arXiv subjects

Moris S. Strub

Publications and source records attributed to Moris S. Strub.

3 recordsLinked to original sources

arXiv2023

Predictable Relative Forward Performance Processes: Multi-Agent and Mean Field Games for Portfolio Management

We introduce predictable relative forward performance processes (PRFPP) as a new framework for studying portfolio management within a competitive and incomplete market environment. Each agent trades a distinct stock following a binomial distribution with probabilities for a positive return depending on the market regime characterized by a non-traded stochastic factor. For both the finite population and mean field games, we construct and analyse PRFPPs for initial data of the CARA class along with the associated equilibrium strategies. We find that relative performance concerns do not necessarily lead to more investment in the risky asset compared to when there are no such concerns. Under some parameter constellations, agents short a stock with positive expected excess return. The binomial market setting facilitates a straightforward adjustment of risky asset skewness, enabling an analysis of its impact on investment behavior, an aspect that continuous-time frameworks cannot capture.

q-fin.MF↗

arXiv2021

Predictable Forward Performance Processes: Infrequent Evaluation and Applications to Human-Machine Interactions

We study discrete-time predictable forward processes when trading times do not coincide with performance evaluation times in a binomial tree model for the financial market. The key step in the construction of these processes is to solve a linear functional equation of higher order associated with the inverse problem driving the evolution of the predictable forward process. We provide sufficient conditions for the existence and uniqueness and an explicit construction of the predictable forward process under these conditions. Furthermore, we find that these processes are inherently myopic in the sense that optimal strategies do not make use of future model parameters even if these are known. Finally, we argue that predictable forward preferences are a viable framework to model human-machine interactions occuring in automated trading or robo-advising. For both applications, we determine an optimal interaction schedule of a human agent interacting infrequently with a machine that is in charge of trading.

q-fin.MF↗

arXiv2019

Forward Rank-Dependent Performance Criteria: Time-Consistent Investment Under Probability Distortion

We introduce the concept of forward rank-dependent performance processes, extending the original notion to forward criteria that incorporate probability distortions. A fundamental challenge is how to reconcile the time-consistent nature of forward performance criteria with the time-inconsistency stemming from probability distortions. For this, we first propose two distinct definitions, one based on the preservation of performance value and the other on the time-consistency of policies and, in turn, establish their equivalence. We then fully characterize the viable class of probability distortion processes, providing a bifurcation-type result. Specifically, it is either the case that the probability distortions are degenerate in the sense that the investor would never invest in the risky assets, or the marginal probability distortion equals to a normalized power of the quantile function of the pricing kernel. We also characterize the optimal wealth process, whose structure motivates the introduction of a new, distorted measure and a related market. We then build a striking correspondence between the forward rank-dependent criteria in the original market and forward criteria without probability distortions in the auxiliary market. This connection also provides a direct construction method for forward rank-dependent criteria. A byproduct of our work are some new results on the so-called dynamic utilities and on time-inconsistent problems in the classical (backward) setting.

q-fin.MF↗