Stochastic monotonicity of dependent variables given their sum

Given a finite set of independent random variables, assume one can observe their sum, and denote with s its value. Efron in 1965, and Lehmann in 1966, described conditions on the involved variables such that each of them stochastically increases in the value s, i.e., such that the expected value of any non-decreasing function of the variable increases as s increases. In this paper, we investigate conditions such that this stochastic monotonicity property is satisfied when the assumption of independence is removed. Comparisons in the stronger likelihood ratio order are considered as well.

Stochastic monotonicity approach for a non-Markovian priority retrial queue

This paper considers a non-Markovian priority retrial queue which serves two types of customers. Customers in the regular queue have priority over the customers in the orbit. This means that the customer in orbit can only start retrying when the regular queue becomes empty. If another customer arrives during a retrial time, this customer is served and the retrial has to start over when the regular queue becomes empty again. In this study, a particular interest is devoted to the stochastic monotonicity approach based on the general theory of stochastic orders. Particularly, we derive insensitive bounds for the stationary joint distribution of the embedded Markov chain of the considered system.

General time interval multidimensional BSDEs with generators satisfying a weak stochastic-monotonicity condition

<p style='text-indent:20px;'>This paper establishes an existence and uniqueness result for the adapted solution of a general time interval multidimensional backward stochastic differential equation (BSDE), where the generator <inline-formula> <tex-math id="M1">\begin{document}$ g $\end{document}</tex-math> </inline-formula> satisfies a weak stochastic-monotonicity condition and a general growth condition in the state variable <inline-formula> <tex-math id="M2">\begin{document}$ y $\end{document}</tex-math> </inline-formula>, and a stochastic-Lipschitz condition in the state variable <inline-formula> <tex-math id="M3">\begin{document}$ z $\end{document}</tex-math> </inline-formula>. This unifies and strengthens some known works. In order to prove this result, we develop some ideas and techniques employed in Xiao and Fan [<xref ref-type="bibr" rid="b25">25</xref>] and Liu et al. [<xref ref-type="bibr" rid="b15">15</xref>]. In particular, we put forward and prove a stochastic Gronwall-type inequality and a stochastic Bihari-type inequality, which generalize the classical ones and may be useful in other applications. The martingale representation theorem, Itô’s formula, and the BMO martingale tool are used to prove these two inequalities. </p>

REFLECTED BSDES WITH STOCHASTIC MONOTONE GENERATOR AND APPLICATION TO VALUING AMERICAN OPTIONS

In this paper, we prove the existence and uniqueness of the solution to backward stochastic differential equations with lower reflecting barrier in a Brownian setting under stochastic monotonicity and general increasing growth conditions. As an application, we study the fair valuation of American options.

AN ADAPTIVE TEST OF STOCHASTIC MONOTONICITY

We propose a new nonparametric test of stochastic monotonicity which adapts to the unknown smoothness of the conditional distribution of interest, possesses desirable asymptotic properties, is conceptually easy to implement, and computationally attractive. In particular, we show that the test asymptotically controls size at a polynomial rate, is nonconservative, and detects certain smooth local alternatives that converge to the null with the fastest possible rate. Our test is based on a data-driven bandwidth value and the critical value for the test takes this randomness into account. Monte Carlo simulations indicate that the test performs well in finite samples. In particular, the simulations show that the test controls size and, under some alternatives, is significantly more powerful than existing procedures.