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

Moawia Alghalith

Abstract


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.



doi:10.1017/S1446181116000171

Keywords


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.