Nota di contenuto |
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Title Page; Contents; Introduction; Chapter 1. Diffusion Phenomena and Models; 1.1. General presentation of diffusion process; 1.2. General balance equations; 1.3. Heat conduction equation; 1.4. Initial and boundary conditions; Chapter 2. Probabilistic Models of Diffusion Processes; 2.1. Stochastic differentiation; 2.1.1. Definition; 2.1.2. Examples; 2.2. Itô's formula; 2.2.1. Stochastic differential of a product; 2.2.2. Itô's formula with time dependence; 2.2.3. Interpretation of Itô's formula; 2.2.4. Other extensions of Itô's formula; 2.3. Stochastic differential equations (SDE) |
2.3.1. Existence and unicity general theorem (Gikhman and Skorokhod [GIK 68])2.3.2. Solution of SDE under the canonical form; 2.4. Itô and diffusion processes; 2.4.1. Itô processes; 2.4.2. Diffusion processes; 2.4.3. Kolmogorov equations; 2.5. Some particular cases of diffusion processes; 2.5.1. Reduced form; 2.5.2. The OUV (Ornstein-Uhlenbeck-Vasicek) SDE; 2.5.3. Solution of the SDE of Black-Scholes-Samuelson; 2.6. Multidimensional diffusion processes; 2.6.1. Multidimensional SDE; |
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2.6.2. Multidimensional Itô and diffusion processes; 2.6.3. Properties of multidimensional diffusion processes |
2.6.4. Kolmogorov equations2.7. The Stroock-Varadhan martingale characterization of diffusions (Karlin and Taylor [KAR 81]); 2.8. The Feynman-Kac formula (Platen and Heath); 2.8.1. Terminal condition; 2.8.2. Discounted payoff function; 2.8.3. Discounted payoff function and payoff rate; Chapter 3. Solving Partial Differential Equations of Second Order; 3.1. Basic definitions on PDE of second order; 3.1.1. Notation; 3.1.2. Characteristics; 3.1.3. Canonical form of PDE; 3.2. Solving the heat equation; 3.2.1. Separation of variables |
3.2.2. Separation of variables in the rectangular Cartesian coordinates3.2.3. Orthogonality of functions; 3.2.4. Fourier series; 3.2.5. Sturm-Liouville problem; 3.2.6. One-dimensional homogeneous problem in a finite medium; 3.3. Solution by the method of Laplace transform; 3.3.1. Definition of the Laplace transform; 3.3.2. Properties of the Laplace transform; 3.4. Green's functions; 3.4.1. Green's function as auxiliary problem to solve diffusive problems; 3.4.2. Analysis for determination of Green's function; Chapter 4. Problems in Finance; 4.1. Basic stochastic models for stock prices |
4.1.1. The Black, Scholes and Samuelson model4.1.2. BSS model with deterministic variation of μ and s; 4.2. The bond investments; 4.2.1. Introduction; 4.2.2. Yield curve; 4.2.3. Yield to maturity for a financial investment and for a bond; 4.3. Dynamic deterministic continuous time model for instantaneous interest rate; 4.3.1. Instantaneous interest rate; 4.3.2. Particular cases; 4.3.3. Yield curve associated with instantaneous interest rate; 4.3.4. Examples of theoretical models; 4.4. Stochastic continuous time dynamic model for instantaneous interest rate; 4.4.1. The OUV stochastic model |
4.4.2. The CIR model (1985) |
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Sommario/riassunto |
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The aim of this book is to promote interaction between engineering, finance and insurance, as these three domains have many models and methods of solution in common for solving real-life problems. The authors point out the strict inter-relations that exist among the diffusion models used in engineering, finance and insurance. In each of the three fields, the basic diffusion models are presented and their strong similarities are discussed. Analytical, numerical and Monte Carlo simulation methods are explained with a view to applying them to obtain the solutions to the different problems pres |
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