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A NOTE ON A NEW APPROACH TO BOTH PRICE AND VOLATILITY JUMPS: AN APPLICATION TO THE PORTFOLIO MODEL

Part of: Markov processes

Published online by Cambridge University Press:  08 September 2016

MOAWIA ALGHALITH
MOAWIA ALGHALITH*
Affiliation:
Department of Economics, University of the West Indies, St. Augustine, Trinidad email malghalith@gmail.com
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Abstract

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A new approach to jump diffusion is introduced, where the jump is treated as a vertical shift of the price (or volatility) function. This method is simpler than the previous methods and it is applied to the portfolio model with a stochastic volatility. Moreover, closed-form solutions for the optimal portfolio are obtained. The optimal closed-form solutions are derived when the value function is not smooth, without relying on the method of viscosity solutions.

Keywords

jump diffusionstochastic volatilitypartial differential equationsHamilton–Jacobi–Bellman equationsviscosity solutions

MSC classification

Primary: 60J75: Jump processes
Type
Research Article
Information
The ANZIAM Journal , Volume 58 , Issue 2 , October 2016 , pp. 182 - 186
Copyright
© 2016 Australian Mathematical Society 

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