Second order stochastic dominance constraints in decision dependent randomness portfolio optimization problems
Abstract
The paper deals with stochastic portfolio optimization problems which maximize a given functional under second - order stochastic dominance constraints in presence of endogenous randomness. Endogenous randomness (or decision dependent randomness) means that the probability distribution of asset returns may depend on the decision variables, i.e. on the weights associated to the assets.
This may occur typically in the high frequency trading or in the illiquid markets, when a massive investment of one investor may attract others investors, at least for a small time period. Firstly, we modify the classical second-order stochastic dominance relation between returns of two given portfolios for the case with endogenous randomness of returns.
Secondly, we apply this new constraint to the portfolio optimization problem. Finally, we present an example demonstrating the differences in optimal portfolios when endogenous randomness is omitted (exogenous randomness is assumed).