LEADER 05617nam 2200745Ia 450 001 9910812555803321 005 20240313194421.0 010 $a1-118-57833-3 010 $a1-118-57834-1 010 $a1-299-47558-2 010 $a1-118-57668-3 035 $a(CKB)2550000001020346 035 $a(EBL)1168522 035 $a(OCoLC)841914036 035 $a(SSID)ssj0000904707 035 $a(PQKBManifestationID)11512245 035 $a(PQKBTitleCode)TC0000904707 035 $a(PQKBWorkID)10924538 035 $a(PQKB)11666983 035 $a(MiAaPQ)EBC1168522 035 $a(Au-PeEL)EBL1168522 035 $a(CaPaEBR)ebr10687765 035 $a(CaONFJC)MIL478808 035 $a(PPN)192204971 035 $a(EXLCZ)992550000001020346 100 $a20130418d2013 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aApplied diffusion processes from engineering to finance$b[electronic resource] /$fJacques Janssen, Oronzio Manca, Raimando Manca 205 $a1st ed. 210 $aLondon $cWiley$d2013 215 $a1 online resource (411 p.) 225 1 $aISTE 300 $aDescription based upon print version of record. 311 $a1-84821-249-6 327 $aTitle 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. Ito?'s formula; 2.2.1. Stochastic differential of a product; 2.2.2. Ito?'s formula with time dependence; 2.2.3. Interpretation of Ito?'s formula; 2.2.4. Other extensions of Ito?'s formula; 2.3. Stochastic differential equations (SDE) 327 $a2.3.1. Existence and unicity general theorem (Gikhman and Skorokhod [GIK 68])2.3.2. Solution of SDE under the canonical form; 2.4. Ito? and diffusion processes; 2.4.1. Ito? 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; 2.6.2. Multidimensional Ito? and diffusion processes; 2.6.3. Properties of multidimensional diffusion processes 327 $a2.6.4. 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 327 $a3.2.2. 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 327 $a4.1.1. The Black, Scholes and Samuelson model4.1.2. BSS model with deterministic variation of ? 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 327 $a4.4.2. The CIR model (1985) 330 $a The aim of this book is to promote interaction between engineering, finance and insurance, as these three domains have many models and methods of solution in common for solving real-life problems. The authors point out the strict inter-relations that exist among the diffusion models used in engineering, finance and insurance. In each of the three fields, the basic diffusion models are presented and their strong similarities are discussed. Analytical, numerical and Monte Carlo simulation methods are explained with a view to applying them to obtain the solutions to the different problems pres 410 0$aISTE. 606 $aBusiness mathematics 606 $aDifferential equations, Partial 606 $aDiffusion processes 606 $aEngineering mathematics 615 0$aBusiness mathematics. 615 0$aDifferential equations, Partial. 615 0$aDiffusion processes. 615 0$aEngineering mathematics. 676 $a519.233 700 $aJanssen$b Jacques$0726990 701 $aManca$b Oronzio$06378 701 $aManca$b Raimondo$0327298 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910812555803321 996 $aApplied diffusion processes from engineering to finance$94114938 997 $aUNINA