金融工程研究中心学术报告：Threshold Brownian Motion

来源：

学校官网

收录时间：

2026-07-11 03:13:47

时间：

2026-07-13 15:40:00

地点：

览秀楼105

报告人：

周晓文

学校：

苏州大学

关键词：

Threshold Brownian Motion, Stochastic Control, SDE, Transition Density, Potential Measure, Laplace Transform

简介：

Motivated by problems in stochastic control, we consider the unique solution X to the following SDE dX_t = (μ_1 1{X_t≤0} + μ_2 1{X_t>0})dt + (σ_1 1{X_t≤0} + σ_2 1{X_t>0})dB_t for μ_1, μ_2 ∈ R and σ_1, σ_2 > 0. For μ_1 = μ_2 an explicit expression for transition density of X was obtained by Keilson and Wellner (1978). For σ_1 = σ_2 the transition density was obtained by Karatzas and Shreve (1984). But the transition density for general X was not known. We first solve the exit problem to process X, and then adopt a perturbation approach to find an expression of potential measure for X. The transition density is found by inverting the Laplace transform.

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