An ODE Approach for the Expected Discounted Penalty at Ruin in a Jump-Diffusion Model

Yu-Ting Chen, Cheng Few Lee and Yuan-Chung Sheu

Chapter 41 in Handbook of Financial Econometrics, Mathematics, Statistics, and Machine Learning:(In 4 Volumes), 2020, pp 1561-1598 from World Scientific Publishing Co. Pte. Ltd.

Abstract: Under the assumption that the asset value follows a phase-type jump-diffusion, we show that the expected discounted penalty satisfies an ODE and obtain a general form for the expected discounted penalty. In particular, if only downward jumps are allowed, we get an explicit formula in terms of the penalty function and jump distribution. On the other hand, if the downward jump distribution is a mixture of exponential distributions (and upward jumps are determined by a general Lévy measure), we obtain closed-form solutions for the expected discounted penalty. As an application, we work out an example in Leland’s structural model with jumps. For earlier and related results, see Gerber and Landry et al. (1998), Hilberink and Rogers et al. (2002), Asmussen et al. (2004), and Kyprianou and Surya et al. (2007).

Keywords: Financial Econometrics; Financial Mathematics; Financial Statistics; Financial Technology; Machine Learning; Covariance Regression; Cluster Effect; Option Bound; Dynamic Capital Budgeting; Big Data (search for similar items in EconPapers)
JEL-codes: C01 C1 G32 (search for similar items in EconPapers)
Date: 2020
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Journal Article: An ODE approach for the expected discounted penalty at ruin in a jump-diffusion model (2007)
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