Abstract
We describe some stochastic control problems in financial engineering arising from the need to find investment strategies to optimize some goal. Typically, these problems are characterized by nonlinear Hamilton-Jacobi-Bellman partial differential equations, and often they can be reduced to linear PDEs with the Legendre transform of convex duality. One situation where this cannot be achieved is in a market with stochastic volatility. In this case, we discuss an approximation using asymptotic analysis in the limit of fast mean-reversion of the process driving volatility. Simulations illustrate that marginal improvement can be achieved with this approach even when volatility is not fluctuating that rapidly.
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Jonsson, M., Sircar, R. (2002). Optimal investment problems and volatility homogenization approximations. In: Bourlioux, A., Gander, M.J., Sabidussi, G. (eds) Modern Methods in Scientific Computing and Applications. NATO Science Series, vol 75. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-0510-4_7
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DOI: https://doi.org/10.1007/978-94-010-0510-4_7
Publisher Name: Springer, Dordrecht
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