State-dependent utility maximization in Lévy markets - Quantitative Finance > Portfolio ManagementReport as inadecuate




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Abstract: We revisit Merton-s portfolio optimization problem under boun-dedstate-dependent utility functions, in a market driven by a L\-evy process $Z$extending results by Karatzas et. al. 1991 and Kunita 2003. The problem issolved using a dual variational problem as it is customarily done fornon-Markovian models. One of the main features here is that the domain of thedual problem enjoys an explicit -parametrization-, built on a multiplicativeoptional decomposition for nonnegative supermartingales due to F\-ollmer andKramkov 1997. As a key step in obtaining the representation result we prove aclosure property for integrals with respect to Poisson random measures, aresult of interest on its own that extends the analog property for integralswith respect to a fixed semimartingale due to M\-emin 1980. In the case thati the L\-evy measure of $Z$ is atomic with a finite number of atoms or thatii $\Delta S {t}-S {t^{-}}=\zeta {t} \vartheta\Delta Z {t}$ for a process$\zeta$ and a deterministic function $\vartheta$, we explicitly characterizethe admissible trading strategies and show that the dual solution is arisk-neutral local martingale.



Author: Jose E. Figueroa-Lopez, Jin Ma

Source: https://arxiv.org/



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