Increasing risk: dynamic mean-preserving spreads (Q2304207)

The paper examines an implication of the Rothschild and Stiglitz definition of mean-preserving spreads to a dynamic framework. The core idea is to adapt the original integral conditions to transition probability densities, providing sufficient conditions for their satisfaction. Moreover a class of nonlinear scalar diffusion processes is considered, that is the super-diffusive ballistic process; this class, unique among Brownian bridges, satisfies the integral conditions. Considering that this class of processes can be generated by a random superposition of linear Markov processes with constant drifts, the authors are ultimately able to get a very simple representation, particularly useful for economic applications. Finally four examples are presented in order to give economic illustrations; in particular, the authors consider interesting applications to portfolio selection, investment under uncertainty, asset dynamics à la Black-Scholes, and firm entry and exit decisions under uncertainty.