Portfolio Optimization for a Large Investor Controlling Market Sentiment Under Partial Information

Abstract

We consider an investor faced with the utility maximization problem in which the risky asset price process has pure-jump dynamics affected by an unobservable continuous-time finite-state Markov chain, the intensity of which can also be controlled by actions of the investor. Using the classical filtering theory, we reduce this problem with partial information to one with full information and solve it for logarithmic and power utility functions. In particular, we apply control theory for piecewise deterministic Markov processes (PDMP) to our problem and derive the optimality equation for the value function and characterize the value function as the unique viscosity solution of the associated dynamic programming equation. Finally, we provide a toy example, where the unobservable state process is driven by a two-state Markov chain, and discuss how investor's ability to control the intensity of the state process affects the optimal portfolio strategies as well as the optimal wealth under both partial and full information cases.

Optimal Investment and Proportional Reinsurance in a Regime-Switching Market Model under Forward Preferences

“…In our paper, we address this modeling issue by assuming that all these exogenous events are aggregated to create different regimes. Examples of regime switching models in a purely financial setting can be found for instance, in Bäuerle and Rieder [16], Mamon and Elliott [17], Sotomayor and Cadenillas [18], Zhou and Yin [19], and more recently Altay et al [20,21], Cretarola and Figà-Talamanca [22], where different problems are analyzed. Although considering regime-switching risk models related to optimal investment and reinsurance is not unusual, see, e.g., Chen et al [23] Jang and Kim [24], Liu et al [25], to the best of our knowledge our contribution is the first which accounts for forward dynamic preferences under dependence between the actuarial and insurance framework.…”

Stochastic filtering and optimal control of pure jump Markov processes with noise-free partial observation

“…More specifically, the separated problem will be a discrete-time one related to a specific Markov decision model formulated in terms of a PDP. The reduction of PDP optimal control problems to discrete-time Markov decision processes is exploited e. g. in [1,2,19,24,26,30,32,37,46].…”