Jump Process Shreve E Stochastic Calculus for Finance Slides: 27 Download presentation Jump Process Shreve E. Stochastic Calculus for Finance II Chap. 11. 1 ~ 11. 4 動機 n Credit Risk: Modeling, Valuation and Hedging Chap. 2. 4. 2 (2. 48 ~ 2. 50) 大綱 Poisson Process n Compound Poisson Process n Jump Process and Their Integrals n Compensated Poisson Process Martingale Property n n n 由 Theorem 11. 2. 3,易知 t > s 時 E[ N(t) – N(s) ] = Var[ N(t) – N(s) ] = λ(t-s) 從而 M(t) = N(t) –λt 是鞅 (martingale)。稱此為 Compensated Poisson 過程。 N(t)在兩次跳躍之間保持為常數。此一性質對 M(t) 並不適用。 大綱 Poisson Process n Compound Poisson Process (Random Jump Size) n Jump Process and Their Integrals n 大綱 Poisson Process n Compound Poisson Process n Jump Process and Their Integrals (黎曼積分 + 伊藤積分 + 純跳躍) n Jump Process之機率空間 Brownian Motion Poisson Process-兩者皆無記憶性,且互相獨立 Jump Process & Its Integral Quadratic Variation Cross Variation We're gonna jump jump jump in the riverTom shreveStochastic calculusStochastic calculusJump conditions assemblyJump triageStochastic process modelStochastic process introductionStochastic process modelingStochastic processStochastic processStochastic processStochastic processRandom processMention the components of time seriesStationary stochastic processStochastic processStochastic roundingStochastic programmingDivbarDeterministic demand vs stochastic demandStochastic vs dynamicAbsorbing stochastic matrixStochastic regressorsNon stochastic theory of agingA first course in stochastic processesStochastic progressive photon mappingDeterministic vs stochastic environment examples