Momentum Effect Problem Based On Ambiguity Aversion

The momentum effect is an anomaly in financial markets that means that stocks that have risen well in the past will remain well in the future,and stocks that have performed badly in the past will fall in the future.The resulting strategy of buying the good past and selling the bad past is a momentum trading strategy.Fuzzy aversion refers to an aversion to uncertainty,a new concept distinct from risk aversion,which does not conform to the von Neumann-Morgenstern principle and cannot be portrayed in terms of expected utility.In this paper,a new wealth equation is constructed by introducing a momentum effect model based on the continuous-time portfolio problem,and then a new portfolio optimisation problem is posed by introducing fuzzy aversion utility.For this new optimisation problem,the stochastic maximum principle cannot be used as the utility function is no longer differentiable.However,observing the concave nature of the equation,consider using the properties of a concave inverse stochastic differential equation.In the theoretical part the solution of the problem,expressed as a variational form accompanying the solution of the linear equation,is thus obtained as a very large minimal control problem.The value function is then constructed and the existence of saddle points is proved using the convex dual method.Finally the analytical form of the problem is solved using the harness principle method.In the numerical modelling section,the analytical form of the problem is substituted back into the original wealth equation to obtain the coupled inverse stochastic differential equation.The deep inverse stochastic differential equation method is used for this high-dimensional problem,where the inverse stochastic differential equation is first transformed into a forward control problem,and then the equivalence between the two solutions is proved.The problem is then discretised,a neural network is constructed and the corresponding loss function is expected to be simulated using Monte Carlo methods,and an algorithm for the numerical solution is given.Finally,the model is analysed using the numerical solution algorithm.The study shows that when the momentum effect parameter in the model increases,the profit obtained increases,but the required allocation in the risky asset decreases;when the terminal utility parameter changes,the change in utility is opposite to the change in the terminal wealth value,while the allocation in the risky asset increases;when the fuzzy aversion coefficient increases,the initial required wealth increases:investors with no high or low fuzzy aversion obtain The excess profit is the least.In addition to this we also make two conjectures based on the model;the model ratios are symmetric about the median of the terminal utility parameters;and the three parameters have a magnifying effect on the characteristics of the stock.In contrast to other papers,this paper gives the existence of saddle points for stochastic control problems coupled with concave generating elements of an SDE and the analytic formula for the saddle points on the theoretical side;on the applied side,it combines the method of solving the analytic formula for convex dyads with the method of solving with deep BSDE,providing a new approach to a class of financial practical problems;on the financial significance side,it is the first study of the momentum effect problem based on fuzzy aversion,providing a In terms of financial significance,the momentum effect problem based on fuzzy aversion is studied for the first time,providing new ideas for the study of momentum effect problems.