Risk conscious investment

Abstract

The risk conscious investor is defined as the maximizer of a conservative valuation or a dynamic nonlinear expectation. Both the static and dynamic problems are addressed using distortions of tail probabilities or distortions of tail measures. The multivariate static problem is solved in the context of the multivariate bilateral gamma model. For the dynamic model states and their transitions are modeled in two ways. The first defines states by a parametric model for the return distribution with transitions described by a continuous-time finite state Markov chain between the distributional possibilities. In the second model states are represented by the first four power variations with transitions given by (OU) equations for modeling stochastically the first four power variations as Tempered Fractional Lévy Processes (TFLP). Numerical solutions for policy functions are implemented in trading 768 equity assets over seven years ending December 2021.