A note on a new approach to both price and volatility jumps: an application to the portfolio model

Moawia Alghalith


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.



jump diffusion, stochastic volatility, partial differential equations, Hamilton–Jacobi–Bellman equations, viscosity solutions

DOI: http://dx.doi.org/10.21914/anziamj.v58i0.8582

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ANZIAM Journal, ISSN 1446-8735, copyright Australian Mathematical Society.