TY - CHAP
T1 - An ODE approach for the expected discounted penalty at ruin in a jump-diffusion model
AU - Chen, Yu Ting
AU - Lee, Cheng Few
AU - Sheu, Yuan Chung
N1 - Publisher Copyright:
© 2021 by World Scientific Publishing Co. Pte. Ltd.
Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.
PY - 2020/1/1
Y1 - 2020/1/1
N2 - 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).
AB - 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).
KW - Expected discounted penalty
KW - Jump-diffusion
KW - Optimal capital structure
KW - Phase-type distribution
UR - http://www.scopus.com/inward/record.url?scp=85096281138&partnerID=8YFLogxK
U2 - 10.1142/9789811202391_0041
DO - 10.1142/9789811202391_0041
M3 - Chapter
AN - SCOPUS:85096281138
SN - 9789811202384
SP - 1561
EP - 1598
BT - Handbook of Financial Econometrics, Mathematics, Statistics, and Machine Learning (In 4 Volumes)
PB - World Scientific Publishing Co.
ER -