State-dependent utility maximization in Lévy markets TeX Export

@article{citeulike:3991493, abstract = {We revisit Merton's portfolio optimization problem under boun-ded state-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 is solved using a dual variational problem as it is customarily done for non-Markovian models. One of the main features here is that the domain of the dual problem enjoys an explicit "parametrization", built on a multiplicative optional decomposition for nonnegative supermartingales due to F\"ollmer and Kramkov (1997). As a key step in obtaining the representation result we prove a closure property for integrals with respect to Poisson random measures, a result of interest on its own that extends the analog property for integrals with respect to a fixed semimartingale due to M\'emin (1980). In the case that (i) the L\'evy measure of \$Z\$ is atomic with a finite number of atoms or that (ii) \$\Delta S\_{t}/S\_{t^{-}}=\zeta\_{t} \vartheta(\Delta Z\_{t})\$ for a process \$\zeta\$ and a deterministic function \$\vartheta\$, we explicitly characterize the admissible trading strategies and show that the dual solution is a risk-neutral local martingale.}, archivePrefix = {arXiv}, author = {Figueroa-Lopez, Jose E. and Ma, Jin}, citeulike-article-id = {3991493}, citeulike-linkout-0 = {http://arxiv.org/abs/0901.2070}, citeulike-linkout-1 = {http://arxiv.org/pdf/0901.2070}, day = {14}, eprint = {0901.2070}, month = {Jan}, posted-at = {2009-02-01 16:28:54}, priority = {3}, title = {State-dependent utility maximization in L\'evy markets}, url = {http://arxiv.org/abs/0901.2070}, year = {2009} }

TY - JOUR ID - citeulike:3991493 L3 - citeulike-article-id:3991493 N2 - We revisit Merton's portfolio optimization problem under boun-ded state-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 is solved using a dual variational problem as it is customarily done for non-Markovian models. One of the main features here is that the domain of the dual problem enjoys an explicit "parametrization", built on a multiplicative optional decomposition for nonnegative supermartingales due to F\"ollmer and Kramkov (1997). As a key step in obtaining the representation result we prove a closure property for integrals with respect to Poisson random measures, a result of interest on its own that extends the analog property for integrals with respect to a fixed semimartingale due to M\'emin (1980). In the case that (i) the L\'evy measure of $Z$ is atomic with a finite number of atoms or that (ii) $\Delta S_{t}/S_{t^{-}}=\zeta_{t} \vartheta(\Delta Z_{t})$ for a process $\zeta$ and a deterministic function $\vartheta$, we explicitly characterize the admissible trading strategies and show that the dual solution is a risk-neutral local martingale. TI - State-dependent utility maximization in L\'evy markets AU - Figueroa-Lopez, Jose AU - Ma, Jin PY - 2009/Jan/14/ UR - http://arxiv.org/abs/0901.2070 ER -