This paper presents the binomial expansion and series with optimized binomial coefficients. The binomial series is built on the building blocks of optimized binomial coefficients and multiple summations of geometric series

We consider social decisions under uncertainty. We show that the ex ante social preference order satisfies a Pareto axiom with respect to ex ante individual preferences, along with an axiom of Statewise Dominance, if and only if all agents admit subjective expected utility (SEU) representations,...

This paper demonstrates that the equilibrium dynamics of a continuous-time macro-finance model can be characterized by the probabilistic solution of a coupled forward-backward stochastic differential equation. The probabilistic approach can, to some extent, overcome the ``curse of...

We derive upper and lower bounds for the Range Value-at-Risk of a unimodal random variable under knowledge of the mean, variance, symmetry, and a possibly bounded support. Moreover, we provide a generalization of the Gauss inequality for symmetric distributions with known support

The multilayer probability of informed trading (MPIN) model, developed by Ersan (2016), releases the assumption of single type of information events in the original PIN model of Easley et al. (1996). Identification of the number of layers in a dataset is applied through a layer detection...

Here we will consider a function of κ-statistics, the κ-Weibull distribution, and compare it to the well-known Weibull distribution. The κ-Weibull will be also compared to the 3-parameter extended Weibull function, obtained according to the Marshall–Olkin extended distributions. The...

In the history of economic thought, Shackle was one of the representative critics about probability based economic theory. Specifically, he constructed his own concept of subjective uncertainty called potential surprise to replace probability. In 1980s, the potential surprise is axiomatized by...