Abstract
We consider the problem of maximizing expected utility from terminal wealth for a power utility of the risk-averse type assuming that the dynamics of the risky assets are affected by hidden “economic factors” that evolve as a finite-state Markov process. For this partially observable stochastic control problem we determine a corresponding complete observation problem that turns out to be of the risk sensitive type and for which the Dynamic programming approach leads to a nonlinear PDE that, via a suitable transformation, can be made linear. By means of a probabilistic representation we obtain a unique viscosity solution to the latter PDE that induces a unique viscosity solution to the former. This probabilistic representation allows us to obtain, on the one hand, regularity results, on the other hand, a computational approach based on Monte Carlo simulation.
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© 2007 Birkhäuser Verlag Basel/Switzerland
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Nagai, H., Runggaldier, W.J. (2007). PDE Approach to Utility Maximization for Market Models with Hidden Markov Factors. In: Dalang, R.C., Russo, F., Dozzi, M. (eds) Seminar on Stochastic Analysis, Random Fields and Applications V. Progress in Probability, vol 59. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-8458-6_27
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DOI: https://doi.org/10.1007/978-3-7643-8458-6_27
Publisher Name: Birkhäuser Basel
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