• Title/Summary/Keyword: Girsanov theorem

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GIRSANOV THEOREM FOR GAUSSIAN PROCESS WITH INDEPENDENT INCREMENTS

  • Im, Man Kyu;Ji, Un Cig;Kim, Jae Hee
    • Journal of the Chungcheong Mathematical Society
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    • v.19 no.4
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    • pp.383-391
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    • 2006
  • A characterization of Gaussian process with independent increments in terms of the support of covariance operator is established. We investigate the Girsanov formula for a Gaussian process with independent increments.

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Calibrated Parameters with Consistency for Option Pricing in the Two-state Regime Switching Black-Scholes Model (국면전환 블랙-숄즈 모형에서 정합성을 가진 모수의 추정)

  • Han, Gyu-Sik
    • Journal of Korean Institute of Industrial Engineers
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    • v.36 no.2
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    • pp.101-107
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    • 2010
  • Among a variety of asset dynamics models in order to explain the common properties of financial underlying assets, parametric models are meaningful when their parameters are set reliably. There are two main methods from which we can obtain them. They are to use time-series data of an underlying price or the market option prices of the underlying at one time. Based on the Girsanov theorem, in the pure diffusion models, the parameters calibrated from the option prices should be partially equivalent to those from time-series underling prices. We call this phenomenon model consistency. In this paper, we verify that the two-state regime switching Black-Scholes model is superior in the sense of model consistency, comparing with two popular conventional models, the Black-Scholes model and Heston model.

A PROBABILISTIC APPROACH FOR VALUING EXCHANGE OPTION WITH DEFAULT RISK

  • Kim, Geonwoo
    • East Asian mathematical journal
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    • v.36 no.1
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    • pp.55-60
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    • 2020
  • We study a probabilistic approach for valuing an exchange option with default risk. The structural model of Klein [6] is used for modeling default risk. Under the structural model, we derive the closed-form pricing formula of the exchange option with default risk. Specifically, we provide the pricing formula of the option with the bivariate normal cumulative function via a change of measure technique and a multidimensional Girsanov's theorem.

STOCHASTIC DIFFERENTIAL EQUATIONS DRIVEN BY AN ADDITIVE FRACTIONAL BROWNIAN SHEET

  • El Barrimi, Oussama;Ouknine, Youssef
    • Bulletin of the Korean Mathematical Society
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    • v.56 no.2
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    • pp.479-489
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    • 2019
  • In this paper, we show the existence of a weak solution for a stochastic differential equation driven by an additive fractional Brownian sheet with Hurst parameters H, H' > 1/2, and a drift coefficient satisfying the linear growth condition. The result is obtained using a suitable Girsanov theorem for the fractional Brownian sheet.

MULTIDIMENSIONAL BSDES WITH UNIFORMLY CONTINUOUS GENERATORS AND GENERAL TIME INTERVALS

  • Fan, Shengjun;Wang, Yanbin;Xiao, Lishun
    • Bulletin of the Korean Mathematical Society
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    • v.52 no.2
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    • pp.483-504
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    • 2015
  • This paper is devoted to solving a multidimensional backward stochastic differential equation with a general time interval, where the generator is uniformly continuous in (y, z) non-uniformly with respect to t. By establishing some results on deterministic backward differential equations with general time intervals, and by virtue of Girsanov's theorem and convolution technique, we prove a new existence and uniqueness result for solutions of this kind of backward stochastic differential equations, which extends the results of [8] and [6] to the general time interval case.

A Note on Series Approximation of Transition Density of Diffusion Processes (확산모형 전이확률밀도의 급수근사법과 그 계수)

  • Lee, Eun-Kyung;Choi, Young-Soo;Lee, Yoon-Dong
    • The Korean Journal of Applied Statistics
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    • v.23 no.2
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    • pp.383-392
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    • 2010
  • Modelling financial phenomena with diffusion processes is frequently used technique. This study reviews the earlier researches on the approximation problem of transition densities of diffusion processes, which takes important roles in estimating diffusion processes, and consider the method to obtain the coefficients of series efficiently, in series approximation method of transition densities. We developed a new efficient algorithm to compute the coefficients which are represented by repeated Dynkin operator on Hermite polynomial.