• 충청수학회지
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• 제19권4호
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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.

• 대한산업공학회지
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• 제36권2호
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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.

• East Asian mathematical journal
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• 제36권1호
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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.

• 대한수학회보
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• 제56권2호
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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.

• 대한수학회보
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• 제52권2호
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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.

• 응용통계연구
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• 제23권2호
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• pp.383-392
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• 2010

확산모형은 최근 금융현상의 연구 등에 자주 사용되는 모형이다. 본 연구에서는 확산모형의 추정에서 중요한 역할을 하는 전이확률밀도를 구하는 방법과 이를 급수전개 방식으로 근사하는 기존 연구들을 검토하여 보고, 급수전개법에서의 계수를 손쉽게 구할 수 있는 방법을 고려하게 된다. 급수전개법 계산과정에서 중요한 허밋다항식에 딘킨연산자를 반복적으로 적용하는 과정을 손쉽게 계산할 수 있는 알고리즘을 제안한다.