Table of Contents

On Optimal Joint Reflective and Refractive Dividend Strategies in Spectrally Positive Lévy Processes

Benjamin Avanzi, UNSW Australia Business School, School of Risk and Actuarial Studies, University of Montreal - Department of Mathematics and Statistics
José-Luis Pérez, Centro de Investigacion en Matematicas (CIMAT) - Department of Probability and Statistics
Bernard Wong, University of New South Wales (UNSW) - School of Actuarial Studies
Kazutoshi Yamazaki, Kansai University - Department of Mathematics

Option Pricing in Some Non-Levy Jump Models

Lingfei Li, The Chinese University of Hong Kong
Gongqiu Zhang, The Chinese University of Hong Kong (CUHK)


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"On Optimal Joint Reflective and Refractive Dividend Strategies in Spectrally Positive Lévy Processes" Free Download
UNSW Business School Research Paper No. 2016ACTL05

BENJAMIN AVANZI, UNSW Australia Business School, School of Risk and Actuarial Studies, University of Montreal - Department of Mathematics and Statistics
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JOSÉ-LUIS PÉREZ, Centro de Investigacion en Matematicas (CIMAT) - Department of Probability and Statistics
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BERNARD WONG, University of New South Wales (UNSW) - School of Actuarial Studies
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KAZUTOSHI YAMAZAKI, Kansai University - Department of Mathematics
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The expected present value of dividends is one of the classical stability criteria in actuarial risk theory. In this context, numerous papers considered threshold (refractive) and barrier (reflective) dividend strategies. These were shown to be optimal in a number of different contexts for bounded and unbounded payout rates, respectively.

In this paper, motivated by the behaviour of some dividend paying stock exchange companies, we determine the optimal dividend strategy when both continuous (refractive) and lump sum (reflective) dividends can be paid at any time, and if they are subject to different transaction rates.

We consider the general family of spectrally positive Lévy processes. Using scale functions, we obtain explicit formulas for the expected present value of dividends until ruin, with a penalty at ruin. We develop a verification lemma, and show that a two-layer $(a,b)$ strategy is optimal. Such a strategy pays continuous dividends when the surplus exceeds level $a>0$, and all of the excess over $b>a$ as lump sum dividend payments. Results are illustrated.

"Option Pricing in Some Non-Levy Jump Models" Free Download
SIAM Journal on Scientific Computing, Forthcoming

LINGFEI LI, The Chinese University of Hong Kong
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GONGQIU ZHANG, The Chinese University of Hong Kong (CUHK)
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This paper considers pricing European options in a large class of one-dimensional Markovian jump processes known as subordinate diffusions, which are obtained by time changing a diffusion process with an independent Levy or additive random clock. These jump processes are non-Levy in general, and they can be viewed as natural generalization of many popular Levy processes used in finance. Subordinate diffusions other richer jump behavior than Levy processes and they have found a variety of applications in financial modelling. The pricing problem for these processes presents unique challenges as existing numerical PIDE schemes fail to be efficient and the applicability of transform methods to many subordinate diffusions is unclear. We develop a novel method based on finite difference approximation of spatial derivatives and matrix eigendecomposition, and it can deal with diffusions that exhibit various types of boundary behavior. Since financial payoffs are typically not smooth, we apply a smoothing technique and use extrapolation to speed up convergence. We provide convergence and error analysis and perform various numerical experiments to show the proposed method is fast and accurate. Extension to pricing path-dependent options will be investigated in a follow-up paper.

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